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\documentclass{mcmthesis}
%\documentclass[CTeX = true]{mcmthesis} % 当使用 CTeX 套装时请注释上一行使用该行的设置
\mcmsetup{tstyle=\color{red}\bfseries,%修改题号，队号的颜色和加粗显示，黑色可以修改为 black
tcn = 2503941, problem = B, %修改队号，参赛题号
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titlepage = false, abstract = true}

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\title{The \LaTeX{} Template for MCM Version \MCMversion}
\author{\small \href{https://www.latexstudio.net/}
{\includegraphics[width=7cm]{mcmthesis-logo}}}
\date{\today}
\begin{document}
\begin{abstract}
\par Use this template to begin typing the first page (summary page) of your electronic report. This template uses a 12-point Times New Roman font. Submit your paper as an Adobe PDF electronic file (e.g. 1111111.pdf), typed in English, with a readable font of at least 12-point type.

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keyword1; keyword2
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\section{Introduction}

\subsection{Problem Background}

Juneau, the capital of Alaska, has a population of 30,000 and is characterised by distinctive natural landscapes and significant tourism resources. The city's tourism sector has undergone substantial growth over the past decade, particularly in its cruise ship industry. As shown in Figure \ref{fig:cruise_volume}, cruise passenger volume has increased steadily from 961,000 in 2014 to 1.67 million in 2023, with only a brief interruption during the COVID-19 pandemic in 2020-2021. During peak season, up to seven cruise ships dock simultaneously, resulting in daily visitor numbers equivalent to two-thirds of the permanent population, generating annual revenues of $375 million.

\begin{figure}[htbp]
\centering
\includegraphics[width=12cm]{figures/近年游客数.png}
\caption{Juneau's Cruise Passenger Volume Growth (2014-2023)}
\label{fig:cruise_volume}
\end{figure}

However, this rapid expansion of tourism has also given rise to significant sustainability challenges, including the retreat of the Mendenhall Glacier since 2007 and increased pressure on local infrastructure, as well as social impacts such as housing shortages and traffic congestion affecting residents' daily lives. Despite the implementation of higher tourist fees and hotel taxes, the balancing act of economic development with environmental protection remains a critical challenge for sustainable tourism in Juneau.

\subsection{Restatement of the Problems}

For sustainable tourism in Juneau, Alaska. We summarise the problem into the following four subtasks:

\begin{itemize}
\item \textbf{Task 1:} Develop a sustainable tourism model for the city of Juneau. Integrate economic, social, and ecological factors.
\item \textbf{Task 2:} Based on the model developed, discuss the constraints and optimisation factors and develop a suitable optimisation plan for sustainable tourism in Juneau.
\item \textbf{Task 3:} Demonstrate how this model can be extended to another site and discuss the impact of location and attraction popularity on the optimisation decision.
\item \textbf{Task 4:} Write a memo to the Juneau Tourism Commission describing our findings and recommendations for optimisation.
\end{itemize}

\subsection{Our Work}

\begin{figure}[h]
\centering
\includegraphics[width=16cm]{figures/绘图1.png}
\caption{Framework of the Sustainable Tourism Development Model for Juneau}
\label{fig:framework}
\end{figure}

\section{Assumptions and Notations}

\subsection{Assumptions}
\begin{itemize}
\item The population of the City of Juneau is expected to remain constant at 31,000 after the year 2000.
\item In terms of infrastructure investment, the City of Juneau invests in each sector in roughly stable proportions. Thus, we can use the investment in public transportation to represent the investment in infrastructure.
\item Pollution in tourist cities comes from the transportation of large numbers of tourists, so the amount associated with air pollution can be used to represent overall pollution in the city of Juneau.
\item During the time period of the data, there have been no emergencies, other than the New Crown epidemic, that were significant enough to have a major, sustained impact on Juneau's tourism industry.
\item All data is accurate and reliable.
\end{itemize}

\subsection{Notations}
Due to the complexity of our model, we separately present the notations for decision variables and evaluation indicators in their respective sections (see Table \ref{tab:decision_vars} and Table \ref{tab:indicators}). Here, we focus on the key variables used in coupling coordination calculation:

\begin{table}[!htbp]
\centering
\caption{Key Variables in Coupling Coordination Calculation}
\begin{tabular}{cl}
\toprule
\textbf{Symbol} & \textbf{Description} \
\midrule
$U_{E}$ & Comprehensive score of economic subsystem \
$U_{S}$ & Comprehensive score of social subsystem \
$U_{Eco}$ & Comprehensive score of ecological subsystem \
$C$ & Coupling degree among three subsystems \
$T$ & Coordination level among three subsystems \
$D$ & Coupling coordination degree of the tourism system \
\bottomrule
\end{tabular}
\label{tab:notation}
\end{table}

\section{Model Preparation}

\subsection{Data Collection}

A comprehensive data set encompassing a multitude of economic, social and environmental indicators for the City of Juneau was obtained through a meticulous examination of statistical reports published by pertinent agencies over the years.

\begin{table}[htbp]
\centering
\caption{Data Source Websites}
\begin{tabular}{ll}
\toprule
Database names & Database website \
\midrule
ACS & \href{https://www.census.gov/programs-surveys/acs/data/data-via-ftp.html}{\texttt{https://www.census.gov/...}} \
EJScreen & \href{https://gaftp.epa.gov/EJSCREEN/}{\texttt{https://gaftp.epa.gov/...}} \
GHGRP & \href{https://www.epa.gov/ghgreporting}{\texttt{https://www.epa.gov/...}} \
AQS & \href{https://aqs.epa.gov/aqsweb/airdata/download_files.html}{\texttt{https://aqs.epa.gov/...}} \
LAUS & \href{https://www.bls.gov/lau/}{\texttt{https://www.bls.gov/...}} \
Juneau Budget Data & \href{https://juneau.org/finance/budget-2}{\texttt{https://juneau.org/...}} \
Travel Juneau Annual Report & \href{https://www.traveljuneau.com/about-travel-juneau/annual-report/}{\texttt{https://www.traveljuneau.com/...}} \
ATIA & \href{https://www.alaskatia.org/resources/research}{\texttt{https://www.alaskatia.org/...}} \
JEDC & \href{https://www.jedc.org/research-library-reports-studies-by-jedc/}{\texttt{https://www.jedc.org/...}} \
\bottomrule
\end{tabular}
\end{table}

\subsection{Data Preprocessing}

The raw data collected from various sources required careful preprocessing to ensure quality and usability. Several key preprocessing steps were taken:

\begin{itemize}
\item \textbf{COVID-19 Impact Handling}: Data from 2020 and 2021 were excluded from our analysis due to the significant disruption to tourism-related indicators caused by the COVID-19 pandemic. This exclusion ensures that our model is built on data that better represents normal operating conditions.

\item \textbf{Composite Indicator Construction}: Some decision variables and indicators were not directly available in the raw data. For instance, infrastructure investment was constructed by aggregating multiple related sub-categories of investment (e.g., street maintenance, facility upgrades) from annual statistical reports. While such aggregation may not capture the complete expenditure in each domain, it serves as a statistically significant proxy for the overall investment level.

\item \textbf{Abstract Variable Quantification}: Several variables and indicators in our model are conceptually abstract. For example, the tourism tax intensity was quantified based on historical tax collection data and tourist numbers. Similarly, the tourist distribution policy intensity was derived from various policy implementation records and their corresponding effects.
\end{itemize}

After preprocessing, we obtained a clean and consistent dataset covering recent years except for the pandemic period, which forms the foundation for our subsequent modeling work.

\subsection{Model Overview}

To address the sustainable tourism development challenges in Juneau, we propose a two-stage modeling approach, as illustrated in Figure \ref{fig:model_structure}. The framework consists of two major components:

\begin{itemize}
\item \textbf{Sustainability Coupling Coordination Model (SCCM)}: This evaluation component assesses the coordination level among economic, social, and ecological subsystems. Through standardization of indicators and subsystem integration, SCCM generates a coupling coordination degree that quantifies the overall system balance.

\item \textbf{Hierarchical Optimization Model (HOM)}: Building upon the SCCM evaluation results, this optimization component determines the optimal policy combinations. HOM employs system dynamics equations and utilizes the NSGA-II algorithm with lexicographic ordering to find solutions that balance multiple objectives with different priorities.
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=11cm]{figures/绘图2.png}
\caption{Framework of the Two-Stage Modeling Approach}
\label{fig:model_structure}
\end{figure}

The workflow proceeds from model preparation through evaluation and optimization to final strategy generation. The connection between SCCM and HOM is established through the coupling coordination degree, which serves both as an evaluation metric and a primary optimization objective. This integrated approach ensures that the proposed solutions maintain a high level of system coordination while meeting specific performance targets.

\section{Sustainability Coupling Coordination Model}

In order to formulate an optimal sustainable tourism development plan for Juneau, the Sustainability Coupling Coordination Model (SCCM) was constructed in order to evaluate the coordination level among economic, social, and ecological development indicators. Based on Juneau's historical reports and comprehensive statistical data, ten key indicators were identified with which to assess the city's integrated development across these three dimensions. The specific indicators, including their symbolic representations, data sources, and measurement units, are detailed in Table~\ref{tab:indicators} below.   

\begin{table}[htbp]
\centering
\caption{Key Indicators for Assessing Sustainable Tourism Development in Juneau}
\label{tab:indicators}
\begin{tabular}{lllll}
\toprule
\textbf{Subsystem} & \textbf{Indicator} & \textbf{Symbol} & \textbf{Unit} & \textbf{Attribute} \
\midrule
Economic & Tourism Revenue & $E_1$ & Million USD & Positive \
& Tourism Fixed Assets & $E_2$ & Million USD & Positive \
\midrule
Social & Resident Attitude & $S_1$ & Scale 0-10 & Positive \
& Congestion Index & $S_2$ & Index Value & Negative \
& Tourism Accessibility & $S_3$ & Index Value & Positive \
& Resident Disposable Income & $S_4$ & USD/Person & Positive \
& Tourism Employment & $S_5$ & Thousand People & Positive \
\midrule
Ecological & Carbon Footprint & $Eco_1$ & Tonnes of CO$_2$ Equivalent & Negative \
& Air Pollution Index & $Eco_2$ & Index Value & Negative \
& Glacier Congestion Index & $Eco_3$ & Index Value & Negative \
\bottomrule
\end{tabular}
\end{table}

\subsection{Standardization of Indicators}

In view of the marked disparities in dimensions and value ranges of the indicators, it is imperative to standardise the raw data with a view to eliminating dimensional impacts. This study employs the range standardisation method to convert all indicator values into a unified interval of $[0,1]$. Different standardisation formulas are applied to positive and negative indicators:

For positive indicators ($E_1$, $E_2$, $S_1$, $S_3$, $S_4$, $S_5$), the following standardisation formula is applied:

For negative indicators ($S_2$, $\text{Eco}_1$, $\text{Eco}_2$, $\text{Eco}_3$), the following standardisation formula is employed:

In this formula, $X'_{ij}$ represents the standardized indicator value, $X_{ij}$ denotes the original indicator value, and $X_{\text{max}}$ and $X_{\text{min}}$ represent the maximum and minimum values of the indicator during the evaluation period, respectively. In order to mitigate the influence of extreme values, this study establishes upper and lower bounds for each indicator based on historical data for standardisation calculations.

\subsection{Calculation of Coupling Coordination Degree}

Utilising the standardised indicators, a composite index is derived for the three subsystems:
\begin{equation}
\begin{cases}
U_E = 0.6E_1 + 0.4E_2 \
U_S = 0.25S_1 + 0.35S_2 + 0.15S_3 + 0.20S_4 + 0.10S_5 \
U_{\text{Eco}} = 0.26\text{Eco}_1 + 0.24\text{Eco}_2 + 0.50\text{Eco}_3
\end{cases}
\label{eq:composite_index}
\end{equation}

The glacier crowding index ($\text{Eco}_3$) was assigned the highest weight of 0.50, reflecting the critical position of glacier resources in the Juneau tourism ecosystem. Utilising the aforementioned formula (see Equation \eqref{eq:composite_index}), the composite economic, social and ecological indicators for the city of Juneau were derived over the preceding triennium, as illustrated in Figure \ref{fig:aa}.

\begin{figure}[h]
\small
\centering
\includegraphics[width=13cm]{figures/3-subsystom.png}
\caption{Composition of Subsystem Development Indices (2022-2024)} \label{fig:aa}
\end{figure}

The coupling coordination of the three subsystems can be calculated based on the combined indices through a three-step process.

First, the coupling degree $C$, which indicates the interaction between subsystems, is calculated as:
\begin{equation}
C = \frac{3 \times (U_E \times U_S \times U_{\text{Eco}})^{1/3}}{U_E + U_S + U_{\text{Eco}}}
\end{equation}

Then, the coordination degree $T$ is determined by:
\begin{equation}
T = 0.28U_E + 0.28U_S + 0.44U_{\text{Eco}}
\end{equation}
where the ecological subsystem is assigned a higher weight (0.44) to reflect its crucial role in sustainable tourism development.

Finally, the coupling coordination degree $D$ is derived as:
\begin{equation}
D = \sqrt{C \times T}
\end{equation}

The value of $D$ ranges from 0 to 1, with higher values indicating better system coordination. Based on this metric, the coordinated development status can be classified into ten levels from extremely dysfunctional to highly coordinated.

The coupling coordination degree calculations for the past three years are presented in Table \ref{tab:ccd_results}.

\begin{table}[htbp]
\centering
\caption{Coupling Coordination Degree Results (2022-2024)}
\label{tab:ccd_results}
\begin{tabular}{cccc}
\toprule
Year & CCD Value & Level & Category \
\midrule
2022 & 0.6211 & 7 & Primary Coordinated \
2023 & 0.6530 & 7 & Primary Coordinated \
2024 & 0.6943 & 7 & Primary Coordinated \
\bottomrule
\end{tabular}
\end{table}

The calculation results indicate that the coupling degree of the economic-social-ecological system of Juneau tourism maintains at the seventh level of 'primary coordination' over the past three years, with a steady upward trend from 0.6211 to 0.6943. This suggests that while the coordination among economic growth, social well-being, and ecological protection in Juneau's tourism development remains at a basic level, the positive interaction among the subsystems has been gradually strengthening.

\section{Hierarchical Optimization Model}

In this section, we propose a hierarchical multi-objective optimisation model to determine the optimal policy combination in order to address the challenges of overtourism while maintaining tourism benefits. This builds upon the Sustainability Coupling Coordination Model (SCCM), which evaluates the coordination level among economic, social, and ecological subsystems.

The hierarchical structure of the model reflects the multi-level relationships: at the foundation level are eight decision variables representing various policy instruments including investments, taxes, and visitor management strategies.These policy instruments then influence ten key indicators across economic, social, and ecological dimensions as identified in the SCCM.Finally, these indicators are aggregated into three subsystem indices that collectively determine the system's overall performance. The model's hierarchical framework is designed to optimise the coupling coordination degree (D), government revenue, and carbon footprint, with the aforementioned objectives arranged in descending order of priority. This arrangement reflects Juneau's commitment to achieving balanced development while addressing overtourism concerns.

\subsection{Decision Variables}

Based on the historical data and policy reports from Juneau's tourism development, we identified eight key decision variables that can be effectively controlled by the city management to influence tourism outcomes. These variables, as shown in Table \ref{tab:decision_vars}, include four types of investment allocations, tourist taxation, visitor distribution policy, and two fundamental tourism volume indicators.

\begin{table}[htbp]
\centering
\caption{Decision Variables for Tourism Development in Juneau}
\label{tab:decision_vars}
\begin{tabular}{lll}
\toprule
\textbf{Indicator} & \textbf{Symbol} & \textbf{Unit} \
\midrule
Environmental Protection Investment & $x_{env}$ & Million USD \
Infrastructure Investment & $x_{infra}$ & Million USD \
Tourism Market Promotion Investment & $x_{mkt}$ & Million USD \
Community Project Investment & $x_{soc}$ & Million USD \
Tourist Per Capita Tourism Tax & $\alpha_{tax}$ & USD \
Tourist Distribution Policy Intensity & $x_{div}$ & Index Value \
Number of Tourists & $N_{T}$ & Thousand People/Year \
Tourist Per Capita Consumption & $x_{con}$ & USD/Person \
\bottomrule
\end{tabular}
\end{table}

Through regression analysis of historical data, we established the complex relationships between these decision variables and the ten assessment indicators. Each indicator is determined by multiple decision variables through non-linear interactions. For instance, the carbon footprint ($Eco_1$) is influenced by environmental protection investment ($x_{env}$), infrastructure investment ($x_{infra}$), and tourist volume ($N_{T}$), while the tourism accessibility ($S_3$) is jointly determined by infrastructure investment ($x_{infra}$), distribution policy intensity ($x_{div}$), and tourist volume ($N_{T}$). These intricate relationships form the foundation of our optimization model, enabling us to evaluate how policy adjustments would impact various aspects of Juneau's tourism system. The complete hierarchical structure of our model is illustrated in Figure \ref{fig:sankey}.

\begin{figure}[h]
\small
\centering
\includegraphics[width=16cm]{figures/sangji.png}
\caption{Hierarchical Structure of the Sustainable Tourism Optimization Model} \label{fig:sankey}
\end{figure}

\subsection{System Dynamics Equations}

The relationships between decision variables and indicators were established through regression analysis of historical data. For the economic subsystem, the government revenue ($E_1$) and tourism fixed assets ($E_2$) are formulated as:

\begin{equation}
\text{E}{1} = \frac{1000N{T}(x_{con} + \alpha_{tax} - 218.3796)}{10^6} + 251.9655
\end{equation}

\begin{equation}
\text{E}{2} = 2.10818 - 0.116903\frac{x{infra}}{10.0054} - 0.331696\frac{x_{mkt}}{1.00168} + 2.10063\ln(1 + \frac{\text{S}_{5}}{0.393086})
\end{equation}

The government revenue equation captures how tourist volume ($N_{T}$), per capita consumption ($x_{con}$), and tourism tax ($\alpha_{tax}$) directly contribute to the city's income. The tourism fixed assets are influenced by infrastructure and market promotion investments, while also showing a logarithmic relationship with tourism employment, indicating diminishing returns on investment.

For the social subsystem, the resident attitude ($S_1$) and congestion index ($S_2$) are particularly critical:

\begin{equation}
\text{S}{1} = 6.05431 + 0.168539x{div} + 0.8668\frac{x_{env}}{10.1057} - 0.00038535T
\end{equation}

\begin{equation}
\text{S}{2} = 3.74014 + 0.000416267N{T} - 0.0586679x_{infra} - 0.160964x_{div}
\end{equation}

These equations reveal that resident attitudes are positively influenced by environmental protection and visitor distribution policies, but negatively impacted by increasing tourist numbers. Meanwhile, the congestion index can be effectively managed through infrastructure investment and tourist distribution strategies.

For the ecological subsystem, the carbon footprint ($\text{Eco}_1$) is of particular concern:

\begin{equation}
\text{Eco}{1} = 1.92453 \times 10^6 + 391.147(1000N{T})^{-30.2898} - 78569.9x_{env} - 805146\ln(1 + x_{infra})
\end{equation}

This equation demonstrates how environmental protection and infrastructure investments can help mitigate the carbon footprint, with infrastructure improvements showing diminishing returns as indicated by the logarithmic term.

The remaining system indicators are formulated as follows:

\begin{equation}
\left{
\begin{aligned}
\text{S}{3} &= 1.5081(\frac{N{T} + 100.004}{0.000231623})^{0.429576}(1 - e^{-0.45747\frac{x_{infra}}{9.99294}})(1 + 0.0590587x_{div}) \
\text{S}{4} &= 49942.2 + 0.00569082(N{T} \cdot x_{con}) + 237.171x_{infra} - 457.361x_{soc} \
\text{S}{5} &= 58.108 + 0.000421N{T} - 19.3388\ln(1 + \frac{x_{con}}{104.465}) + 33.4503(1 + \frac{\alpha_{tax}}{-3.93095})^{-1} \
\text{Eco}{2} &= 20.7266 + 2.31625 \times 10^{-6}(1000N{T}) - 4.16471x_{env} - 1.44831x_{infra} - 0.0736647x_{div} \
\text{Eco}{3} &= 0.252585 + 0.00266493\ln(1 + N{T}) - 1.24836x_{div}
\end{aligned}
\right.
\end{equation}

\subsection{Objective Functions}

Based on the established system dynamics and Juneau's development priorities, we formulate a hierarchical multi-objective optimization problem with three objectives:

\begin{equation}
\left{
\begin{aligned}
\min f_1 &= -D \
\min f_2 &= -\text{E}{1} \
\min f_3 &= \text{E}{CO_{1}}
\end{aligned}
\right.
\end{equation}

where $D$ is the coupling coordination degree calculated using the SCCM framework. The negative signs before $D$ and $E_{1}$ convert their maximization into minimization problems. These objectives are arranged in descending order of priority, reflecting Juneau's primary focus on achieving system coordination, followed by economic benefits, while maintaining environmental responsibility through carbon footprint control.

\subsection{Constraints}

The optimization model is subject to several constraints to ensure the feasibility and practicality of solutions. First, all decision variables must fall within their respective reasonable ranges:

\begin{equation}
\left{
\begin{aligned}
10.0 \leq x_{env} \leq 25.0 & \quad \text{(Million USD)} \
40.0 \leq x_{infra} \leq 60.0 & \quad \text{(Million USD)} \
0.0 \leq x_{mkt} \leq 10.0 & \quad \text{(Million USD)} \
15.0 \leq x_{soc} \leq 30.0 & \quad \text{(Million USD)} \
0.0 \leq \alpha_{tax} \leq 10.0 & \quad \text{(USD)} \
0.2 \leq x_{div} \leq 0.4 & \quad \text{(Index Value)} \
500 \leq N_{T} \leq 2200 & \quad \text{(Thousand People/Year)} \
200 \leq x_{con} \leq 260 & \quad \text{(USD/Person)}
\end{aligned}
\right.
\end{equation}

Second, a budget constraint is imposed to ensure that the total investment does not exceed the government revenue:

\begin{equation}
x_{env} + x_{infra} + x_{mkt} + x_{soc} \leq \text{E}_{1}
\end{equation}

Third, to maintain a satisfactory level of system coordination, we require:

\begin{equation}
D \geq 0.8
\end{equation}

\subsection{Solution Methodology}

To solve this hierarchical multi-objective optimization problem, we employ the NSGA-II (Non-dominated Sorting Genetic Algorithm II) algorithm with a customized lexicographic dominator. The lexicographic dominance relationship is defined as follows: for two solutions $A$ and $B$ with objective vectors $F_A=[f_1^A,f_2^A,f_3^A]$ and $F_B=[f_1^B,f_2^B,f_3^B]$, solution $A$ dominates solution $B$ if and only if:

\begin{equation}
\left{
\begin{aligned}
& f_1^A < f_1^B - \epsilon_1, \text{ or} \
& |f_1^A - f_1^B| \leq \epsilon_1 \text{ and } f_2^A < f_2^B - \epsilon_2, \text{ or} \
& |f_1^A - f_1^B| \leq \epsilon_1 \text{ and } |f_2^A - f_2^B| \leq \epsilon_2 \text{ and } f_3^A < f_3^B - \epsilon_3
\end{aligned}
\right.
\end{equation}

where $\epsilon_1 = 0.5$, $\epsilon_2 = 50$, and $\epsilon_3 = 1000$ are tolerance parameters that define the indifference thresholds for each objective. This dominance relationship ensures that solutions are primarily compared based on the coupling coordination degree, followed by government revenue, and finally carbon footprint.

\subsection{Algorithm Implementation}

The NSGA-II algorithm was implemented with carefully selected parameters to ensure efficient exploration of the solution space while maintaining solution diversity. The population size was set to 300 individuals with 100 offspring per generation, and the algorithm was run for 400 generations to ensure convergence. The implementation details are as follows:

\begin{itemize}
\item \textbf{Population Initialization}: The initial population was randomly generated within the feasible region defined by the variable bounds. To improve the quality of initial solutions, we employed a constraint handling method that ensures all initial individuals satisfy the budget constraint.

text
\item \textbf{Genetic Operators}: The Simulated Binary Crossover (SBX) operator was used for crossover with a probability of 0.9, and the Polynomial Mutation operator was applied with a probability of $1/n$ where $n$ is the number of decision variables. These operators were chosen for their ability to handle real-valued decision variables effectively.

\item \textbf{Constraint Handling}: The constraints were handled using a penalty function approach. Solutions violating the coupling coordination degree constraint ($D \geq 0.8$) or the carbon footprint ceiling were penalized proportionally to their degree of violation.

\end{itemize}

The evolution of the three objectives over generations is shown in Figure \ref{fig:convergence}. The coupling coordination degree ($D$) shows rapid improvement in the early stages and stabilizes around 0.84 after 200 generations. The government revenue exhibits a similar pattern, reaching a plateau at approximately 350 million USD. The carbon footprint initially fluctuates but gradually decreases and stabilizes around 54,000 tonnes CO$_2$ equivalent, demonstrating the algorithm's ability to balance multiple competing objectives.

\begin{figure}[htbp]
\centering
\includegraphics[width=18cm]{figures/evolution.png}
\caption{Mean Objective Values Evolution During the Optimization Process}
\label{fig:convergence}
\end{figure}

The final population's distribution in the objective space is visualized in Figure \ref{fig:scatter}, where each point represents a non-dominated solution. The scatter plot reveals clear trade-offs between the three objectives, with solutions clustering in distinct regions. The color gradient indicates the carbon footprint level, showing how solutions with higher coordination degrees and government revenues tend to have slightly higher carbon footprints, though all remain within the specified constraints.

\begin{figure}[htbp]
\centering
\includegraphics[width=16cm]{figures/sandian.png}
\caption{3D Scatter Plot of Non-dominated Solutions in the Final Population}
\label{fig:scatter}
\end{figure}

\subsection{Optimization Results and Investment Strategy}
Through the hierarchical multi-objective optimization process, we obtained a set of non-dominated solutions representing different trade-offs among the objectives. Based on the lexicographic ordering principle and our problem constraints, we identified the optimal solution with the following performance metrics:
\begin{itemize}
\item Coupling Coordination Degree ($D$): 0.8447
\item Government Revenue: 352.18 million USD
\item Carbon Footprint: 53,728.75 tonnes CO$_2$ equivalent
\end{itemize}

The corresponding optimal policy combination is presented in Table \ref{tab:optimal_solution}.

\begin{table}[htbp]
\centering
\caption{Optimal Policy Combination for Juneau's Sustainable Tourism Development}
\label{tab:optimal_solution}
\begin{tabular}{lll}
\toprule
\textbf{Decision Variable} & \textbf{Optimal Value} & \textbf{Unit} \
\midrule
Environmental Protection Investment & 18.21 & Million USD \
Infrastructure Investment & 59.37 & Million USD \
Tourism Market Promotion Investment & 1.52 & Million USD \
Community Project Investment & 15.23 & Million USD \
Tourist Per Capita Tourism Tax & 3.93 & USD \
Tourist Distribution Policy Intensity & 0.20 & Index Value \
Number of Tourists & 2,200 & Thousand People/Year \
Tourist Per Capita Consumption & 260 & USD/Person \
\bottomrule
\end{tabular}
\end{table}

Based on the optimization results, we propose an integrated investment strategy that creates reinforcing feedback mechanisms in the tourism system:

\begin{itemize}
\item \textbf{Infrastructure-Focused Investment}: The solution allocates the largest portion of the budget (59.37 million USD, 62.8%) to infrastructure improvement. This investment directly enhances tourism accessibility ($S_{3}$) and reduces congestion ($S_2$), creating a positive feedback loop that enables higher visitor capacity while maintaining service quality.

\item \textbf{Strategic Environmental Protection}: A significant investment of 18.21 million USD (19.3%) in environmental protection demonstrates the city's commitment to ecological preservation. This investment reduces carbon footprint and improves resident attitudes ($S_{1}$), ensuring the sustainability of natural attractions.

\item \textbf{Community Development}: The community project investment of 15.23 million USD (16.1%), combined with a modest distribution policy intensity (0.20), prioritizes local community benefits. This enhances resident disposable income ($S_{4}$) and strengthens social acceptance of tourism.

\item \textbf{Market Management}: The moderate tourism tax (3.93 USD per capita) and conservative market promotion investment (1.52 million USD, 1.8%) maintain tourism attractiveness while generating necessary revenue for sustainable development.
\end{itemize}

This investment strategy achieves the highest possible coupling coordination degree while satisfying all constraints. The high coordination degree of 0.8447 indicates a well-balanced development state among economic, social, and ecological subsystems, demonstrating how appropriate revenue allocation can promote sustainable tourism development.

\section{Model Adaptation to Nanjing}

To demonstrate the adaptability of our modeling approach, we apply the framework to Nanjing, China, a historic city facing overtourism challenges. As a cultural tourism destination with a population of over 8 million, Nanjing presents different characteristics from Juneau, allowing us to test the model's versatility.

\subsection{Model Adjustment}

The adaptation of our model requires several modifications to accommodate Nanjing's unique context:

\begin{itemize}
\item \textbf{Indicator Selection}: The glacier congestion index ($\text{Eco}_3$) was removed as it is specific to Juneau. The remaining nine indicators were retained as they are universal measures of tourism sustainability.

\item \textbf{System Integration}: The weights in SCCM were adjusted to reflect the changed composition of the ecological subsystem:
\begin{equation}
\begin{aligned}
U_E &= 0.6E_1 + 0.4E_2 \
U_S &= 0.25S_1 + 0.35S_2 + 0.15S_3 + 0.20S_4 + 0.10S_5 \
U_{Eco} &= 0.5\text{Eco}_1 + 0.5\text{Eco}_2
\end{aligned}
\end{equation}
\end{itemize}

The decision variables remain unchanged as they represent universal policy instruments, though their operational ranges were adjusted according to Nanjing's scale:

\begin{equation}
\left{
\begin{aligned}
20.0 \leq x_{env} \leq 70.0 & \quad \text{(Million USD)} \
150.0 \leq x_{infra} \leq 250.0 & \quad \text{(Million USD)} \
20.0 \leq x_{mkt} \leq 50.0 & \quad \text{(Million USD)} \
200.0 \leq x_{soc} \leq 250.0 & \quad \text{(Million USD)} \
0.0 \leq \alpha_{tax} \leq 5.0 & \quad \text{(USD)} \
0.2 \leq x_{div} \leq 0.5 & \quad \text{(Index Value)} \
90000 \leq N_{T} \leq 120000 & \quad \text{(Thousand People/Year)} \
1500 \leq x_{con} \leq 2300 & \quad \text{(USD/Person)}
\end{aligned}
\right.
\end{equation}

Based on regression analysis of Nanjing's historical data, the system dynamics equations were recalibrated. For example, the government revenue equation was updated to:

\begin{equation}
\text{E}{1} = \frac{1000N{T}(x_{con} + \alpha_{tax} \times 1327.1274)}{10^8} - 4401.0535
\end{equation}

The Hierarchical Optimization Model (HOM) retains its structure with the same three objectives but different parameters, demonstrating the framework's adaptability to various contexts while maintaining its core methodology.

\subsection{Optimization Results for Nanjing}

The optimization for Nanjing achieved a coupling coordination degree of 0.8848, demonstrating the model's effectiveness in a different context. The optimal policy combination is characterized by:

\begin{itemize}
\item \textbf{Maximum Environmental Protection}: Environmental investment reaches its upper limit (70M USD), reflecting the critical importance of environmental quality in urban tourism.

text
\item \textbf{Substantial Infrastructure Support}: A high infrastructure investment (197.7M USD) focuses on urban tourism facilities and transportation capacity.

\item \textbf{Active Market Promotion}: Nearly maximum market promotion investment (49.9M USD) suggests the importance of destination marketing in competitive urban tourism.

\item \textbf{Basic Social Programs}: Minimum social project investment (200M USD) indicates a focus on essential community support.

\item \textbf{Moderate Tourism Management}: A tourism tax of 4.45 USD and conservative distribution policy intensity (0.20) suggest a market-driven approach to tourist flow management.

\end{itemize}

This solution achieves a government revenue of 2,998.48M USD while maintaining carbon emissions at 3,098,827.61 tonnes CO$_2$ equivalent. The results demonstrate different priorities from Juneau, with a stronger emphasis on environmental protection and market promotion in the urban context. As shown in Figure \ref{fig:nanjing_scatter}, the final population of solutions exhibits clear trade-offs between the three objectives, with our selected solution representing an optimal balance according to the lexicographic ordering principle.

\begin{figure}[htbp]
\centering
\includegraphics[width=16cm]{figures/nanjing.png}
\caption{3D Scatter Plot of Non-dominated Solutions for Nanjing's Optimization}
\label{fig:nanjing_scatter}
\end{figure}

\subsection{Impact of Location Characteristics}

The comparative study between Juneau and Nanjing reveals how geographical characteristics significantly influence the relative importance of different measures in sustainable tourism management:

\begin{itemize}
\item \textbf{Tourism Resource Type}: In Juneau, where tourism depends heavily on natural attractions like glaciers, environmental protection investment becomes the primary concern, directly impacting both tourist satisfaction and ecological sustainability. Conversely, Nanjing's cultural-historical tourism necessitates greater emphasis on infrastructure capacity and preservation.

\item \textbf{Tourist Flow Pattern}: Juneau's cruise-dominated tourism creates significant seasonal fluctuations, making the distribution policy ($x_{div}$) crucial for peak-season management. In contrast, Nanjing's year-round tourism pattern shifts the focus to sustained infrastructure optimization and continuous flow management.

\item \textbf{Transportation Structure}: The singular dependence on cruise ships in Juneau results in concentrated tourist arrivals, requiring precise temporal control. Nanjing's diverse transportation network enables more flexible spatial distribution, as reflected in its higher optimal infrastructure investment ($x_{infra}$).
\end{itemize}

\subsection{Promoting Tourism Balance}

Our model incorporates the tourism accessibility index ($S_3$) and infrastructure investment ($x_{infra}$) to promote balanced tourism development:

\begin{itemize}
\item \textbf{Accessibility Enhancement}: The tourism accessibility index ($S_3$) in our model measures the ease of reaching different attractions. Through optimizing infrastructure investment and distribution policies, the model promotes higher accessibility for all attractions, including less-visited ones. This is reflected in Nanjing's optimization result where $S_3$ reaches [value], indicating improved access to diverse tourist locations.

\item \textbf{Infrastructure Support}: The optimal infrastructure investment of 197.7M USD can enhance the basic facilities and transportation networks connecting different attractions. The system dynamics equation for accessibility shows that improved infrastructure directly contributes to better tourist access across all sites:
\begin{equation}
S_{3} = 1.5081(\frac{N_{T} + 100.004}{0.000231623})^{0.429576}(1 - e^{-0.45747\frac{x_{infra}}{9.99294}})(1 + 0.0590587x_{div})
\end{equation}
\end{itemize}

These mechanisms demonstrate how our model naturally promotes tourism balance by incorporating accessibility measures and infrastructure support in its optimization framework.

\section{Sensitivity Analysis}

To validate our model's reliability and stability, we conducted three levels of sensitivity analysis targeting both the evaluation model (SCCM) and optimization model (HOM).

\subsection{Indicator Sensitivity in SCCM}
For the evaluation model, we performed a standardized sensitivity analysis on all ten indicators:

\begin{itemize}
\item \textbf{Analysis Method:} Each indicator was varied by ±15% from its baseline value while keeping others constant. The changes in coupling coordination degree (D) were recorded for each variation.

text
\item \textbf{Standardization Process:} All indicators were first normalized to [0,1] scale to ensure comparability. For positive indicators (E1, E2, S1, S3, S4, S5), we used the formula $(x-x_{min})/(x_{max}-x_{min})$; for negative indicators (S2, Eco1, Eco2), we used $(x_{max}-x)/(x_{max}-x_{min})$.

\item \textbf{Results Interpretation:} The sensitivity was quantified by the ratio of D's percentage change to indicator's percentage change. As shown in Figure \ref{fig:indicator_sensitivity}, steeper curves indicate higher sensitivity.

\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=14cm]{figures/sensitive 1.png}
\caption{Sensitivity of Coupling Coordination Degree to Individual Indicator Variations (±15%)}
\label{fig:indicator_sensitivity}
\end{figure}

\subsection{Weight Perturbation Analysis in HOM}
We then tested the optimization model's robustness through systematic weight perturbations:

\begin{itemize}
\item \textbf{Perturbation Method:} Random perturbations were applied to weights in each subsystem while maintaining their sum as 1. For example, at 20% perturbation level, each weight was randomly varied within ±20% of its original value, then renormalized.

text
\item \textbf{Evolution Analysis:} For each perturbation level (0\%, 10\%, ..., 70\%), we ran the NSGA-II algorithm for 400 generations with population size 200. Figure \ref{fig:weight_evolution} tracks the mean coordination degree across generations.

\item \textbf{Convergence Criteria:} The algorithm was considered converged when the mean D value change remained below 0.001 for 50 consecutive generations.

\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=14cm]{figures/sensitive 2.png}
\caption{Evolutionary Trajectories of Mean Coordination Degree under Different Weight Perturbation Levels}
\label{fig:weight_evolution}
\end{figure}

\subsection{Solution Space Analysis}
Finally, we examined the stability of optimal solutions under weight perturbations:

\begin{itemize}
\item \textbf{Variable Selection:} Infrastructure investment (x_infra) and environmental protection investment (x_env) were chosen as key variables due to their high sensitivity in previous analyses.

text
\item \textbf{Solution Mapping:} All feasible solutions from different perturbation scenarios were plotted in the x\_env-x\_infra space. Colors indicate perturbation levels (0\%-70\%).

\item \textbf{Clustering Analysis:} As shown in Figure \ref{fig:solution_space}, optimal solutions cluster within x\_env [16.5-18.5M USD] and x\_infra [52-60M USD], demonstrating strong solution stability.

\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=10cm]{figures/sensitive3.png}
\caption{Distribution of Optimal Investment Solutions under Weight Perturbations with Local Magnification}
\label{fig:solution_space}
\end{figure}

The results reveal several key findings:
\begin{itemize}
\item The evaluation model (SCCM) shows highest sensitivity to economic indicators, followed by ecological indicators
\item The optimization model (HOM) maintains convergence even under 70% weight perturbations, demonstrating robust performance
\item The positive correlation between x_env and x_infra validates our model's ability to promote balanced development
\end{itemize}

% \subsection{How to cite?}
% bibliography cite use \cite{1,2,3}

% AI cite use \AIcite{AI1,AI2,AI3}

\begin{thebibliography}{99}
\bibitem{1} D.~E. KNUTH The \TeX{}book the American
Mathematical Society and Addison-Wesley
Publishing Company , 1984-1986.
\bibitem{2}Lamport, Leslie, \LaTeX{}: `` A Document Preparation System '',
Addison-Wesley Publishing Company, 1986.
\bibitem{3}\url{https://www.latexstudio.net/}
\end{thebibliography}

\begin{appendices}

\section{First appendix}

In addition, your report must include a letter to the Chief Financial Officer (CFO) of the Goodgrant Foundation, Mr. Alpha Chiang, that describes the optimal investment strategy, your modeling approach and major results, and a brief discussion of your proposed concept of a return-on-investment (ROI). This letter should be no more than two pages in length.

\begin{letter}{Dear, Mr. Alpha Chiang}

\lipsum[1-2]

\vspace{\parskip}

Sincerely yours,

Your friends

\end{letter}
Here are simulation programmes we used in our model as follow.\

\textbf{\textcolor[rgb]{0.98,0.00,0.00}{Input matlab source:}}
\lstinputlisting[language=Matlab]{./code/mcmthesis-matlab1.m}

\section{Second appendix}

some more text \textcolor[rgb]{0.98,0.00,0.00}{\textbf{Input C++ source:}}
\lstinputlisting[language=C++]{./code/mcmthesis-sudoku.cpp}

\end{appendices}

\AImatter

\begin{ReportAiUse}{9}
\bibitem{AI1}
ChatGPT\
Query1: Besides the COVID-19 pandemic, has the city of Juneau in Alaska experienced any particularly major events that would severely impact its tourism industry?''\\ Output: According to public sources, Juneau has not seen a single event comparable in severity to COVID-19 over the past two or three decades. While factors such as global economic recessions (like the 2008 financial crisis), fluctuations in the cruise industry, temporary transportation disruptions, localized natural events, and broader incidents (e.g., the 9/11 attacks) have occasionally affected tourism, none has caused a large-scale or prolonged impact on Juneau's visitor economy akin to the pandemic.''
\end{ReportAiUse}

\end{document}
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这是我们研究后的Juneau市过度旅游所得出来的论文。根据我们的论文，你可以发现各项参数：如政府在保护环境、宣传营销方面的投入等，在Juneau市的经济、社会、环境产生了不同的作用。根据我们的研究结果 给朱诺旅游委员会写一份的备忘录，概述您的预测、各种措施的效果以及如何优化结果的建议，越详细越好

太专业了，你这样写没人看得懂。我希望能把知识融合起来，把我们得到的专业知识融合在一个普通人都能听懂的话里，写出一份诚恳的、善意的建议。

这是一些参考。这些文章中最后也给特定目标写了信或者备忘录。建议你参考这些文章的风格、语言，来继续完善这篇备忘录

另外，你要避免在用语中使用非常不专业或不严谨的语言。例如，你提到说“每年增加约 5900 万美元用于基础设施升级”，这是在原来的基础上增加5900万美元？还是增加至5900万美元？用词一定要严谨、准确

The phenomenon of momentum in tennis has long been debated, with the 2023 Wimbledon final serving as a testament to its potential impact. Our study delves into the intricacies of match flow, focusing on the dynamics that drive momentum swings and their predictable patterns.
We developed a Dynamic Play Index (DPI) by integrating data preprocessing techniques and advanced statistical models such as Gradient Boosting Trees and the Hidden Markov Model. Our DPI synthesizes performance metrics, personal strengths, and serving advantages into a comprehensive measure of match flow, yielding insights with 82.4% accuracy.
Understanding and capitalizing on momentum is paramount in competitive tennis. Our data indicates that the following elements are critical in maintaining and exploiting momentum:

• Score Streaks: Teach players to focus on the next point to build and maintain dominance. Recognize and adjust quickly if the streak is broken to prevent momentum shift.
• Endurance in Rallies: Use high rally counts as a measure of player stamina and competitive edge. Train players to stay mentally engaged and look for opportunities to conclude rallies with strategic plays
• Decisive Shots: Encourage players to develop precision in aggressive shots, such as winners and aces, which can change the game’s tempo and put psychological pressure on the opponent.
• Opponent Analysis: Implement drills that mimic rivals’ play styles and weaknesses, enabling players to adapt their strategies during actual match play
  In the ebb and flow of a tennis match, players will inevitably face moments that test their resolve and adaptability. Our study highlights several scenarios where preparation can make a significant difference:
• Closing the Gap: Teach players to compartmentalize the score when down, focusing solely on earning the next point. This laser focus can help in gradually diminishing the lead of the opponent.
• Shifting Back Momentum: Introduce drills where players lose points on purpose and then work to recover, teaching them to identify and counteract momentum shifts
• Pressure Points: Simulate break points and tiebreaks in practice sessions, encouraging players to employ specific, practiced responses to these high-stakes moments.
• Break Point Strategies: Have players practice aggressive returns and pinpoint the opponent’s weak spots during simulated break opportunities to take charge of the game’s flow
• Lead Protection: Use drills that start with the player in the lead, emphasizing the need to continue playing offensively to secure the win, rather than passively trying to maintain the lead.
  Our predictive model is not only a tool for analysis but a cornerstone for building mental toughness and tactical agility in players. As a coach, your role transcends physical training. You are the architect of your players’ mental resilience, equipping them to maneuver through the psychological battles intrinsic to competitive tennis. The strategies we’ve detailed are crafted to embolden your players, enabling them to confront the challenges of match play with assured confidence and grace.
  Transitioning from mental preparation to real-time match analysis, our model excels by offering assessments of a player’s dynamic state as the game unfolds. This granular insight into the flow of play is pivotal for making strategic decisions that harness the power of momentum swings. By leveraging this data, you can guide players to make intelligent, on-the-fly adjustments that can alter the course of a match
  It’s important to acknowledge, however, that our model, while comprehensive, is not without its limitations. One such area is the nuanced influence of different court surfaces on a player’s momentum — a variable that we aim to better understand and integrate into future iterations of the model. This presents an exciting opportunity for further enhancement, ensuring that our tool evolves in line with the complexities of the sport.
  In conclusion, the integration of our model into your coaching methodology can be transformative. By translating our insights into practical training exercises, players can be adeptly prepared to exploit the ebb and flow of play, turning what was once an intangible concept into a quantifiable advantage. We are committed to continuous improvement, working alongside you to refine our system and support your efforts in forging champions on the court.
  请模仿这样的风格改写。先简明扼要的指出我们干了什么，然后清晰地指出我们的计算结果是什么，有理有据，用数据说话。最好不要使用小标题，用无序列表列出怎样做是正确的。

你是傻了吗，我是要你改写我们的备忘录，就是Juneau市的那个！网球的这篇文章不过是让你参考它的风格。再发一遍源代码
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\begin{document}
\begin{abstract}
\par Juneau, the capital of Alaska with a population of 30,000, has experienced substantial tourism growth in recent years, bringing significant economic benefits while introducing critical sustainability challenges. To address these issues, this paper presents a two-stage modeling approach. We first develop a Sustainability Coupling Coordination Model (SCCM) to evaluate the coordination among economic, social, and ecological subsystems, then construct a Hierarchical Optimization Model (HOM) that integrates system dynamics with the NSGA-II algorithm, using lexicographic ordering to balance multiple prioritized objectives.

The SCCM evaluates system coordination using ten key indicators across economic, social, and ecological dimensions, selected from comprehensive statistical data of Juneau. Through standardization of indicators and weighted coupling analysis, the model reveals a steady improvement in the tourism system's coordination, with the coupling coordination degree rising from 0.6211 to 0.6943 during 2022--2024, indicating a gradually strengthening interaction among subsystems.

Based on the SCCM evaluation, the HOM identifies eight key decision variables including environmental protection investment, infrastructure investment, tourism taxes, and visitor management strategies. The model employs system dynamics equations to capture the complex interactions between policy interventions and system indicators, optimizing three objectives in descending order of priority: coupling coordination degree, government revenue, and carbon footprint. Through NSGA-II algorithm optimization under practical constraints including budget limitations and minimum coordination requirements, we obtain an optimal policy combination that achieves a coordination degree of 0.8447 and annual revenue of $352.18 million. The solution suggests a balanced investment strategy, allocating 62.8% of the budget to infrastructure improvement, 19.3% to environmental protection, and the remainder to community development and market management, creating positive feedback loops that promote sustainable tourism development.

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keyword1; keyword2
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\section{Introduction}

\subsection{Problem Background}

Juneau, the capital of Alaska, has a population of 30,000 and is characterised by distinctive natural landscapes and significant tourism resources. The city's tourism sector has undergone substantial growth over the past decade, particularly in its cruise ship industry. As shown in Figure \ref{fig:cruise_volume}, cruise passenger volume has increased steadily from 961,000 in 2014 to 1.67 million in 2023, with only a brief interruption during the COVID-19 pandemic in 2020-2021. During peak season, up to seven cruise ships dock simultaneously, resulting in daily visitor numbers equivalent to two-thirds of the permanent population, generating annual revenues of $375 million.

\begin{figure}[htbp]
\centering
\includegraphics[width=12cm]{figures/近年游客数.png}
\caption{Juneau's Cruise Passenger Volume Growth (2014-2023)}
\label{fig:cruise_volume}
\end{figure}

However, this rapid expansion of tourism has also given rise to significant sustainability challenges, including the retreat of the Mendenhall Glacier since 2007 and increased pressure on local infrastructure, as well as social impacts such as housing shortages and traffic congestion affecting residents' daily lives. Despite the implementation of higher tourist fees and hotel taxes, the balancing act of economic development with environmental protection remains a critical challenge for sustainable tourism in Juneau.

\subsection{Restatement of the Problems}

For sustainable tourism in Juneau, Alaska. We summarise the problem into the following four subtasks:

\begin{itemize}
\item \textbf{Task 1:} Develop a sustainable tourism model for the city of Juneau. Integrate economic, social, and ecological factors.
\item \textbf{Task 2:} Based on the model developed, discuss the constraints and optimisation factors and develop a suitable optimisation plan for sustainable tourism in Juneau.
\item \textbf{Task 3:} Demonstrate how this model can be extended to another site and discuss the impact of location and attraction popularity on the optimisation decision.
\item \textbf{Task 4:} Write a memo to the Juneau Tourism Commission describing our findings and recommendations for optimisation.
\end{itemize}

\subsection{Our Work}

\begin{figure}[h]
\centering
\includegraphics[width=16cm]{figures/绘图1.png}
\caption{Framework of the Sustainable Tourism Development Model for Juneau}
\label{fig:framework}
\end{figure}

\section{Assumptions and Notations}

\subsection{Assumptions}
\begin{itemize}
\item The population of the City of Juneau is expected to remain constant at 31,000 after the year 2000.
\item In terms of infrastructure investment, the City of Juneau invests in each sector in roughly stable proportions. Thus, we can use the investment in public transportation to represent the investment in infrastructure.
\item Pollution in tourist cities comes from the transportation of large numbers of tourists, so the amount associated with air pollution can be used to represent overall pollution in the city of Juneau.
\item During the time period of the data, there have been no emergencies, other than the New Crown epidemic, that were significant enough to have a major, sustained impact on Juneau's tourism industry.
\item All data is accurate and reliable.
\end{itemize}

\subsection{Notations}
Due to the complexity of our model, we separately present the notations for decision variables and evaluation indicators in their respective sections (see Table \ref{tab:decision_vars} and Table \ref{tab:indicators}). Here, we focus on the key variables used in coupling coordination calculation:

\begin{table}[!htbp]
\centering
\caption{Key Variables in Coupling Coordination Calculation}
\begin{tabular}{cl}
\toprule
\textbf{Symbol} & \textbf{Description} \
\midrule
$U_{E}$ & Comprehensive score of economic subsystem \
$U_{S}$ & Comprehensive score of social subsystem \
$U_{Eco}$ & Comprehensive score of ecological subsystem \
$C$ & Coupling degree among three subsystems \
$T$ & Coordination level among three subsystems \
$D$ & Coupling coordination degree of the tourism system \
\bottomrule
\end{tabular}
\label{tab:notation}
\end{table}

\section{Model Preparation}

\subsection{Data Collection}

A comprehensive data set encompassing a multitude of economic, social and environmental indicators for the City of Juneau was obtained through a meticulous examination of statistical reports published by pertinent agencies over the years.

\begin{table}[htbp]
\centering
\caption{Data Source Websites}
\begin{tabular}{ll}
\toprule
Database names & Database website \
\midrule
ACS & \href{https://www.census.gov/programs-surveys/acs/data/data-via-ftp.html}{\texttt{https://www.census.gov/...}} \
EJScreen & \href{https://gaftp.epa.gov/EJSCREEN/}{\texttt{https://gaftp.epa.gov/...}} \
GHGRP & \href{https://www.epa.gov/ghgreporting}{\texttt{https://www.epa.gov/...}} \
AQS & \href{https://aqs.epa.gov/aqsweb/airdata/download_files.html}{\texttt{https://aqs.epa.gov/...}} \
LAUS & \href{https://www.bls.gov/lau/}{\texttt{https://www.bls.gov/...}} \
Juneau Budget Data & \href{https://juneau.org/finance/budget-2}{\texttt{https://juneau.org/...}} \
Travel Juneau Annual Report & \href{https://www.traveljuneau.com/about-travel-juneau/annual-report/}{\texttt{https://www.traveljuneau.com/...}} \
ATIA & \href{https://www.alaskatia.org/resources/research}{\texttt{https://www.alaskatia.org/...}} \
JEDC & \href{https://www.jedc.org/research-library-reports-studies-by-jedc/}{\texttt{https://www.jedc.org/...}} \
\bottomrule
\end{tabular}
\end{table}

\subsection{Data Preprocessing}

The raw data collected from various sources required careful preprocessing to ensure quality and usability. Several key preprocessing steps were taken:

\begin{itemize}
\item \textbf{COVID-19 Impact Handling}: Data from 2020 and 2021 were excluded from our analysis due to the significant disruption to tourism-related indicators caused by the COVID-19 pandemic. This exclusion ensures that our model is built on data that better represents normal operating conditions.

\item \textbf{Composite Indicator Construction}: Some decision variables and indicators were not directly available in the raw data. For instance, infrastructure investment was constructed by aggregating multiple related sub-categories of investment (e.g., street maintenance, facility upgrades) from annual statistical reports. While such aggregation may not capture the complete expenditure in each domain, it serves as a statistically significant proxy for the overall investment level.

\item \textbf{Abstract Variable Quantification}: Several variables and indicators in our model are conceptually abstract. For example, the tourism tax intensity was quantified based on historical tax collection data and tourist numbers. Similarly, the tourist distribution policy intensity was derived from various policy implementation records and their corresponding effects.
\end{itemize}

After preprocessing, we obtained a clean and consistent dataset covering recent years except for the pandemic period, which forms the foundation for our subsequent modeling work.

\subsection{Model Overview}

To address the sustainable tourism development challenges in Juneau, we propose a two-stage modeling approach, as illustrated in Figure \ref{fig:model_structure}. The framework consists of two major components:

\begin{itemize}
\item \textbf{Sustainability Coupling Coordination Model (SCCM)}: This evaluation component assesses the coordination level among economic, social, and ecological subsystems. Through standardization of indicators and subsystem integration, SCCM generates a coupling coordination degree that quantifies the overall system balance.

\item \textbf{Hierarchical Optimization Model (HOM)}: Building upon the SCCM evaluation results, this optimization component determines the optimal policy combinations. HOM employs system dynamics equations and utilizes the NSGA-II algorithm with lexicographic ordering to find solutions that balance multiple objectives with different priorities.
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=11cm]{figures/绘图2.png}
\caption{Framework of the Two-Stage Modeling Approach}
\label{fig:model_structure}
\end{figure}

The workflow proceeds from model preparation through evaluation and optimization to final strategy generation. The connection between SCCM and HOM is established through the coupling coordination degree, which serves both as an evaluation metric and a primary optimization objective. This integrated approach ensures that the proposed solutions maintain a high level of system coordination while meeting specific performance targets.

\section{Sustainability Coupling Coordination Model}

In order to formulate an optimal sustainable tourism development plan for Juneau, the Sustainability Coupling Coordination Model (SCCM) was constructed in order to evaluate the coordination level among economic, social, and ecological development indicators. Based on Juneau's historical reports and comprehensive statistical data, ten key indicators were identified with which to assess the city's integrated development across these three dimensions. The specific indicators, including their symbolic representations, data sources, and measurement units, are detailed in Table~\ref{tab:indicators} below.   

\begin{table}[htbp]
\centering
\caption{Key Indicators for Assessing Sustainable Tourism Development in Juneau}
\label{tab:indicators}
\begin{tabular}{lllll}
\toprule
\textbf{Subsystem} & \textbf{Indicator} & \textbf{Symbol} & \textbf{Unit} & \textbf{Attribute} \
\midrule
Economic & Tourism Revenue & $E_1$ & Million USD & Positive \
& Tourism Fixed Assets & $E_2$ & Million USD & Positive \
\midrule
Social & Resident Attitude & $S_1$ & Scale 0-10 & Positive \
& Congestion Index & $S_2$ & Index Value & Negative \
& Tourism Accessibility & $S_3$ & Index Value & Positive \
& Resident Disposable Income & $S_4$ & USD/Person & Positive \
& Tourism Employment & $S_5$ & Thousand People & Positive \
\midrule
Ecological & Carbon Footprint & $Eco_1$ & Tonnes of CO$_2$ Equivalent & Negative \
& Air Pollution Index & $Eco_2$ & Index Value & Negative \
& Glacier Congestion Index & $Eco_3$ & Index Value & Negative \
\bottomrule
\end{tabular}
\end{table}

\subsection{Standardization of Indicators}

In view of the marked disparities in dimensions and value ranges of the indicators, it is imperative to standardise the raw data with a view to eliminating dimensional impacts. This study employs the range standardisation method to convert all indicator values into a unified interval of $[0,1]$. Different standardisation formulas are applied to positive and negative indicators:

For positive indicators ($E_1$, $E_2$, $S_1$, $S_3$, $S_4$, $S_5$), the following standardisation formula is applied:

For negative indicators ($S_2$, $\text{Eco}_1$, $\text{Eco}_2$, $\text{Eco}_3$), the following standardisation formula is employed:

In this formula, $X'_{ij}$ represents the standardized indicator value, $X_{ij}$ denotes the original indicator value, and $X_{\text{max}}$ and $X_{\text{min}}$ represent the maximum and minimum values of the indicator during the evaluation period, respectively. In order to mitigate the influence of extreme values, this study establishes upper and lower bounds for each indicator based on historical data for standardisation calculations.

\subsection{Calculation of Coupling Coordination Degree}

Utilising the standardised indicators, a composite index is derived for the three subsystems:
\begin{equation}
\begin{cases}
U_E = 0.6E_1 + 0.4E_2 \
U_S = 0.25S_1 + 0.35S_2 + 0.15S_3 + 0.20S_4 + 0.10S_5 \
U_{\text{Eco}} = 0.26\text{Eco}_1 + 0.24\text{Eco}_2 + 0.50\text{Eco}_3
\end{cases}
\label{eq:composite_index}
\end{equation}

The glacier crowding index ($\text{Eco}_3$) was assigned the highest weight of 0.50, reflecting the critical position of glacier resources in the Juneau tourism ecosystem. Utilising the aforementioned formula (see Equation \eqref{eq:composite_index}), the composite economic, social and ecological indicators for the city of Juneau were derived over the preceding triennium, as illustrated in Figure \ref{fig:aa}.

\begin{figure}[h]
\small
\centering
\includegraphics[width=13cm]{figures/3-subsystom.png}
\caption{Composition of Subsystem Development Indices (2022-2024)} \label{fig:aa}
\end{figure}

The coupling coordination of the three subsystems can be calculated based on the combined indices through a three-step process.

First, the coupling degree $C$, which indicates the interaction between subsystems, is calculated as:
\begin{equation}
C = \frac{3 \times (U_E \times U_S \times U_{\text{Eco}})^{1/3}}{U_E + U_S + U_{\text{Eco}}}
\end{equation}

Then, the coordination degree $T$ is determined by:
\begin{equation}
T = 0.28U_E + 0.28U_S + 0.44U_{\text{Eco}}
\end{equation}
where the ecological subsystem is assigned a higher weight (0.44) to reflect its crucial role in sustainable tourism development.

Finally, the coupling coordination degree $D$ is derived as:
\begin{equation}
D = \sqrt{C \times T}
\end{equation}

The value of $D$ ranges from 0 to 1, with higher values indicating better system coordination. Based on this metric, the coordinated development status can be classified into ten levels from extremely dysfunctional to highly coordinated.

The coupling coordination degree calculations for the past three years are presented in Table \ref{tab:ccd_results}.

\begin{table}[htbp]
\centering
\caption{Coupling Coordination Degree Results (2022-2024)}
\label{tab:ccd_results}
\begin{tabular}{cccc}
\toprule
Year & CCD Value & Level & Category \
\midrule
2022 & 0.6211 & 7 & Primary Coordinated \
2023 & 0.6530 & 7 & Primary Coordinated \
2024 & 0.6943 & 7 & Primary Coordinated \
\bottomrule
\end{tabular}
\end{table}

The calculation results indicate that the coupling degree of the economic-social-ecological system of Juneau tourism maintains at the seventh level of 'primary coordination' over the past three years, with a steady upward trend from 0.6211 to 0.6943. This suggests that while the coordination among economic growth, social well-being, and ecological protection in Juneau's tourism development remains at a basic level, the positive interaction among the subsystems has been gradually strengthening.

\section{Hierarchical Optimization Model}

In this section, we propose a hierarchical multi-objective optimisation model to determine the optimal policy combination in order to address the challenges of overtourism while maintaining tourism benefits. This builds upon the Sustainability Coupling Coordination Model (SCCM), which evaluates the coordination level among economic, social, and ecological subsystems.

The hierarchical structure of the model reflects the multi-level relationships: at the foundation level are eight decision variables representing various policy instruments including investments, taxes, and visitor management strategies.These policy instruments then influence ten key indicators across economic, social, and ecological dimensions as identified in the SCCM.Finally, these indicators are aggregated into three subsystem indices that collectively determine the system's overall performance. The model's hierarchical framework is designed to optimise the coupling coordination degree (D), government revenue, and carbon footprint, with the aforementioned objectives arranged in descending order of priority. This arrangement reflects Juneau's commitment to achieving balanced development while addressing overtourism concerns.

\subsection{Decision Variables}

Based on the historical data and policy reports from Juneau's tourism development, we identified eight key decision variables that can be effectively controlled by the city management to influence tourism outcomes. These variables, as shown in Table \ref{tab:decision_vars}, include four types of investment allocations, tourist taxation, visitor distribution policy, and two fundamental tourism volume indicators.

\begin{table}[htbp]
\centering
\caption{Decision Variables for Tourism Development in Juneau}
\label{tab:decision_vars}
\begin{tabular}{lll}
\toprule
\textbf{Indicator} & \textbf{Symbol} & \textbf{Unit} \
\midrule
Environmental Protection Investment & $x_{env}$ & Million USD \
Infrastructure Investment & $x_{infra}$ & Million USD \
Tourism Market Promotion Investment & $x_{mkt}$ & Million USD \
Community Project Investment & $x_{soc}$ & Million USD \
Tourist Per Capita Tourism Tax & $\alpha_{tax}$ & USD \
Tourist Distribution Policy Intensity & $x_{div}$ & Index Value \
Number of Tourists & $N_{T}$ & Thousand People/Year \
Tourist Per Capita Consumption & $x_{con}$ & USD/Person \
\bottomrule
\end{tabular}
\end{table}

Through regression analysis of historical data, we established the complex relationships between these decision variables and the ten assessment indicators. Each indicator is determined by multiple decision variables through non-linear interactions. For instance, the carbon footprint ($Eco_1$) is influenced by environmental protection investment ($x_{env}$), infrastructure investment ($x_{infra}$), and tourist volume ($N_{T}$), while the tourism accessibility ($S_3$) is jointly determined by infrastructure investment ($x_{infra}$), distribution policy intensity ($x_{div}$), and tourist volume ($N_{T}$). These intricate relationships form the foundation of our optimization model, enabling us to evaluate how policy adjustments would impact various aspects of Juneau's tourism system. The complete hierarchical structure of our model is illustrated in Figure \ref{fig:sankey}.

\begin{figure}[h]
\small
\centering
\includegraphics[width=16cm]{figures/sangji.png}
\caption{Hierarchical Structure of the Sustainable Tourism Optimization Model} \label{fig:sankey}
\end{figure}

\subsection{System Dynamics Equations}

The relationships between decision variables and indicators were established through regression analysis of historical data. For the economic subsystem, the government revenue ($E_1$) and tourism fixed assets ($E_2$) are formulated as:

\begin{equation}
\text{E}{1} = \frac{1000N{T}(x_{con} + \alpha_{tax} - 218.3796)}{10^6} + 251.9655
\end{equation}

\begin{equation}
\text{E}{2} = 2.10818 - 0.116903\frac{x{infra}}{10.0054} - 0.331696\frac{x_{mkt}}{1.00168} + 2.10063\ln(1 + \frac{\text{S}_{5}}{0.393086})
\end{equation}

The government revenue equation captures how tourist volume ($N_{T}$), per capita consumption ($x_{con}$), and tourism tax ($\alpha_{tax}$) directly contribute to the city's income. The tourism fixed assets are influenced by infrastructure and market promotion investments, while also showing a logarithmic relationship with tourism employment, indicating diminishing returns on investment.

For the social subsystem, the resident attitude ($S_1$) and congestion index ($S_2$) are particularly critical:

\begin{equation}
\text{S}{1} = 6.05431 + 0.168539x{div} + 0.8668\frac{x_{env}}{10.1057} - 0.00038535T
\end{equation}

\begin{equation}
\text{S}{2} = 3.74014 + 0.000416267N{T} - 0.0586679x_{infra} - 0.160964x_{div}
\end{equation}

These equations reveal that resident attitudes are positively influenced by environmental protection and visitor distribution policies, but negatively impacted by increasing tourist numbers. Meanwhile, the congestion index can be effectively managed through infrastructure investment and tourist distribution strategies.

For the ecological subsystem, the carbon footprint ($\text{Eco}_1$) is of particular concern:

\begin{equation}
\text{Eco}{1} = 1.92453 \times 10^6 + 391.147(1000N{T})^{-30.2898} - 78569.9x_{env} - 805146\ln(1 + x_{infra})
\end{equation}

This equation demonstrates how environmental protection and infrastructure investments can help mitigate the carbon footprint, with infrastructure improvements showing diminishing returns as indicated by the logarithmic term.

The remaining system indicators are formulated as follows:

\begin{equation}
\left{
\begin{aligned}
\text{S}{3} &= 1.5081(\frac{N{T} + 100.004}{0.000231623})^{0.429576}(1 - e^{-0.45747\frac{x_{infra}}{9.99294}})(1 + 0.0590587x_{div}) \
\text{S}{4} &= 49942.2 + 0.00569082(N{T} \cdot x_{con}) + 237.171x_{infra} - 457.361x_{soc} \
\text{S}{5} &= 58.108 + 0.000421N{T} - 19.3388\ln(1 + \frac{x_{con}}{104.465}) + 33.4503(1 + \frac{\alpha_{tax}}{-3.93095})^{-1} \
\text{Eco}{2} &= 20.7266 + 2.31625 \times 10^{-6}(1000N{T}) - 4.16471x_{env} - 1.44831x_{infra} - 0.0736647x_{div} \
\text{Eco}{3} &= 0.252585 + 0.00266493\ln(1 + N{T}) - 1.24836x_{div}
\end{aligned}
\right.
\end{equation}

\subsection{Objective Functions}

Based on the established system dynamics and Juneau's development priorities, we formulate a hierarchical multi-objective optimization problem with three objectives:

\begin{equation}
\left{
\begin{aligned}
\min f_1 &= -D \
\min f_2 &= -\text{E}{1} \
\min f_3 &= \text{E}{CO_{1}}
\end{aligned}
\right.
\end{equation}

where $D$ is the coupling coordination degree calculated using the SCCM framework. The negative signs before $D$ and $E_{1}$ convert their maximization into minimization problems. These objectives are arranged in descending order of priority, reflecting Juneau's primary focus on achieving system coordination, followed by economic benefits, while maintaining environmental responsibility through carbon footprint control.

\subsection{Constraints}

The optimization model is subject to several constraints to ensure the feasibility and practicality of solutions. First, all decision variables must fall within their respective reasonable ranges:

\begin{equation}
\left{
\begin{aligned}
10.0 \leq x_{env} \leq 25.0 & \quad \text{(Million USD)} \
40.0 \leq x_{infra} \leq 60.0 & \quad \text{(Million USD)} \
0.0 \leq x_{mkt} \leq 10.0 & \quad \text{(Million USD)} \
15.0 \leq x_{soc} \leq 30.0 & \quad \text{(Million USD)} \
0.0 \leq \alpha_{tax} \leq 10.0 & \quad \text{(USD)} \
0.2 \leq x_{div} \leq 0.4 & \quad \text{(Index Value)} \
500 \leq N_{T} \leq 2200 & \quad \text{(Thousand People/Year)} \
200 \leq x_{con} \leq 260 & \quad \text{(USD/Person)}
\end{aligned}
\right.
\end{equation}

Second, a budget constraint is imposed to ensure that the total investment does not exceed the government revenue:

\begin{equation}
x_{env} + x_{infra} + x_{mkt} + x_{soc} \leq \text{E}_{1}
\end{equation}

Third, to maintain a satisfactory level of system coordination, we require:

\begin{equation}
D \geq 0.8
\end{equation}

\subsection{Solution Methodology}

To solve this hierarchical multi-objective optimization problem, we employ the NSGA-II (Non-dominated Sorting Genetic Algorithm II) algorithm with a customized lexicographic dominator. The lexicographic dominance relationship is defined as follows: for two solutions $A$ and $B$ with objective vectors $F_A=[f_1^A,f_2^A,f_3^A]$ and $F_B=[f_1^B,f_2^B,f_3^B]$, solution $A$ dominates solution $B$ if and only if:

\begin{equation}
\left{
\begin{aligned}
& f_1^A < f_1^B - \epsilon_1, \text{ or} \
& |f_1^A - f_1^B| \leq \epsilon_1 \text{ and } f_2^A < f_2^B - \epsilon_2, \text{ or} \
& |f_1^A - f_1^B| \leq \epsilon_1 \text{ and } |f_2^A - f_2^B| \leq \epsilon_2 \text{ and } f_3^A < f_3^B - \epsilon_3
\end{aligned}
\right.
\end{equation}

where $\epsilon_1 = 0.5$, $\epsilon_2 = 50$, and $\epsilon_3 = 1000$ are tolerance parameters that define the indifference thresholds for each objective. This dominance relationship ensures that solutions are primarily compared based on the coupling coordination degree, followed by government revenue, and finally carbon footprint.

\subsection{Algorithm Implementation}

The NSGA-II algorithm was implemented with carefully selected parameters to ensure efficient exploration of the solution space while maintaining solution diversity. The population size was set to 300 individuals with 100 offspring per generation, and the algorithm was run for 400 generations to ensure convergence. The implementation details are as follows:

\begin{itemize}
\item \textbf{Population Initialization}: The initial population was randomly generated within the feasible region defined by the variable bounds. To improve the quality of initial solutions, we employed a constraint handling method that ensures all initial individuals satisfy the budget constraint.

text
\item \textbf{Genetic Operators}: The Simulated Binary Crossover (SBX) operator was used for crossover with a probability of 0.9, and the Polynomial Mutation operator was applied with a probability of $1/n$ where $n$ is the number of decision variables. These operators were chosen for their ability to handle real-valued decision variables effectively.

\item \textbf{Constraint Handling}: The constraints were handled using a penalty function approach. Solutions violating the coupling coordination degree constraint ($D \geq 0.8$) or the carbon footprint ceiling were penalized proportionally to their degree of violation.

\end{itemize}

The evolution of the three objectives over generations is shown in Figure \ref{fig:convergence}. The coupling coordination degree ($D$) shows rapid improvement in the early stages and stabilizes around 0.84 after 200 generations. The government revenue exhibits a similar pattern, reaching a plateau at approximately 350 million USD. The carbon footprint initially fluctuates but gradually decreases and stabilizes around 54,000 tonnes CO$_2$ equivalent, demonstrating the algorithm's ability to balance multiple competing objectives.

\begin{figure}[htbp]
\centering
\includegraphics[width=18cm]{figures/evolution.png}
\caption{Mean Objective Values Evolution During the Optimization Process}
\label{fig:convergence}
\end{figure}

The final population's distribution in the objective space is visualized in Figure \ref{fig:scatter}, where each point represents a non-dominated solution. The scatter plot reveals clear trade-offs between the three objectives, with solutions clustering in distinct regions. The color gradient indicates the carbon footprint level, showing how solutions with higher coordination degrees and government revenues tend to have slightly higher carbon footprints, though all remain within the specified constraints.

\begin{figure}[htbp]
\centering
\includegraphics[width=16cm]{figures/sandian.png}
\caption{3D Scatter Plot of Non-dominated Solutions in the Final Population}
\label{fig:scatter}
\end{figure}

\subsection{Optimization Results and Investment Strategy}
Through the hierarchical multi-objective optimization process, we obtained a set of non-dominated solutions representing different trade-offs among the objectives. Based on the lexicographic ordering principle and our problem constraints, we identified the optimal solution with the following performance metrics:
\begin{itemize}
\item Coupling Coordination Degree ($D$): 0.8447
\item Government Revenue: 352.18 million USD
\item Carbon Footprint: 53,728.75 tonnes CO$_2$ equivalent
\end{itemize}

The corresponding optimal policy combination is presented in Table \ref{tab:optimal_solution}.

\begin{table}[htbp]
\centering
\caption{Optimal Policy Combination for Juneau's Sustainable Tourism Development}
\label{tab:optimal_solution}
\begin{tabular}{lll}
\toprule
\textbf{Decision Variable} & \textbf{Optimal Value} & \textbf{Unit} \
\midrule
Environmental Protection Investment & 18.21 & Million USD \
Infrastructure Investment & 59.37 & Million USD \
Tourism Market Promotion Investment & 1.52 & Million USD \
Community Project Investment & 15.23 & Million USD \
Tourist Per Capita Tourism Tax & 3.93 & USD \
Tourist Distribution Policy Intensity & 0.20 & Index Value \
Number of Tourists & 2,200 & Thousand People/Year \
Tourist Per Capita Consumption & 260 & USD/Person \
\bottomrule
\end{tabular}
\end{table}

Based on the optimization results, we propose an integrated investment strategy that creates reinforcing feedback mechanisms in the tourism system:

\begin{itemize}
\item \textbf{Infrastructure-Focused Investment}: The solution allocates the largest portion of the budget (59.37 million USD, 62.8%) to infrastructure improvement. This investment directly enhances tourism accessibility ($S_{3}$) and reduces congestion ($S_2$), creating a positive feedback loop that enables higher visitor capacity while maintaining service quality.

\item \textbf{Strategic Environmental Protection}: A significant investment of 18.21 million USD (19.3%) in environmental protection demonstrates the city's commitment to ecological preservation. This investment reduces carbon footprint and improves resident attitudes ($S_{1}$), ensuring the sustainability of natural attractions.

\item \textbf{Community Development}: The community project investment of 15.23 million USD (16.1%), combined with a modest distribution policy intensity (0.20), prioritizes local community benefits. This enhances resident disposable income ($S_{4}$) and strengthens social acceptance of tourism.

\item \textbf{Market Management}: The moderate tourism tax (3.93 USD per capita) and conservative market promotion investment (1.52 million USD, 1.8%) maintain tourism attractiveness while generating necessary revenue for sustainable development.
\end{itemize}

This investment strategy achieves the highest possible coupling coordination degree while satisfying all constraints. The high coordination degree of 0.8447 indicates a well-balanced development state among economic, social, and ecological subsystems, demonstrating how appropriate revenue allocation can promote sustainable tourism development.

\section{Model Adaptation to Nanjing}

To demonstrate the adaptability of our modeling approach, we apply the framework to Nanjing, China, a historic city facing overtourism challenges. As a cultural tourism destination with a population of over 8 million, Nanjing presents different characteristics from Juneau, allowing us to test the model's versatility.

\subsection{Model Adjustment}

The adaptation of our model requires several modifications to accommodate Nanjing's unique context:

\begin{itemize}
\item \textbf{Indicator Selection}: The glacier congestion index ($\text{Eco}_3$) was removed as it is specific to Juneau. The remaining nine indicators were retained as they are universal measures of tourism sustainability.

\item \textbf{System Integration}: The weights in SCCM were adjusted to reflect the changed composition of the ecological subsystem:
\begin{equation}
\begin{aligned}
U_E &= 0.6E_1 + 0.4E_2 \
U_S &= 0.25S_1 + 0.35S_2 + 0.15S_3 + 0.20S_4 + 0.10S_5 \
U_{Eco} &= 0.5\text{Eco}_1 + 0.5\text{Eco}_2
\end{aligned}
\end{equation}
\end{itemize}

The decision variables remain unchanged as they represent universal policy instruments, though their operational ranges were adjusted according to Nanjing's scale:

\begin{equation}
\left{
\begin{aligned}
20.0 \leq x_{env} \leq 70.0 & \quad \text{(Million USD)} \
150.0 \leq x_{infra} \leq 250.0 & \quad \text{(Million USD)} \
20.0 \leq x_{mkt} \leq 50.0 & \quad \text{(Million USD)} \
200.0 \leq x_{soc} \leq 250.0 & \quad \text{(Million USD)} \
0.0 \leq \alpha_{tax} \leq 5.0 & \quad \text{(USD)} \
0.2 \leq x_{div} \leq 0.5 & \quad \text{(Index Value)} \
90000 \leq N_{T} \leq 120000 & \quad \text{(Thousand People/Year)} \
1500 \leq x_{con} \leq 2300 & \quad \text{(USD/Person)}
\end{aligned}
\right.
\end{equation}

Based on regression analysis of Nanjing's historical data, the system dynamics equations were recalibrated. For example, the government revenue equation was updated to:

\begin{equation}
\text{E}{1} = \frac{1000N{T}(x_{con} + \alpha_{tax} \times 1327.1274)}{10^8} - 4401.0535
\end{equation}

The Hierarchical Optimization Model (HOM) retains its structure with the same three objectives but different parameters, demonstrating the framework's adaptability to various contexts while maintaining its core methodology.

\subsection{Optimization Results for Nanjing}

The optimization for Nanjing achieved a coupling coordination degree of 0.8848, demonstrating the model's effectiveness in a different context. The optimal policy combination is characterized by:

\begin{itemize}
\item \textbf{Maximum Environmental Protection}: Environmental investment reaches its upper limit (70M USD), reflecting the critical importance of environmental quality in urban tourism.

text
\item \textbf{Substantial Infrastructure Support}: A high infrastructure investment (197.7M USD) focuses on urban tourism facilities and transportation capacity.

\item \textbf{Active Market Promotion}: Nearly maximum market promotion investment (49.9M USD) suggests the importance of destination marketing in competitive urban tourism.

\item \textbf{Basic Social Programs}: Minimum social project investment (200M USD) indicates a focus on essential community support.

\item \textbf{Moderate Tourism Management}: A tourism tax of 4.45 USD and conservative distribution policy intensity (0.20) suggest a market-driven approach to tourist flow management.

\end{itemize}

This solution achieves a government revenue of 2,998.48M USD while maintaining carbon emissions at 3,098,827.61 tonnes CO$_2$ equivalent. The results demonstrate different priorities from Juneau, with a stronger emphasis on environmental protection and market promotion in the urban context. As shown in Figure \ref{fig:nanjing_scatter}, the final population of solutions exhibits clear trade-offs between the three objectives, with our selected solution representing an optimal balance according to the lexicographic ordering principle.

\begin{figure}[htbp]
\centering
\includegraphics[width=16cm]{figures/nanjing.png}
\caption{3D Scatter Plot of Non-dominated Solutions for Nanjing's Optimization}
\label{fig:nanjing_scatter}
\end{figure}

\subsection{Impact of Location Characteristics}

The comparative study between Juneau and Nanjing reveals how geographical characteristics significantly influence the relative importance of different measures in sustainable tourism management:

\begin{itemize}
\item \textbf{Tourism Resource Type}: In Juneau, where tourism depends heavily on natural attractions like glaciers, environmental protection investment becomes the primary concern, directly impacting both tourist satisfaction and ecological sustainability. Conversely, Nanjing's cultural-historical tourism necessitates greater emphasis on infrastructure capacity and preservation.

\item \textbf{Tourist Flow Pattern}: Juneau's cruise-dominated tourism creates significant seasonal fluctuations, making the distribution policy ($x_{div}$) crucial for peak-season management. In contrast, Nanjing's year-round tourism pattern shifts the focus to sustained infrastructure optimization and continuous flow management.

\item \textbf{Transportation Structure}: The singular dependence on cruise ships in Juneau results in concentrated tourist arrivals, requiring precise temporal control. Nanjing's diverse transportation network enables more flexible spatial distribution, as reflected in its higher optimal infrastructure investment ($x_{infra}$).
\end{itemize}

\subsection{Promoting Tourism Balance}

Our model incorporates the tourism accessibility index ($S_3$) and infrastructure investment ($x_{infra}$) to promote balanced tourism development:

\begin{itemize}
\item \textbf{Accessibility Enhancement}: The tourism accessibility index ($S_3$) in our model measures the ease of reaching different attractions. Through optimizing infrastructure investment and distribution policies, the model promotes higher accessibility for all attractions, including less-visited ones. This is reflected in Nanjing's optimization result where $S_3$ reaches [value], indicating improved access to diverse tourist locations.

\item \textbf{Infrastructure Support}: The optimal infrastructure investment of 197.7M USD can enhance the basic facilities and transportation networks connecting different attractions. The system dynamics equation for accessibility shows that improved infrastructure directly contributes to better tourist access across all sites:
\begin{equation}
S_{3} = 1.5081(\frac{N_{T} + 100.004}{0.000231623})^{0.429576}(1 - e^{-0.45747\frac{x_{infra}}{9.99294}})(1 + 0.0590587x_{div})
\end{equation}
\end{itemize}

These mechanisms demonstrate how our model naturally promotes tourism balance by incorporating accessibility measures and infrastructure support in its optimization framework.

\section{Sensitivity Analysis}

To validate our model's reliability and stability, we conducted three levels of sensitivity analysis targeting both the evaluation model (SCCM) and optimization model (HOM).

\subsection{Indicator Sensitivity in SCCM}
For the evaluation model, we performed a standardized sensitivity analysis on all ten indicators:

\begin{itemize}
\item \textbf{Analysis Method:} Each indicator was varied by ±15% from its baseline value while keeping others constant. The changes in coupling coordination degree (D) were recorded for each variation.

text
\item \textbf{Standardization Process:} All indicators were first normalized to [0,1] scale to ensure comparability. For positive indicators (E1, E2, S1, S3, S4, S5), we used the formula $(x-x_{min})/(x_{max}-x_{min})$; for negative indicators (S2, Eco1, Eco2), we used $(x_{max}-x)/(x_{max}-x_{min})$.

\item \textbf{Results Interpretation:} The sensitivity was quantified by the ratio of D's percentage change to indicator's percentage change. As shown in Figure \ref{fig:indicator_sensitivity}, steeper curves indicate higher sensitivity.

\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=14cm]{figures/sensitive 1.png}
\caption{Sensitivity of Coupling Coordination Degree to Individual Indicator Variations (±15%)}
\label{fig:indicator_sensitivity}
\end{figure}

\subsection{Weight Perturbation Analysis in HOM}
We then tested the optimization model's robustness through systematic weight perturbations:

\begin{itemize}
\item \textbf{Perturbation Method:} Random perturbations were applied to weights in each subsystem while maintaining their sum as 1. For example, at 20% perturbation level, each weight was randomly varied within ±20% of its original value, then renormalized.

text
\item \textbf{Evolution Analysis:} For each perturbation level (0\%, 10\%, ..., 70\%), we ran the NSGA-II algorithm for 400 generations with population size 200. Figure \ref{fig:weight_evolution} tracks the mean coordination degree across generations.

\item \textbf{Convergence Criteria:} The algorithm was considered converged when the mean D value change remained below 0.001 for 50 consecutive generations.

\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=14cm]{figures/sensitive 2.png}
\caption{Evolutionary Trajectories of Mean Coordination Degree under Different Weight Perturbation Levels}
\label{fig:weight_evolution}
\end{figure}

\subsection{Optimal Solution Stability Analysis}
Finally, we examined the stability of optimal solutions under weight perturbations:

\begin{itemize}
\item \textbf{Variable Selection:} Infrastructure investment (x_infra) and environmental protection investment (x_env) were chosen as key variables due to their high sensitivity in previous analyses.

text
\item \textbf{Solution Mapping:} All feasible solutions from different perturbation scenarios were plotted in the x\_env-x\_infra space. Colors indicate perturbation levels (0\%-70\%).

\item \textbf{Clustering Analysis:} As shown in Figure \ref{fig:solution_space}, optimal solutions cluster within x\_env [16.5-18.5M USD] and x\_infra [52-60M USD], demonstrating strong solution stability.

\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=10cm]{figures/sensitive3.png}
\caption{Distribution of Optimal Investment Solutions under Weight Perturbations with Local Magnification}
\label{fig:solution_space}
\end{figure}

The results reveal several key findings:
\begin{itemize}
\item The evaluation model (SCCM) shows highest sensitivity to economic indicators, followed by ecological indicators
\item The optimization model (HOM) maintains convergence even under 70% weight perturbations, demonstrating robust performance
\item The positive correlation between x_env and x_infra validates our model's ability to promote balanced development
\end{itemize}

% \subsection{How to cite?}
% bibliography cite use \cite{1,2,3}

% AI cite use \AIcite{AI1,AI2,AI3}

\begin{thebibliography}{99}
\bibitem{1} D.~E. KNUTH The \TeX{}book the American
Mathematical Society and Addison-Wesley
Publishing Company , 1984-1986.
\bibitem{2}Lamport, Leslie, \LaTeX{}: `` A Document Preparation System '',
Addison-Wesley Publishing Company, 1986.
\bibitem{3}\url{https://www.latexstudio.net/}
\end{thebibliography}

\begin{appendices}

\section{First appendix}

In addition, your report must include a letter to the Chief Financial Officer (CFO) of the Goodgrant Foundation, Mr. Alpha Chiang, that describes the optimal investment strategy, your modeling approach and major results, and a brief discussion of your proposed concept of a return-on-investment (ROI). This letter should be no more than two pages in length.

\begin{letter}{Dear, Mr. Alpha Chiang}

\lipsum[1-2]

\vspace{\parskip}

Sincerely yours,

Your friends

\end{letter}
Here are simulation programmes we used in our model as follow.\

\textbf{\textcolor[rgb]{0.98,0.00,0.00}{Input matlab source:}}
\lstinputlisting[language=Matlab]{./code/mcmthesis-matlab1.m}

\section{Second appendix}

some more text \textcolor[rgb]{0.98,0.00,0.00}{\textbf{Input C++ source:}}
\lstinputlisting[language=C++]{./code/mcmthesis-sudoku.cpp}

\end{appendices}

\AImatter

\begin{ReportAiUse}{9}
\bibitem{AI1}
ChatGPT\
Query1: Besides the COVID-19 pandemic, has the city of Juneau in Alaska experienced any particularly major events that would severely impact its tourism industry?''\\ Output: According to public sources, Juneau has not seen a single event comparable in severity to COVID-19 over the past two or three decades. While factors such as global economic recessions (like the 2008 financial crisis), fluctuations in the cruise industry, temporary transportation disruptions, localized natural events, and broader incidents (e.g., the 9/11 attacks) have occasionally affected tourism, none has caused a large-scale or prolonged impact on Juneau's visitor economy akin to the pandemic.''
\end{ReportAiUse}

\end{document}
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致：朱诺旅游委员会（Juneau Tourism Commission）
时间：2025年1月27日

我们针对朱诺近年来迅速增长的旅游需求，构建了一个量化模型来评估经济、社会与环境三方面的平衡度，并用求解算法找到一套能兼顾收益与生态保护的政策组合。过去三年（2022-2024年）的数据显示，朱诺在经济、社会与环境三大子系统的协调度从 0.6211 稳步提升至 0.6943，证明只要选对方向，发展与保护并非不可兼得。借助模型的进一步优化，我们找到了能让协调度升至 0.8447、年收入约达 3.52 亿美元的方案，关键在于合理分配预算与调整游客管理方式。

我们发现以下做法能最大化地发挥“经济收益与环境、社区共赢”的潜力：

• 将基础设施投入集中在 59.37 百万美元左右，以改善道路交通与港口设施，让旺季时也能应对大规模游客，减少对居民生活的冲击
• 将 18.21 百万美元专门用于环境保护，包括对冰川区域的维护、减少排放和监控污染源
• 在确保城市魅力不受影响的前提下，每位游客征收 3.93 美元的税费，既能增加公共财力，也能避免盲目追求过多低效游客
• 每年投入约 15.23 百万美元给社区项目，以改善公共服务、居民福利，并让市民更直观地分享到旅游发展的好处
• 保持适度的市场推广力度（约 1.52 百万美元），重点放在发展高附加值的旅游体验，而非单纯提高客流量
• 利用简单的分流或预约制度（强度约 0.20）来缓解个别景区的过度拥堵，同时提升整体旅游品质

在此基础上，我们还强调通过定期收集数据与跟踪指标（如碳排放、居民满意度、拥堵程度等），及时微调投资和管理策略。我们的测算显示，只要财政投入总和不超过当年旅游收入，且保持对生态与社区的关注，就能让朱诺在未来数年内继续保持较高水平的经济收益，并避免不可逆的环境破坏或社会矛盾。

这套方案展现了定量分析在解决“经济 VS. 生态”这种复杂议题上的价值，也证明只要在投资结构和游客管控上做好精细化安排，朱诺完全有机会平衡好“游客持续增长”和“城市与自然资源长远发展”之间的关系。若您希望进一步讨论具体措施或需要更多技术支持，我们会随时待命，为朱诺的可持续繁荣贡献力量。

此致
敬礼

研究团队 | 可持续旅游发展项目组
我们觉得数据还是不要放上去了，用通俗易懂的方式介绍一下吧

你能把这篇备忘录翻译成英文吗？最好是地道的纯正的英文，就按照这个文章里的诚恳语气翻译

那么现在我们已经有了这个备忘录，我要把他加到这篇论文里去，代码要怎么加呢？
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\date{\today}
\begin{document}
\begin{abstract}
\par Juneau, the capital of Alaska with a population of 30,000, has experienced substantial tourism growth in recent years, bringing significant economic benefits while introducing critical sustainability challenges. To address these issues, this paper presents a two-stage modeling approach. We first develop a Sustainability Coupling Coordination Model (SCCM) to evaluate the coordination among economic, social, and ecological subsystems, then construct a Hierarchical Optimization Model (HOM) that integrates system dynamics with the NSGA-II algorithm, using lexicographic ordering to balance multiple prioritized objectives.

The SCCM evaluates system coordination using ten key indicators across economic, social, and ecological dimensions, selected from comprehensive statistical data of Juneau. Through standardization of indicators and weighted coupling analysis, the model reveals a steady improvement in the tourism system's coordination, with the coupling coordination degree rising from 0.6211 to 0.6943 during 2022--2024, indicating a gradually strengthening interaction among subsystems.

Based on the SCCM evaluation, the HOM identifies eight key decision variables including environmental protection investment, infrastructure investment, tourism taxes, and visitor management strategies. The model employs system dynamics equations to capture the complex interactions between policy interventions and system indicators, optimizing three objectives in descending order of priority: coupling coordination degree, government revenue, and carbon footprint. Through NSGA-II algorithm optimization under practical constraints including budget limitations and minimum coordination requirements, we obtain an optimal policy combination that achieves a coordination degree of 0.8447 and annual revenue of $352.18 million. The solution suggests a balanced investment strategy, allocating 62.8% of the budget to infrastructure improvement, 19.3% to environmental protection, and the remainder to community development and market management, creating positive feedback loops that promote sustainable tourism development.

To validate the model's adaptability, we apply the framework to Nanjing, China, a metropolitan area with distinct tourism characteristics from Juneau. Comparative analysis reveals how geographical characteristics influence optimal strategies: Juneau's nature-based tourism requires focused environmental protection, while Nanjing's cultural attractions demand greater infrastructure capacity. This adaptability enables the model to promote balanced tourism development through optimized investment policies, enhancing accessibility for less-visited attractions.

Sensitivity analysis is conducted at three levels to validate model reliability. The evaluation model shows highest sensitivity to economic indicators, while the optimization model maintains convergence even under 70% weight perturbations. Furthermore, stability analysis reveals strong clustering of optimal investment strategies, demonstrating the robustness of our proposed approach.

Finally, based on these findings, we provide specific recommendations to Juneau's Tourism Council for implementing sustainable tourism strategies and optimizing long-term development outcomes.

\begin{keywords}
Sustainable Tourism; Coupling Coordination Model; Multi-objective Optimization; NSGA-II Algorithm; System Dynamics
\end{keywords}
\end{abstract}
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\section{Introduction}

\subsection{Problem Background}

Juneau, the capital of Alaska, has a population of 30,000 and is characterised by distinctive natural landscapes and significant tourism resources. The city's tourism sector has undergone substantial growth over the past decade, particularly in its cruise ship industry. As shown in Figure \ref{fig:cruise_volume}, cruise passenger volume has increased steadily from 961,000 in 2014 to 1.67 million in 2023, with only a brief interruption during the COVID-19 pandemic in 2020-2021. During peak season, up to seven cruise ships dock simultaneously, resulting in daily visitor numbers equivalent to two-thirds of the permanent population, generating annual revenues of $375 million.

\begin{figure}[htbp]
\centering
\includegraphics[width=12cm]{figures/近年游客数.png}
\caption{Juneau's Cruise Passenger Volume Growth (2014-2023)}
\label{fig:cruise_volume}
\end{figure}

However, this rapid expansion of tourism has also given rise to significant sustainability challenges, including the retreat of the Mendenhall Glacier since 2007 and increased pressure on local infrastructure, as well as social impacts such as housing shortages and traffic congestion affecting residents' daily lives. Despite the implementation of higher tourist fees and hotel taxes, the balancing act of economic development with environmental protection remains a critical challenge for sustainable tourism in Juneau.

\subsection{Restatement of the Problems}

For sustainable tourism in Juneau, Alaska. We summarise the problem into the following four subtasks:

\begin{itemize}
\item \textbf{Task 1:} Develop a sustainable tourism model for the city of Juneau. Integrate economic, social, and ecological factors.
\item \textbf{Task 2:} Based on the model developed, discuss the constraints and optimisation factors and develop a suitable optimisation plan for sustainable tourism in Juneau.
\item \textbf{Task 3:} Demonstrate how this model can be extended to another site and discuss the impact of location and attraction popularity on the optimisation decision.
\item \textbf{Task 4:} Write a memo to the Juneau Tourism Commission describing our findings and recommendations for optimisation.
\end{itemize}

\subsection{Our Work}

\begin{figure}[h]
\centering
\includegraphics[width=16cm]{figures/绘图1.png}
\caption{Framework of the Sustainable Tourism Development Model for Juneau}
\label{fig:framework}
\end{figure}

\section{Assumptions and Notations}

\subsection{Assumptions}
\begin{itemize}
\item The population of the City of Juneau is expected to remain constant at 31,000 after the year 2000.
\item In terms of infrastructure investment, the City of Juneau invests in each sector in roughly stable proportions. Thus, we can use the investment in public transportation to represent the investment in infrastructure.
\item Pollution in tourist cities comes from the transportation of large numbers of tourists, so the amount associated with air pollution can be used to represent overall pollution in the city of Juneau.
\item During the time period of the data, there have been no emergencies, other than the New Crown epidemic, that were significant enough to have a major, sustained impact on Juneau's tourism industry.
\item All data is accurate and reliable.
\end{itemize}

\subsection{Notations}
Due to the complexity of our model, we separately present the notations for decision variables and evaluation indicators in their respective sections (see Table \ref{tab:decision_vars} and Table \ref{tab:indicators}). Here, we focus on the key variables used in coupling coordination calculation:

\begin{table}[!htbp]
\centering
\caption{Key Variables in Coupling Coordination Calculation}
\begin{tabular}{cl}
\toprule
\textbf{Symbol} & \textbf{Description} \
\midrule
$U_{E}$ & Comprehensive score of economic subsystem \
$U_{S}$ & Comprehensive score of social subsystem \
$U_{Eco}$ & Comprehensive score of ecological subsystem \
$C$ & Coupling degree among three subsystems \
$T$ & Coordination level among three subsystems \
$D$ & Coupling coordination degree of the tourism system \
\bottomrule
\end{tabular}
\label{tab:notation}
\end{table}

\section{Model Preparation}

\subsection{Data Collection}

A comprehensive data set encompassing a multitude of economic, social and environmental indicators for the City of Juneau was obtained through a meticulous examination of statistical reports published by pertinent agencies over the years.

\begin{table}[htbp]
\centering
\caption{Data Source Websites}
\begin{tabular}{ll}
\toprule
Database names & Database website \
\midrule
ACS & \href{https://www.census.gov/programs-surveys/acs/data/data-via-ftp.html}{\texttt{https://www.census.gov/...}} \
EJScreen & \href{https://gaftp.epa.gov/EJSCREEN/}{\texttt{https://gaftp.epa.gov/...}} \
GHGRP & \href{https://www.epa.gov/ghgreporting}{\texttt{https://www.epa.gov/...}} \
AQS & \href{https://aqs.epa.gov/aqsweb/airdata/download_files.html}{\texttt{https://aqs.epa.gov/...}} \
LAUS & \href{https://www.bls.gov/lau/}{\texttt{https://www.bls.gov/...}} \
Juneau Budget Data & \href{https://juneau.org/finance/budget-2}{\texttt{https://juneau.org/...}} \
Travel Juneau Annual Report & \href{https://www.traveljuneau.com/about-travel-juneau/annual-report/}{\texttt{https://www.traveljuneau.com/...}} \
ATIA & \href{https://www.alaskatia.org/resources/research}{\texttt{https://www.alaskatia.org/...}} \
JEDC & \href{https://www.jedc.org/research-library-reports-studies-by-jedc/}{\texttt{https://www.jedc.org/...}} \
\bottomrule
\end{tabular}
\end{table}

\subsection{Data Preprocessing}

The raw data collected from various sources required careful preprocessing to ensure quality and usability. Several key preprocessing steps were taken:

\begin{itemize}
\item \textbf{COVID-19 Impact Handling}: Data from 2020 and 2021 were excluded from our analysis due to the significant disruption to tourism-related indicators caused by the COVID-19 pandemic. This exclusion ensures that our model is built on data that better represents normal operating conditions.

\item \textbf{Composite Indicator Construction}: Some decision variables and indicators were not directly available in the raw data. For instance, infrastructure investment was constructed by aggregating multiple related sub-categories of investment (e.g., street maintenance, facility upgrades) from annual statistical reports. While such aggregation may not capture the complete expenditure in each domain, it serves as a statistically significant proxy for the overall investment level.

\item \textbf{Abstract Variable Quantification}: Several variables and indicators in our model are conceptually abstract. For example, the tourism tax intensity was quantified based on historical tax collection data and tourist numbers. Similarly, the tourist distribution policy intensity was derived from various policy implementation records and their corresponding effects.
\end{itemize}

After preprocessing, we obtained a clean and consistent dataset covering recent years except for the pandemic period, which forms the foundation for our subsequent modeling work.

\subsection{Model Overview}

To address the sustainable tourism development challenges in Juneau, we propose a two-stage modeling approach, as illustrated in Figure \ref{fig:model_structure}. The framework consists of two major components:

\begin{itemize}
\item \textbf{Sustainability Coupling Coordination Model (SCCM)}: This evaluation component assesses the coordination level among economic, social, and ecological subsystems. Through standardization of indicators and subsystem integration, SCCM generates a coupling coordination degree that quantifies the overall system balance.

\item \textbf{Hierarchical Optimization Model (HOM)}: Building upon the SCCM evaluation results, this optimization component determines the optimal policy combinations. HOM employs system dynamics equations and utilizes the NSGA-II algorithm with lexicographic ordering to find solutions that balance multiple objectives with different priorities.
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=11cm]{figures/绘图2.png}
\caption{Framework of the Two-Stage Modeling Approach}
\label{fig:model_structure}
\end{figure}

The workflow proceeds from model preparation through evaluation and optimization to final strategy generation. The connection between SCCM and HOM is established through the coupling coordination degree, which serves both as an evaluation metric and a primary optimization objective. This integrated approach ensures that the proposed solutions maintain a high level of system coordination while meeting specific performance targets.

\section{Sustainability Coupling Coordination Model}

In order to formulate an optimal sustainable tourism development plan for Juneau, the Sustainability Coupling Coordination Model (SCCM) was constructed in order to evaluate the coordination level among economic, social, and ecological development indicators. Based on Juneau's historical reports and comprehensive statistical data, ten key indicators were identified with which to assess the city's integrated development across these three dimensions. The specific indicators, including their symbolic representations, data sources, and measurement units, are detailed in Table~\ref{tab:indicators} below.   

\begin{table}[htbp]
\centering
\caption{Key Indicators for Assessing Sustainable Tourism Development in Juneau}
\label{tab:indicators}
\begin{tabular}{lllll}
\toprule
\textbf{Subsystem} & \textbf{Indicator} & \textbf{Symbol} & \textbf{Unit} & \textbf{Attribute} \
\midrule
Economic & Tourism Revenue & $E_1$ & Million USD & Positive \
& Tourism Fixed Assets & $E_2$ & Million USD & Positive \
\midrule
Social & Resident Attitude & $S_1$ & Scale 0-10 & Positive \
& Congestion Index & $S_2$ & Index Value & Negative \
& Tourism Accessibility & $S_3$ & Index Value & Positive \
& Resident Disposable Income & $S_4$ & USD/Person & Positive \
& Tourism Employment & $S_5$ & Thousand People & Positive \
\midrule
Ecological & Carbon Footprint & $Eco_1$ & Tonnes of CO$_2$ Equivalent & Negative \
& Air Pollution Index & $Eco_2$ & Index Value & Negative \
& Glacier Congestion Index & $Eco_3$ & Index Value & Negative \
\bottomrule
\end{tabular}
\end{table}

\subsection{Standardization of Indicators}

In view of the marked disparities in dimensions and value ranges of the indicators, it is imperative to standardise the raw data with a view to eliminating dimensional impacts. This study employs the range standardisation method to convert all indicator values into a unified interval of $[0,1]$. Different standardisation formulas are applied to positive and negative indicators:

For positive indicators ($E_1$, $E_2$, $S_1$, $S_3$, $S_4$, $S_5$), the following standardisation formula is applied:

For negative indicators ($S_2$, $\text{Eco}_1$, $\text{Eco}_2$, $\text{Eco}_3$), the following standardisation formula is employed:

In this formula, $X'_{ij}$ represents the standardized indicator value, $X_{ij}$ denotes the original indicator value, and $X_{\text{max}}$ and $X_{\text{min}}$ represent the maximum and minimum values of the indicator during the evaluation period, respectively. In order to mitigate the influence of extreme values, this study establishes upper and lower bounds for each indicator based on historical data for standardisation calculations.

\subsection{Calculation of Coupling Coordination Degree}

Utilising the standardised indicators, a composite index is derived for the three subsystems:
\begin{equation}
\begin{cases}
U_E = 0.6E_1 + 0.4E_2 \
U_S = 0.25S_1 + 0.35S_2 + 0.15S_3 + 0.20S_4 + 0.10S_5 \
U_{\text{Eco}} = 0.26\text{Eco}_1 + 0.24\text{Eco}_2 + 0.50\text{Eco}_3
\end{cases}
\label{eq:composite_index}
\end{equation}

The glacier crowding index ($\text{Eco}_3$) was assigned the highest weight of 0.50, reflecting the critical position of glacier resources in the Juneau tourism ecosystem. Utilising the aforementioned formula (see Equation \eqref{eq:composite_index}), the composite economic, social and ecological indicators for the city of Juneau were derived over the preceding triennium, as illustrated in Figure \ref{fig:aa}.

\begin{figure}[h]
\small
\centering
\includegraphics[width=13cm]{figures/3-subsystom.png}
\caption{Composition of Subsystem Development Indices (2022-2024)} \label{fig:aa}
\end{figure}

The coupling coordination of the three subsystems can be calculated based on the combined indices through a three-step process.

First, the coupling degree $C$, which indicates the interaction between subsystems, is calculated as:
\begin{equation}
C = \frac{3 \times (U_E \times U_S \times U_{\text{Eco}})^{1/3}}{U_E + U_S + U_{\text{Eco}}}
\end{equation}

Then, the coordination degree $T$ is determined by:
\begin{equation}
T = 0.28U_E + 0.28U_S + 0.44U_{\text{Eco}}
\end{equation}
where the ecological subsystem is assigned a higher weight (0.44) to reflect its crucial role in sustainable tourism development.

Finally, the coupling coordination degree $D$ is derived as:
\begin{equation}
D = \sqrt{C \times T}
\end{equation}

The value of $D$ ranges from 0 to 1, with higher values indicating better system coordination. Based on this metric, the coordinated development status can be classified into ten levels from extremely dysfunctional to highly coordinated.

The coupling coordination degree calculations for the past three years are presented in Table \ref{tab:ccd_results}.

\begin{table}[htbp]
\centering
\caption{Coupling Coordination Degree Results (2022-2024)}
\label{tab:ccd_results}
\begin{tabular}{cccc}
\toprule
Year & CCD Value & Level & Category \
\midrule
2022 & 0.6211 & 7 & Primary Coordinated \
2023 & 0.6530 & 7 & Primary Coordinated \
2024 & 0.6943 & 7 & Primary Coordinated \
\bottomrule
\end{tabular}
\end{table}

The calculation results indicate that the coupling degree of the economic-social-ecological system of Juneau tourism maintains at the seventh level of 'primary coordination' over the past three years, with a steady upward trend from 0.6211 to 0.6943. This suggests that while the coordination among economic growth, social well-being, and ecological protection in Juneau's tourism development remains at a basic level, the positive interaction among the subsystems has been gradually strengthening.

\section{Hierarchical Optimization Model}

In this section, we propose a hierarchical multi-objective optimisation model to determine the optimal policy combination in order to address the challenges of overtourism while maintaining tourism benefits. This builds upon the Sustainability Coupling Coordination Model (SCCM), which evaluates the coordination level among economic, social, and ecological subsystems.

The hierarchical structure of the model reflects the multi-level relationships: at the foundation level are eight decision variables representing various policy instruments including investments, taxes, and visitor management strategies.These policy instruments then influence ten key indicators across economic, social, and ecological dimensions as identified in the SCCM.Finally, these indicators are aggregated into three subsystem indices that collectively determine the system's overall performance. The model's hierarchical framework is designed to optimise the coupling coordination degree (D), government revenue, and carbon footprint, with the aforementioned objectives arranged in descending order of priority. This arrangement reflects Juneau's commitment to achieving balanced development while addressing overtourism concerns.

\subsection{Decision Variables}

Based on the historical data and policy reports from Juneau's tourism development, we identified eight key decision variables that can be effectively controlled by the city management to influence tourism outcomes. These variables, as shown in Table \ref{tab:decision_vars}, include four types of investment allocations, tourist taxation, visitor distribution policy, and two fundamental tourism volume indicators.

\begin{table}[htbp]
\centering
\caption{Decision Variables for Tourism Development in Juneau}
\label{tab:decision_vars}
\begin{tabular}{lll}
\toprule
\textbf{Indicator} & \textbf{Symbol} & \textbf{Unit} \
\midrule
Environmental Protection Investment & $x_{env}$ & Million USD \
Infrastructure Investment & $x_{infra}$ & Million USD \
Tourism Market Promotion Investment & $x_{mkt}$ & Million USD \
Community Project Investment & $x_{soc}$ & Million USD \
Tourist Per Capita Tourism Tax & $\alpha_{tax}$ & USD \
Tourist Distribution Policy Intensity & $x_{div}$ & Index Value \
Number of Tourists & $N_{T}$ & Thousand People/Year \
Tourist Per Capita Consumption & $x_{con}$ & USD/Person \
\bottomrule
\end{tabular}
\end{table}

Through regression analysis of historical data, we established the complex relationships between these decision variables and the ten assessment indicators. Each indicator is determined by multiple decision variables through non-linear interactions. For instance, the carbon footprint ($Eco_1$) is influenced by environmental protection investment ($x_{env}$), infrastructure investment ($x_{infra}$), and tourist volume ($N_{T}$), while the tourism accessibility ($S_3$) is jointly determined by infrastructure investment ($x_{infra}$), distribution policy intensity ($x_{div}$), and tourist volume ($N_{T}$). These intricate relationships form the foundation of our optimization model, enabling us to evaluate how policy adjustments would impact various aspects of Juneau's tourism system. The complete hierarchical structure of our model is illustrated in Figure \ref{fig:sankey}.

\begin{figure}[h]
\small
\centering
\includegraphics[width=16cm]{figures/sangji.png}
\caption{Hierarchical Structure of the Sustainable Tourism Optimization Model} \label{fig:sankey}
\end{figure}

\subsection{System Dynamics Equations}

The relationships between decision variables and indicators were established through regression analysis of historical data. For the economic subsystem, the government revenue ($E_1$) and tourism fixed assets ($E_2$) are formulated as:

\begin{equation}
\text{E}{1} = \frac{1000N{T}(x_{con} + \alpha_{tax} - 218.3796)}{10^6} + 251.9655
\end{equation}

\begin{equation}
\text{E}{2} = 2.10818 - 0.116903\frac{x{infra}}{10.0054} - 0.331696\frac{x_{mkt}}{1.00168} + 2.10063\ln(1 + \frac{\text{S}_{5}}{0.393086})
\end{equation}

The government revenue equation captures how tourist volume ($N_{T}$), per capita consumption ($x_{con}$), and tourism tax ($\alpha_{tax}$) directly contribute to the city's income. The tourism fixed assets are influenced by infrastructure and market promotion investments, while also showing a logarithmic relationship with tourism employment, indicating diminishing returns on investment.

For the social subsystem, the resident attitude ($S_1$) and congestion index ($S_2$) are particularly critical:

\begin{equation}
\text{S}{1} = 6.05431 + 0.168539x{div} + 0.8668\frac{x_{env}}{10.1057} - 0.00038535T
\end{equation}

\begin{equation}
\text{S}{2} = 3.74014 + 0.000416267N{T} - 0.0586679x_{infra} - 0.160964x_{div}
\end{equation}

These equations reveal that resident attitudes are positively influenced by environmental protection and visitor distribution policies, but negatively impacted by increasing tourist numbers. Meanwhile, the congestion index can be effectively managed through infrastructure investment and tourist distribution strategies.

For the ecological subsystem, the carbon footprint ($\text{Eco}_1$) is of particular concern:

\begin{equation}
\text{Eco}{1} = 1.92453 \times 10^6 + 391.147(1000N{T})^{-30.2898} - 78569.9x_{env} - 805146\ln(1 + x_{infra})
\end{equation}

This equation demonstrates how environmental protection and infrastructure investments can help mitigate the carbon footprint, with infrastructure improvements showing diminishing returns as indicated by the logarithmic term.

The remaining system indicators are formulated as follows:

\begin{equation}
\left{
\begin{aligned}
\text{S}{3} &= 1.5081(\frac{N{T} + 100.004}{0.000231623})^{0.429576}(1 - e^{-0.45747\frac{x_{infra}}{9.99294}})(1 + 0.0590587x_{div}) \
\text{S}{4} &= 49942.2 + 0.00569082(N{T} \cdot x_{con}) + 237.171x_{infra} - 457.361x_{soc} \
\text{S}{5} &= 58.108 + 0.000421N{T} - 19.3388\ln(1 + \frac{x_{con}}{104.465}) + 33.4503(1 + \frac{\alpha_{tax}}{-3.93095})^{-1} \
\text{Eco}{2} &= 20.7266 + 2.31625 \times 10^{-6}(1000N{T}) - 4.16471x_{env} - 1.44831x_{infra} - 0.0736647x_{div} \
\text{Eco}{3} &= 0.252585 + 0.00266493\ln(1 + N{T}) - 1.24836x_{div}
\end{aligned}
\right.
\end{equation}

\subsection{Objective Functions}

Based on the established system dynamics and Juneau's development priorities, we formulate a hierarchical multi-objective optimization problem with three objectives:

\begin{equation}
\left{
\begin{aligned}
\min f_1 &= -D \
\min f_2 &= -\text{E}{1} \
\min f_3 &= \text{E}{CO_{1}}
\end{aligned}
\right.
\end{equation}

where $D$ is the coupling coordination degree calculated using the SCCM framework. The negative signs before $D$ and $E_{1}$ convert their maximization into minimization problems. These objectives are arranged in descending order of priority, reflecting Juneau's primary focus on achieving system coordination, followed by economic benefits, while maintaining environmental responsibility through carbon footprint control.

\subsection{Constraints}

The optimization model is subject to several constraints to ensure the feasibility and practicality of solutions. First, all decision variables must fall within their respective reasonable ranges:

\begin{equation}
\left{
\begin{aligned}
10.0 \leq x_{env} \leq 25.0 & \quad \text{(Million USD)} \
40.0 \leq x_{infra} \leq 60.0 & \quad \text{(Million USD)} \
0.0 \leq x_{mkt} \leq 10.0 & \quad \text{(Million USD)} \
15.0 \leq x_{soc} \leq 30.0 & \quad \text{(Million USD)} \
0.0 \leq \alpha_{tax} \leq 10.0 & \quad \text{(USD)} \
0.2 \leq x_{div} \leq 0.4 & \quad \text{(Index Value)} \
500 \leq N_{T} \leq 2200 & \quad \text{(Thousand People/Year)} \
200 \leq x_{con} \leq 260 & \quad \text{(USD/Person)}
\end{aligned}
\right.
\end{equation}

Second, a budget constraint is imposed to ensure that the total investment does not exceed the government revenue:

\begin{equation}
x_{env} + x_{infra} + x_{mkt} + x_{soc} \leq \text{E}_{1}
\end{equation}

Third, to maintain a satisfactory level of system coordination, we require:

\begin{equation}
D \geq 0.8
\end{equation}

\subsection{Solution Methodology}

To solve this hierarchical multi-objective optimization problem, we employ the NSGA-II (Non-dominated Sorting Genetic Algorithm II) algorithm with a customized lexicographic dominator. The lexicographic dominance relationship is defined as follows: for two solutions $A$ and $B$ with objective vectors $F_A=[f_1^A,f_2^A,f_3^A]$ and $F_B=[f_1^B,f_2^B,f_3^B]$, solution $A$ dominates solution $B$ if and only if:

\begin{equation}
\left{
\begin{aligned}
& f_1^A < f_1^B - \epsilon_1, \text{ or} \
& |f_1^A - f_1^B| \leq \epsilon_1 \text{ and } f_2^A < f_2^B - \epsilon_2, \text{ or} \
& |f_1^A - f_1^B| \leq \epsilon_1 \text{ and } |f_2^A - f_2^B| \leq \epsilon_2 \text{ and } f_3^A < f_3^B - \epsilon_3
\end{aligned}
\right.
\end{equation}

where $\epsilon_1 = 0.5$, $\epsilon_2 = 50$, and $\epsilon_3 = 1000$ are tolerance parameters that define the indifference thresholds for each objective. This dominance relationship ensures that solutions are primarily compared based on the coupling coordination degree, followed by government revenue, and finally carbon footprint.

\subsection{Algorithm Implementation}

The NSGA-II algorithm was implemented with carefully selected parameters to ensure efficient exploration of the solution space while maintaining solution diversity. The population size was set to 300 individuals with 100 offspring per generation, and the algorithm was run for 400 generations to ensure convergence. The implementation details are as follows:

\begin{itemize}
\item \textbf{Population Initialization}: The initial population was randomly generated within the feasible region defined by the variable bounds. To improve the quality of initial solutions, we employed a constraint handling method that ensures all initial individuals satisfy the budget constraint.

text
\item \textbf{Genetic Operators}: The Simulated Binary Crossover (SBX) operator was used for crossover with a probability of 0.9, and the Polynomial Mutation operator was applied with a probability of $1/n$ where $n$ is the number of decision variables. These operators were chosen for their ability to handle real-valued decision variables effectively.

\item \textbf{Constraint Handling}: The constraints were handled using a penalty function approach. Solutions violating the coupling coordination degree constraint ($D \geq 0.8$) or the carbon footprint ceiling were penalized proportionally to their degree of violation.

\end{itemize}

The evolution of the three objectives over generations is shown in Figure \ref{fig:convergence}. The coupling coordination degree ($D$) shows rapid improvement in the early stages and stabilizes around 0.84 after 200 generations. The government revenue exhibits a similar pattern, reaching a plateau at approximately 350 million USD. The carbon footprint initially fluctuates but gradually decreases and stabilizes around 54,000 tonnes CO$_2$ equivalent, demonstrating the algorithm's ability to balance multiple competing objectives.

\begin{figure}[htbp]
\centering
\includegraphics[width=18cm]{figures/evolution.png}
\caption{Mean Objective Values Evolution During the Optimization Process}
\label{fig:convergence}
\end{figure}

The final population's distribution in the objective space is visualized in Figure \ref{fig:scatter}, where each point represents a non-dominated solution. The scatter plot reveals clear trade-offs between the three objectives, with solutions clustering in distinct regions. The color gradient indicates the carbon footprint level, showing how solutions with higher coordination degrees and government revenues tend to have slightly higher carbon footprints, though all remain within the specified constraints.

\begin{figure}[htbp]
\centering
\includegraphics[width=16cm]{figures/sandian.png}
\caption{3D Scatter Plot of Non-dominated Solutions in the Final Population}
\label{fig:scatter}
\end{figure}

\subsection{Optimization Results and Investment Strategy}
Through the hierarchical multi-objective optimization process, we obtained a set of non-dominated solutions representing different trade-offs among the objectives. Based on the lexicographic ordering principle and our problem constraints, we identified the optimal solution with the following performance metrics:
\begin{itemize}
\item Coupling Coordination Degree ($D$): 0.8447
\item Government Revenue: 352.18 million USD
\item Carbon Footprint: 53,728.75 tonnes CO$_2$ equivalent
\end{itemize}

The corresponding optimal policy combination is presented in Table \ref{tab:optimal_solution}.

\begin{table}[htbp]
\centering
\caption{Optimal Policy Combination for Juneau's Sustainable Tourism Development}
\label{tab:optimal_solution}
\begin{tabular}{lll}
\toprule
\textbf{Decision Variable} & \textbf{Optimal Value} & \textbf{Unit} \
\midrule
Environmental Protection Investment & 18.21 & Million USD \
Infrastructure Investment & 59.37 & Million USD \
Tourism Market Promotion Investment & 1.52 & Million USD \
Community Project Investment & 15.23 & Million USD \
Tourist Per Capita Tourism Tax & 3.93 & USD \
Tourist Distribution Policy Intensity & 0.20 & Index Value \
Number of Tourists & 2,200 & Thousand People/Year \
Tourist Per Capita Consumption & 260 & USD/Person \
\bottomrule
\end{tabular}
\end{table}

Based on the optimization results, we propose an integrated investment strategy that creates reinforcing feedback mechanisms in the tourism system:

\begin{itemize}
\item \textbf{Infrastructure-Focused Investment}: The solution allocates the largest portion of the budget (59.37 million USD, 62.8%) to infrastructure improvement. This investment directly enhances tourism accessibility ($S_{3}$) and reduces congestion ($S_2$), creating a positive feedback loop that enables higher visitor capacity while maintaining service quality.

\item \textbf{Strategic Environmental Protection}: A significant investment of 18.21 million USD (19.3%) in environmental protection demonstrates the city's commitment to ecological preservation. This investment reduces carbon footprint and improves resident attitudes ($S_{1}$), ensuring the sustainability of natural attractions.

\item \textbf{Community Development}: The community project investment of 15.23 million USD (16.1%), combined with a modest distribution policy intensity (0.20), prioritizes local community benefits. This enhances resident disposable income ($S_{4}$) and strengthens social acceptance of tourism.

\item \textbf{Market Management}: The moderate tourism tax (3.93 USD per capita) and conservative market promotion investment (1.52 million USD, 1.8%) maintain tourism attractiveness while generating necessary revenue for sustainable development.
\end{itemize}

This investment strategy achieves the highest possible coupling coordination degree while satisfying all constraints. The high coordination degree of 0.8447 indicates a well-balanced development state among economic, social, and ecological subsystems, demonstrating how appropriate revenue allocation can promote sustainable tourism development.

\section{Model Adaptation to Nanjing}

To demonstrate the adaptability of our modeling approach, we apply the framework to Nanjing, China, a historic city facing overtourism challenges. As a cultural tourism destination with a population of over 8 million, Nanjing presents different characteristics from Juneau, allowing us to test the model's versatility.

\subsection{Model Adjustment}

The adaptation of our model requires several modifications to accommodate Nanjing's unique context:

\begin{itemize}
\item \textbf{Indicator Selection}: The glacier congestion index ($\text{Eco}_3$) was removed as it is specific to Juneau. The remaining nine indicators were retained as they are universal measures of tourism sustainability.

\item \textbf{System Integration}: The weights in SCCM were adjusted to reflect the changed composition of the ecological subsystem:
\begin{equation}
\begin{aligned}
U_E &= 0.6E_1 + 0.4E_2 \
U_S &= 0.25S_1 + 0.35S_2 + 0.15S_3 + 0.20S_4 + 0.10S_5 \
U_{Eco} &= 0.5\text{Eco}_1 + 0.5\text{Eco}_2
\end{aligned}
\end{equation}
\end{itemize}

The decision variables remain unchanged as they represent universal policy instruments, though their operational ranges were adjusted according to Nanjing's scale:

\begin{equation}
\left{
\begin{aligned}
20.0 \leq x_{env} \leq 70.0 & \quad \text{(Million USD)} \
150.0 \leq x_{infra} \leq 250.0 & \quad \text{(Million USD)} \
20.0 \leq x_{mkt} \leq 50.0 & \quad \text{(Million USD)} \
200.0 \leq x_{soc} \leq 250.0 & \quad \text{(Million USD)} \
0.0 \leq \alpha_{tax} \leq 5.0 & \quad \text{(USD)} \
0.2 \leq x_{div} \leq 0.5 & \quad \text{(Index Value)} \
90000 \leq N_{T} \leq 120000 & \quad \text{(Thousand People/Year)} \
1500 \leq x_{con} \leq 2300 & \quad \text{(USD/Person)}
\end{aligned}
\right.
\end{equation}

Based on regression analysis of Nanjing's historical data, the system dynamics equations were recalibrated. For example, the government revenue equation was updated to:

\begin{equation}
\text{E}{1} = \frac{1000N{T}(x_{con} + \alpha_{tax} \times 1327.1274)}{10^8} - 4401.0535
\end{equation}

The Hierarchical Optimization Model (HOM) retains its structure with the same three objectives but different parameters, demonstrating the framework's adaptability to various contexts while maintaining its core methodology.

\subsection{Optimization Results for Nanjing}

The optimization for Nanjing achieved a coupling coordination degree of 0.8848, demonstrating the model's effectiveness in a different context. The optimal policy combination is characterized by:

\begin{itemize}
\item \textbf{Maximum Environmental Protection}: Environmental investment reaches its upper limit (70M USD), reflecting the critical importance of environmental quality in urban tourism.

text
\item \textbf{Substantial Infrastructure Support}: A high infrastructure investment (197.7M USD) focuses on urban tourism facilities and transportation capacity.

\item \textbf{Active Market Promotion}: Nearly maximum market promotion investment (49.9M USD) suggests the importance of destination marketing in competitive urban tourism.

\item \textbf{Basic Social Programs}: Minimum social project investment (200M USD) indicates a focus on essential community support.

\item \textbf{Moderate Tourism Management}: A tourism tax of 4.45 USD and conservative distribution policy intensity (0.20) suggest a market-driven approach to tourist flow management.

\end{itemize}

This solution achieves a government revenue of 2,998.48M USD while maintaining carbon emissions at 3,098,827.61 tonnes CO$_2$ equivalent. The results demonstrate different priorities from Juneau, with a stronger emphasis on environmental protection and market promotion in the urban context. As shown in Figure \ref{fig:nanjing_scatter}, the final population of solutions exhibits clear trade-offs between the three objectives, with our selected solution representing an optimal balance according to the lexicographic ordering principle.

\begin{figure}[htbp]
\centering
\includegraphics[width=16cm]{figures/nanjing.png}
\caption{3D Scatter Plot of Non-dominated Solutions for Nanjing's Optimization}
\label{fig:nanjing_scatter}
\end{figure}

\subsection{Impact of Location Characteristics}

The comparative study between Juneau and Nanjing reveals how geographical characteristics significantly influence the relative importance of different measures in sustainable tourism management:

\begin{itemize}
\item \textbf{Tourism Resource Type}: In Juneau, where tourism depends heavily on natural attractions like glaciers, environmental protection investment becomes the primary concern, directly impacting both tourist satisfaction and ecological sustainability. Conversely, Nanjing's cultural-historical tourism necessitates greater emphasis on infrastructure capacity and preservation.

\item \textbf{Tourist Flow Pattern}: Juneau's cruise-dominated tourism creates significant seasonal fluctuations, making the distribution policy ($x_{div}$) crucial for peak-season management. In contrast, Nanjing's year-round tourism pattern shifts the focus to sustained infrastructure optimization and continuous flow management.

\item \textbf{Transportation Structure}: The singular dependence on cruise ships in Juneau results in concentrated tourist arrivals, requiring precise temporal control. Nanjing's diverse transportation network enables more flexible spatial distribution, as reflected in its higher optimal infrastructure investment ($x_{infra}$).
\end{itemize}

\subsection{Promoting Tourism Balance}

Our model incorporates the tourism accessibility index ($S_3$) and infrastructure investment ($x_{infra}$) to promote balanced tourism development:

\begin{itemize}
\item \textbf{Accessibility Enhancement}: The tourism accessibility index ($S_3$) in our model measures the ease of reaching different attractions. Through optimizing infrastructure investment and distribution policies, the model promotes higher accessibility for all attractions, including less-visited ones. This is reflected in Nanjing's optimization result where $S_3$ reaches [value], indicating improved access to diverse tourist locations.

\item \textbf{Infrastructure Support}: The optimal infrastructure investment of 197.7M USD can enhance the basic facilities and transportation networks connecting different attractions. The system dynamics equation for accessibility shows that improved infrastructure directly contributes to better tourist access across all sites:
\begin{equation}
S_{3} = 1.5081(\frac{N_{T} + 100.004}{0.000231623})^{0.429576}(1 - e^{-0.45747\frac{x_{infra}}{9.99294}})(1 + 0.0590587x_{div})
\end{equation}
\end{itemize}

These mechanisms demonstrate how our model naturally promotes tourism balance by incorporating accessibility measures and infrastructure support in its optimization framework.

\section{Sensitivity Analysis}

To validate our model's reliability and stability, we conducted three levels of sensitivity analysis targeting both the evaluation model (SCCM) and optimization model (HOM).

\subsection{Indicator Sensitivity in SCCM}
For the evaluation model, we performed a standardized sensitivity analysis on all ten indicators:

\begin{itemize}
\item \textbf{Analysis Method:} Each indicator was varied by ±15% from its baseline value while keeping others constant. The changes in coupling coordination degree (D) were recorded for each variation.

text
\item \textbf{Standardization Process:} All indicators were first normalized to [0,1] scale to ensure comparability. For positive indicators (E1, E2, S1, S3, S4, S5), we used the formula $(x-x_{min})/(x_{max}-x_{min})$; for negative indicators (S2, Eco1, Eco2), we used $(x_{max}-x)/(x_{max}-x_{min})$.

\item \textbf{Results Interpretation:} The sensitivity was quantified by the ratio of D's percentage change to indicator's percentage change. As shown in Figure \ref{fig:indicator_sensitivity}, steeper curves indicate higher sensitivity.

\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=14cm]{figures/sensitive 1.png}
\caption{Sensitivity of Coupling Coordination Degree to Individual Indicator Variations (±15%)}
\label{fig:indicator_sensitivity}
\end{figure}

\subsection{Weight Perturbation Analysis in HOM}
We then tested the optimization model's robustness through systematic weight perturbations:

\begin{itemize}
\item \textbf{Perturbation Method:} Random perturbations were applied to weights in each subsystem while maintaining their sum as 1. For example, at 20% perturbation level, each weight was randomly varied within ±20% of its original value, then renormalized.

text
\item \textbf{Evolution Analysis:} For each perturbation level (0\%, 10\%, ..., 70\%), we ran the NSGA-II algorithm for 400 generations with population size 200. Figure \ref{fig:weight_evolution} tracks the mean coordination degree across generations.

\item \textbf{Convergence Criteria:} The algorithm was considered converged when the mean D value change remained below 0.001 for 50 consecutive generations.

\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=14cm]{figures/sensitive 2.png}
\caption{Evolutionary Trajectories of Mean Coordination Degree under Different Weight Perturbation Levels}
\label{fig:weight_evolution}
\end{figure}

\subsection{Optimal Solution Stability Analysis}
Finally, we examined the stability of optimal solutions under weight perturbations:

\begin{itemize}
\item \textbf{Variable Selection:} Infrastructure investment (x_infra) and environmental protection investment (x_env) were chosen as key variables due to their high sensitivity in previous analyses.

text
\item \textbf{Solution Mapping:} All feasible solutions from different perturbation scenarios were plotted in the x\_env-x\_infra space. Colors indicate perturbation levels (0\%-70\%).

\item \textbf{Clustering Analysis:} As shown in Figure \ref{fig:solution_space}, optimal solutions cluster within x\_env [16.5-18.5M USD] and x\_infra [52-60M USD], demonstrating strong solution stability.

\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=10cm]{figures/sensitive3.png}
\caption{Distribution of Optimal Investment Solutions under Weight Perturbations with Local Magnification}
\label{fig:solution_space}
\end{figure}

The results reveal several key findings:
\begin{itemize}
\item The evaluation model (SCCM) shows highest sensitivity to economic indicators, followed by ecological indicators
\item The optimization model (HOM) maintains convergence even under 70% weight perturbations, demonstrating robust performance
\item The positive correlation between x_env and x_infra validates our model's ability to promote balanced development
\end{itemize}

% \subsection{How to cite?}
% bibliography cite use \cite{1,2,3}

% AI cite use \AIcite{AI1,AI2,AI3}

\begin{thebibliography}{99}
\bibitem{1} D.~E. KNUTH The \TeX{}book the American
Mathematical Society and Addison-Wesley
Publishing Company , 1984-1986.
\bibitem{2}Lamport, Leslie, \LaTeX{}: `` A Document Preparation System '',
Addison-Wesley Publishing Company, 1986.
\bibitem{3}\url{https://www.latexstudio.net/}
\end{thebibliography}

\begin{appendices}

\section{First appendix}

In addition, your report must include a letter to the Chief Financial Officer (CFO) of the Goodgrant Foundation, Mr. Alpha Chiang, that describes the optimal investment strategy, your modeling approach and major results, and a brief discussion of your proposed concept of a return-on-investment (ROI). This letter should be no more than two pages in length.

\begin{letter}{Dear, Mr. Alpha Chiang}

\lipsum[1-2]

\vspace{\parskip}

Sincerely yours,

Your friends

\end{letter}
Here are simulation programmes we used in our model as follow.\

\textbf{\textcolor[rgb]{0.98,0.00,0.00}{Input matlab source:}}
\lstinputlisting[language=Matlab]{./code/mcmthesis-matlab1.m}

\section{Second appendix}

some more text \textcolor[rgb]{0.98,0.00,0.00}{\textbf{Input C++ source:}}
\lstinputlisting[language=C++]{./code/mcmthesis-sudoku.cpp}

\end{appendices}

\AImatter

\begin{ReportAiUse}{9}
\bibitem{AI1}
ChatGPT\
Query1: Besides the COVID-19 pandemic, has the city of Juneau in Alaska experienced any particularly major events that would severely impact its tourism industry?''\\ Output: According to public sources, Juneau has not seen a single event comparable in severity to COVID-19 over the past two or three decades. While factors such as global economic recessions (like the 2008 financial crisis), fluctuations in the cruise industry, temporary transportation disruptions, localized natural events, and broader incidents (e.g., the 9/11 attacks) have occasionally affected tourism, none has caused a large-scale or prolonged impact on Juneau's visitor economy akin to the pandemic.''
\end{ReportAiUse}

\end{document}
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\documentclass{mcmthesis}
%\documentclass[CTeX = true]{mcmthesis} % 当使用 CTeX 套装时请注释上一行使用该行的设置
\mcmsetup{tstyle=\color{red}\bfseries,%修改题号，队号的颜色和加粗显示，黑色可以修改为 black
tcn = 2503941, problem = B, %修改队号，参赛题号
sheet = true, titleinsheet = true, keywordsinsheet = true,
titlepage = false, abstract = true}

%四款字体可以选择
%\usepackage{times}
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\usepackage{txfonts}

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\begin{document}
\begin{abstract}
\par Juneau, the capital of Alaska with a population of 30,000, has experienced substantial tourism growth in recent years, bringing significant economic benefits while introducing critical sustainability challenges. To address these issues, this paper presents a two-stage modeling approach. We first develop a Sustainability Coupling Coordination Model (SCCM) to evaluate the coordination among economic, social, and ecological subsystems, then construct a Hierarchical Optimization Model (HOM) that integrates system dynamics with the NSGA-II algorithm, using lexicographic ordering to balance multiple prioritized objectives.

The SCCM evaluates system coordination using ten key indicators across economic, social, and ecological dimensions, selected from comprehensive statistical data of Juneau. Through standardization of indicators and weighted coupling analysis, the model reveals a steady improvement in the tourism system's coordination, with the coupling coordination degree rising from 0.6211 to 0.6943 during 2022--2024, indicating a gradually strengthening interaction among subsystems.

Based on the SCCM evaluation, the HOM identifies eight key decision variables including environmental protection investment, infrastructure investment, tourism taxes, and visitor management strategies. The model employs system dynamics equations to capture the complex interactions between policy interventions and system indicators, optimizing three objectives in descending order of priority: coupling coordination degree, government revenue, and carbon footprint. Through NSGA-II algorithm optimization under practical constraints including budget limitations and minimum coordination requirements, we obtain an optimal policy combination that achieves a coordination degree of 0.8447 and annual revenue of $352.18 million. The solution suggests a balanced investment strategy, allocating 62.8% of the budget to infrastructure improvement, 19.3% to environmental protection, and the remainder to community development and market management, creating positive feedback loops that promote sustainable tourism development.

To validate the model's adaptability, we apply the framework to Nanjing, China, a metropolitan area with distinct tourism characteristics from Juneau. Comparative analysis reveals how geographical characteristics influence optimal strategies: Juneau's nature-based tourism requires focused environmental protection, while Nanjing's cultural attractions demand greater infrastructure capacity. This adaptability enables the model to promote balanced tourism development through optimized investment policies, enhancing accessibility for less-visited attractions.

Sensitivity analysis is conducted at three levels to validate model reliability. The evaluation model shows highest sensitivity to economic indicators, while the optimization model maintains convergence even under 70% weight perturbations. Furthermore, stability analysis reveals strong clustering of optimal investment strategies, demonstrating the robustness of our proposed approach.

Finally, based on these findings, we provide specific recommendations to Juneau's Tourism Council for implementing sustainable tourism strategies and optimizing long-term development outcomes.

\begin{keywords}
Sustainable Tourism; Coupling Coordination Model; Multi-objective Optimization; NSGA-II Algorithm; System Dynamics
\end{keywords}
\end{abstract}
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\section{Introduction}

\subsection{Problem Background}

Juneau, the capital of Alaska, has a population of 30,000 and is characterised by distinctive natural landscapes and significant tourism resources. The city's tourism sector has undergone substantial growth over the past decade, particularly in its cruise ship industry. As shown in Figure \ref{fig:cruise_volume}, cruise passenger volume has increased steadily from 961,000 in 2014 to 1.67 million in 2023, with only a brief interruption during the COVID-19 pandemic in 2020-2021. During peak season, up to seven cruise ships dock simultaneously, resulting in daily visitor numbers equivalent to two-thirds of the permanent population, generating annual revenues of $375 million.

\begin{figure}[htbp]
\centering
\includegraphics[width=12cm]{figures/近年游客数.png}
\caption{Juneau's Cruise Passenger Volume Growth (2014-2023)}
\label{fig:cruise_volume}
\end{figure}

However, this rapid expansion of tourism has also given rise to significant sustainability challenges, including the retreat of the Mendenhall Glacier since 2007 and increased pressure on local infrastructure, as well as social impacts such as housing shortages and traffic congestion affecting residents' daily lives. Despite the implementation of higher tourist fees and hotel taxes, the balancing act of economic development with environmental protection remains a critical challenge for sustainable tourism in Juneau.

\subsection{Restatement of the Problems}

For sustainable tourism in Juneau, Alaska. We summarise the problem into the following four subtasks:

\begin{itemize}
\item \textbf{Task 1:} Develop a sustainable tourism model for the city of Juneau. Integrate economic, social, and ecological factors.
\item \textbf{Task 2:} Based on the model developed, discuss the constraints and optimisation factors and develop a suitable optimisation plan for sustainable tourism in Juneau.
\item \textbf{Task 3:} Demonstrate how this model can be extended to another site and discuss the impact of location and attraction popularity on the optimisation decision.
\item \textbf{Task 4:} Write a memo to the Juneau Tourism Commission describing our findings and recommendations for optimisation.
\end{itemize}

\subsection{Our Work}

\begin{figure}[h]
\centering
\includegraphics[width=16cm]{figures/绘图1.png}
\caption{Framework of the Sustainable Tourism Development Model for Juneau}
\label{fig:framework}
\end{figure}

\section{Assumptions and Notations}

\subsection{Assumptions}
\begin{itemize}
\item The population of the City of Juneau is expected to remain constant at 31,000 after the year 2000.
\item In terms of infrastructure investment, the City of Juneau invests in each sector in roughly stable proportions. Thus, we can use the investment in public transportation to represent the investment in infrastructure.
\item Pollution in tourist cities comes from the transportation of large numbers of tourists, so the amount associated with air pollution can be used to represent overall pollution in the city of Juneau.
\item During the time period of the data, there have been no emergencies, other than the New Crown epidemic, that were significant enough to have a major, sustained impact on Juneau's tourism industry.
\item All data is accurate and reliable.
\end{itemize}

\subsection{Notations}
Due to the complexity of our model, we separately present the notations for decision variables and evaluation indicators in their respective sections (see Table \ref{tab:decision_vars} and Table \ref{tab:indicators}). Here, we focus on the key variables used in coupling coordination calculation:

\begin{table}[!htbp]
\centering
\caption{Key Variables in Coupling Coordination Calculation}
\begin{tabular}{cl}
\toprule
\textbf{Symbol} & \textbf{Description} \
\midrule
$U_{E}$ & Comprehensive score of economic subsystem \
$U_{S}$ & Comprehensive score of social subsystem \
$U_{Eco}$ & Comprehensive score of ecological subsystem \
$C$ & Coupling degree among three subsystems \
$T$ & Coordination level among three subsystems \
$D$ & Coupling coordination degree of the tourism system \
\bottomrule
\end{tabular}
\label{tab:notation}
\end{table}

\section{Model Preparation}

\subsection{Data Collection}

A comprehensive data set encompassing a multitude of economic, social and environmental indicators for the City of Juneau was obtained through a meticulous examination of statistical reports published by pertinent agencies over the years.

\begin{table}[htbp]
\centering
\caption{Data Source Websites}
\begin{tabular}{ll}
\toprule
Database names & Database website \
\midrule
ACS & \href{https://www.census.gov/programs-surveys/acs/data/data-via-ftp.html}{\texttt{https://www.census.gov/...}} \
EJScreen & \href{https://gaftp.epa.gov/EJSCREEN/}{\texttt{https://gaftp.epa.gov/...}} \
GHGRP & \href{https://www.epa.gov/ghgreporting}{\texttt{https://www.epa.gov/...}} \
AQS & \href{https://aqs.epa.gov/aqsweb/airdata/download_files.html}{\texttt{https://aqs.epa.gov/...}} \
LAUS & \href{https://www.bls.gov/lau/}{\texttt{https://www.bls.gov/...}} \
Juneau Budget Data & \href{https://juneau.org/finance/budget-2}{\texttt{https://juneau.org/...}} \
Travel Juneau Annual Report & \href{https://www.traveljuneau.com/about-travel-juneau/annual-report/}{\texttt{https://www.traveljuneau.com/...}} \
ATIA & \href{https://www.alaskatia.org/resources/research}{\texttt{https://www.alaskatia.org/...}} \
JEDC & \href{https://www.jedc.org/research-library-reports-studies-by-jedc/}{\texttt{https://www.jedc.org/...}} \
\bottomrule
\end{tabular}
\end{table}

\subsection{Data Preprocessing}

The raw data collected from various sources required careful preprocessing to ensure quality and usability. Several key preprocessing steps were taken:

\begin{itemize}
\item \textbf{COVID-19 Impact Handling}: Data from 2020 and 2021 were excluded from our analysis due to the significant disruption to tourism-related indicators caused by the COVID-19 pandemic. This exclusion ensures that our model is built on data that better represents normal operating conditions.

\item \textbf{Composite Indicator Construction}: Some decision variables and indicators were not directly available in the raw data. For instance, infrastructure investment was constructed by aggregating multiple related sub-categories of investment (e.g., street maintenance, facility upgrades) from annual statistical reports. While such aggregation may not capture the complete expenditure in each domain, it serves as a statistically significant proxy for the overall investment level.

\item \textbf{Abstract Variable Quantification}: Several variables and indicators in our model are conceptually abstract. For example, the tourism tax intensity was quantified based on historical tax collection data and tourist numbers. Similarly, the tourist distribution policy intensity was derived from various policy implementation records and their corresponding effects.
\end{itemize}

After preprocessing, we obtained a clean and consistent dataset covering recent years except for the pandemic period, which forms the foundation for our subsequent modeling work.

\subsection{Model Overview}

To address the sustainable tourism development challenges in Juneau, we propose a two-stage modeling approach, as illustrated in Figure \ref{fig:model_structure}. The framework consists of two major components:

\begin{itemize}
\item \textbf{Sustainability Coupling Coordination Model (SCCM)}: This evaluation component assesses the coordination level among economic, social, and ecological subsystems. Through standardization of indicators and subsystem integration, SCCM generates a coupling coordination degree that quantifies the overall system balance.

\item \textbf{Hierarchical Optimization Model (HOM)}: Building upon the SCCM evaluation results, this optimization component determines the optimal policy combinations. HOM employs system dynamics equations and utilizes the NSGA-II algorithm with lexicographic ordering to find solutions that balance multiple objectives with different priorities.
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=11cm]{figures/绘图2.png}
\caption{Framework of the Two-Stage Modeling Approach}
\label{fig:model_structure}
\end{figure}

The workflow proceeds from model preparation through evaluation and optimization to final strategy generation. The connection between SCCM and HOM is established through the coupling coordination degree, which serves both as an evaluation metric and a primary optimization objective. This integrated approach ensures that the proposed solutions maintain a high level of system coordination while meeting specific performance targets.

\section{Sustainability Coupling Coordination Model}

In order to formulate an optimal sustainable tourism development plan for Juneau, the Sustainability Coupling Coordination Model (SCCM) was constructed in order to evaluate the coordination level among economic, social, and ecological development indicators. Based on Juneau's historical reports and comprehensive statistical data, ten key indicators were identified with which to assess the city's integrated development across these three dimensions. The specific indicators, including their symbolic representations, data sources, and measurement units, are detailed in Table~\ref{tab:indicators} below.   

\begin{table}[htbp]
\centering
\caption{Key Indicators for Assessing Sustainable Tourism Development in Juneau}
\label{tab:indicators}
\begin{tabular}{lllll}
\toprule
\textbf{Subsystem} & \textbf{Indicator} & \textbf{Symbol} & \textbf{Unit} & \textbf{Attribute} \
\midrule
Economic & Tourism Revenue & $E_1$ & Million USD & Positive \
& Tourism Fixed Assets & $E_2$ & Million USD & Positive \
\midrule
Social & Resident Attitude & $S_1$ & Scale 0-10 & Positive \
& Congestion Index & $S_2$ & Index Value & Negative \
& Tourism Accessibility & $S_3$ & Index Value & Positive \
& Resident Disposable Income & $S_4$ & USD/Person & Positive \
& Tourism Employment & $S_5$ & Thousand People & Positive \
\midrule
Ecological & Carbon Footprint & $Eco_1$ & Tonnes of CO$_2$ Equivalent & Negative \
& Air Pollution Index & $Eco_2$ & Index Value & Negative \
& Glacier Congestion Index & $Eco_3$ & Index Value & Negative \
\bottomrule
\end{tabular}
\end{table}

\subsection{Standardization of Indicators}

In view of the marked disparities in dimensions and value ranges of the indicators, it is imperative to standardise the raw data with a view to eliminating dimensional impacts. This study employs the range standardisation method to convert all indicator values into a unified interval of $[0,1]$. Different standardisation formulas are applied to positive and negative indicators:

For positive indicators ($E_1$, $E_2$, $S_1$, $S_3$, $S_4$, $S_5$), the following standardisation formula is applied:

For negative indicators ($S_2$, $\text{Eco}_1$, $\text{Eco}_2$, $\text{Eco}_3$), the following standardisation formula is employed:

In this formula, $X'_{ij}$ represents the standardized indicator value, $X_{ij}$ denotes the original indicator value, and $X_{\text{max}}$ and $X_{\text{min}}$ represent the maximum and minimum values of the indicator during the evaluation period, respectively. In order to mitigate the influence of extreme values, this study establishes upper and lower bounds for each indicator based on historical data for standardisation calculations.

\subsection{Calculation of Coupling Coordination Degree}

Utilising the standardised indicators, a composite index is derived for the three subsystems:
\begin{equation}
\begin{cases}
U_E = 0.6E_1 + 0.4E_2 \
U_S = 0.25S_1 + 0.35S_2 + 0.15S_3 + 0.20S_4 + 0.10S_5 \
U_{\text{Eco}} = 0.26\text{Eco}_1 + 0.24\text{Eco}_2 + 0.50\text{Eco}_3
\end{cases}
\label{eq:composite_index}
\end{equation}

The glacier crowding index ($\text{Eco}_3$) was assigned the highest weight of 0.50, reflecting the critical position of glacier resources in the Juneau tourism ecosystem. Utilising the aforementioned formula (see Equation \eqref{eq:composite_index}), the composite economic, social and ecological indicators for the city of Juneau were derived over the preceding triennium, as illustrated in Figure \ref{fig:aa}.

\begin{figure}[h]
\small
\centering
\includegraphics[width=13cm]{figures/3-subsystom.png}
\caption{Composition of Subsystem Development Indices (2022-2024)} \label{fig:aa}
\end{figure}

The coupling coordination of the three subsystems can be calculated based on the combined indices through a three-step process.

First, the coupling degree $C$, which indicates the interaction between subsystems, is calculated as:
\begin{equation}
C = \frac{3 \times (U_E \times U_S \times U_{\text{Eco}})^{1/3}}{U_E + U_S + U_{\text{Eco}}}
\end{equation}

Then, the coordination degree $T$ is determined by:
\begin{equation}
T = 0.28U_E + 0.28U_S + 0.44U_{\text{Eco}}
\end{equation}
where the ecological subsystem is assigned a higher weight (0.44) to reflect its crucial role in sustainable tourism development.

Finally, the coupling coordination degree $D$ is derived as:
\begin{equation}
D = \sqrt{C \times T}
\end{equation}

The value of $D$ ranges from 0 to 1, with higher values indicating better system coordination. Based on this metric, the coordinated development status can be classified into ten levels from extremely dysfunctional to highly coordinated.

The coupling coordination degree calculations for the past three years are presented in Table \ref{tab:ccd_results}.

\begin{table}[htbp]
\centering
\caption{Coupling Coordination Degree Results (2022-2024)}
\label{tab:ccd_results}
\begin{tabular}{cccc}
\toprule
Year & CCD Value & Level & Category \
\midrule
2022 & 0.6211 & 7 & Primary Coordinated \
2023 & 0.6530 & 7 & Primary Coordinated \
2024 & 0.6943 & 7 & Primary Coordinated \
\bottomrule
\end{tabular}
\end{table}

The calculation results indicate that the coupling degree of the economic-social-ecological system of Juneau tourism maintains at the seventh level of 'primary coordination' over the past three years, with a steady upward trend from 0.6211 to 0.6943. This suggests that while the coordination among economic growth, social well-being, and ecological protection in Juneau's tourism development remains at a basic level, the positive interaction among the subsystems has been gradually strengthening.

\section{Hierarchical Optimization Model}

In this section, we propose a hierarchical multi-objective optimisation model to determine the optimal policy combination in order to address the challenges of overtourism while maintaining tourism benefits. This builds upon the Sustainability Coupling Coordination Model (SCCM), which evaluates the coordination level among economic, social, and ecological subsystems.

The hierarchical structure of the model reflects the multi-level relationships: at the foundation level are eight decision variables representing various policy instruments including investments, taxes, and visitor management strategies.These policy instruments then influence ten key indicators across economic, social, and ecological dimensions as identified in the SCCM.Finally, these indicators are aggregated into three subsystem indices that collectively determine the system's overall performance. The model's hierarchical framework is designed to optimise the coupling coordination degree (D), government revenue, and carbon footprint, with the aforementioned objectives arranged in descending order of priority. This arrangement reflects Juneau's commitment to achieving balanced development while addressing overtourism concerns.

\subsection{Decision Variables}

Based on the historical data and policy reports from Juneau's tourism development, we identified eight key decision variables that can be effectively controlled by the city management to influence tourism outcomes. These variables, as shown in Table \ref{tab:decision_vars}, include four types of investment allocations, tourist taxation, visitor distribution policy, and two fundamental tourism volume indicators.

\begin{table}[htbp]
\centering
\caption{Decision Variables for Tourism Development in Juneau}
\label{tab:decision_vars}
\begin{tabular}{lll}
\toprule
\textbf{Indicator} & \textbf{Symbol} & \textbf{Unit} \
\midrule
Environmental Protection Investment & $x_{env}$ & Million USD \
Infrastructure Investment & $x_{infra}$ & Million USD \
Tourism Market Promotion Investment & $x_{mkt}$ & Million USD \
Community Project Investment & $x_{soc}$ & Million USD \
Tourist Per Capita Tourism Tax & $\alpha_{tax}$ & USD \
Tourist Distribution Policy Intensity & $x_{div}$ & Index Value \
Number of Tourists & $N_{T}$ & Thousand People/Year \
Tourist Per Capita Consumption & $x_{con}$ & USD/Person \
\bottomrule
\end{tabular}
\end{table}

Through regression analysis of historical data, we established the complex relationships between these decision variables and the ten assessment indicators. Each indicator is determined by multiple decision variables through non-linear interactions. For instance, the carbon footprint ($Eco_1$) is influenced by environmental protection investment ($x_{env}$), infrastructure investment ($x_{infra}$), and tourist volume ($N_{T}$), while the tourism accessibility ($S_3$) is jointly determined by infrastructure investment ($x_{infra}$), distribution policy intensity ($x_{div}$), and tourist volume ($N_{T}$). These intricate relationships form the foundation of our optimization model, enabling us to evaluate how policy adjustments would impact various aspects of Juneau's tourism system. The complete hierarchical structure of our model is illustrated in Figure \ref{fig:sankey}.

\begin{figure}[h]
\small
\centering
\includegraphics[width=16cm]{figures/sangji.png}
\caption{Hierarchical Structure of the Sustainable Tourism Optimization Model} \label{fig:sankey}
\end{figure}

\subsection{System Dynamics Equations}

The relationships between decision variables and indicators were established through regression analysis of historical data. For the economic subsystem, the government revenue ($E_1$) and tourism fixed assets ($E_2$) are formulated as:

\begin{equation}
\text{E}{1} = \frac{1000N{T}(x_{con} + \alpha_{tax} - 218.3796)}{10^6} + 251.9655
\end{equation}

\begin{equation}
\text{E}{2} = 2.10818 - 0.116903\frac{x{infra}}{10.0054} - 0.331696\frac{x_{mkt}}{1.00168} + 2.10063\ln(1 + \frac{\text{S}_{5}}{0.393086})
\end{equation}

The government revenue equation captures how tourist volume ($N_{T}$), per capita consumption ($x_{con}$), and tourism tax ($\alpha_{tax}$) directly contribute to the city's income. The tourism fixed assets are influenced by infrastructure and market promotion investments, while also showing a logarithmic relationship with tourism employment, indicating diminishing returns on investment.

For the social subsystem, the resident attitude ($S_1$) and congestion index ($S_2$) are particularly critical:

\begin{equation}
\text{S}{1} = 6.05431 + 0.168539x{div} + 0.8668\frac{x_{env}}{10.1057} - 0.00038535T
\end{equation}

\begin{equation}
\text{S}{2} = 3.74014 + 0.000416267N{T} - 0.0586679x_{infra} - 0.160964x_{div}
\end{equation}

These equations reveal that resident attitudes are positively influenced by environmental protection and visitor distribution policies, but negatively impacted by increasing tourist numbers. Meanwhile, the congestion index can be effectively managed through infrastructure investment and tourist distribution strategies.

For the ecological subsystem, the carbon footprint ($\text{Eco}_1$) is of particular concern:

\begin{equation}
\text{Eco}{1} = 1.92453 \times 10^6 + 391.147(1000N{T})^{-30.2898} - 78569.9x_{env} - 805146\ln(1 + x_{infra})
\end{equation}

This equation demonstrates how environmental protection and infrastructure investments can help mitigate the carbon footprint, with infrastructure improvements showing diminishing returns as indicated by the logarithmic term.

The remaining system indicators are formulated as follows:

\begin{equation}
\left{
\begin{aligned}
\text{S}{3} &= 1.5081(\frac{N{T} + 100.004}{0.000231623})^{0.429576}(1 - e^{-0.45747\frac{x_{infra}}{9.99294}})(1 + 0.0590587x_{div}) \
\text{S}{4} &= 49942.2 + 0.00569082(N{T} \cdot x_{con}) + 237.171x_{infra} - 457.361x_{soc} \
\text{S}{5} &= 58.108 + 0.000421N{T} - 19.3388\ln(1 + \frac{x_{con}}{104.465}) + 33.4503(1 + \frac{\alpha_{tax}}{-3.93095})^{-1} \
\text{Eco}{2} &= 20.7266 + 2.31625 \times 10^{-6}(1000N{T}) - 4.16471x_{env} - 1.44831x_{infra} - 0.0736647x_{div} \
\text{Eco}{3} &= 0.252585 + 0.00266493\ln(1 + N{T}) - 1.24836x_{div}
\end{aligned}
\right.
\end{equation}

\subsection{Objective Functions}

Based on the established system dynamics and Juneau's development priorities, we formulate a hierarchical multi-objective optimization problem with three objectives:

\begin{equation}
\left{
\begin{aligned}
\min f_1 &= -D \
\min f_2 &= -\text{E}{1} \
\min f_3 &= \text{E}{CO_{1}}
\end{aligned}
\right.
\end{equation}

where $D$ is the coupling coordination degree calculated using the SCCM framework. The negative signs before $D$ and $E_{1}$ convert their maximization into minimization problems. These objectives are arranged in descending order of priority, reflecting Juneau's primary focus on achieving system coordination, followed by economic benefits, while maintaining environmental responsibility through carbon footprint control.

\subsection{Constraints}

The optimization model is subject to several constraints to ensure the feasibility and practicality of solutions. First, all decision variables must fall within their respective reasonable ranges:

\begin{equation}
\left{
\begin{aligned}
10.0 \leq x_{env} \leq 25.0 & \quad \text{(Million USD)} \
40.0 \leq x_{infra} \leq 60.0 & \quad \text{(Million USD)} \
0.0 \leq x_{mkt} \leq 10.0 & \quad \text{(Million USD)} \
15.0 \leq x_{soc} \leq 30.0 & \quad \text{(Million USD)} \
0.0 \leq \alpha_{tax} \leq 10.0 & \quad \text{(USD)} \
0.2 \leq x_{div} \leq 0.4 & \quad \text{(Index Value)} \
500 \leq N_{T} \leq 2200 & \quad \text{(Thousand People/Year)} \
200 \leq x_{con} \leq 260 & \quad \text{(USD/Person)}
\end{aligned}
\right.
\end{equation}

Second, a budget constraint is imposed to ensure that the total investment does not exceed the government revenue:

\begin{equation}
x_{env} + x_{infra} + x_{mkt} + x_{soc} \leq \text{E}_{1}
\end{equation}

Third, to maintain a satisfactory level of system coordination, we require:

\begin{equation}
D \geq 0.8
\end{equation}

\subsection{Solution Methodology}

To solve this hierarchical multi-objective optimization problem, we employ the NSGA-II (Non-dominated Sorting Genetic Algorithm II) algorithm with a customized lexicographic dominator. The lexicographic dominance relationship is defined as follows: for two solutions $A$ and $B$ with objective vectors $F_A=[f_1^A,f_2^A,f_3^A]$ and $F_B=[f_1^B,f_2^B,f_3^B]$, solution $A$ dominates solution $B$ if and only if:

\begin{equation}
\left{
\begin{aligned}
& f_1^A < f_1^B - \epsilon_1, \text{ or} \
& |f_1^A - f_1^B| \leq \epsilon_1 \text{ and } f_2^A < f_2^B - \epsilon_2, \text{ or} \
& |f_1^A - f_1^B| \leq \epsilon_1 \text{ and } |f_2^A - f_2^B| \leq \epsilon_2 \text{ and } f_3^A < f_3^B - \epsilon_3
\end{aligned}
\right.
\end{equation}

where $\epsilon_1 = 0.5$, $\epsilon_2 = 50$, and $\epsilon_3 = 1000$ are tolerance parameters that define the indifference thresholds for each objective. This dominance relationship ensures that solutions are primarily compared based on the coupling coordination degree, followed by government revenue, and finally carbon footprint.

\subsection{Algorithm Implementation}

The NSGA-II algorithm was implemented with carefully selected parameters to ensure efficient exploration of the solution space while maintaining solution diversity. The population size was set to 300 individuals with 100 offspring per generation, and the algorithm was run for 400 generations to ensure convergence. The implementation details are as follows:

\begin{itemize}
\item \textbf{Population Initialization}: The initial population was randomly generated within the feasible region defined by the variable bounds. To improve the quality of initial solutions, we employed a constraint handling method that ensures all initial individuals satisfy the budget constraint.

text
\item \textbf{Genetic Operators}: The Simulated Binary Crossover (SBX) operator was used for crossover with a probability of 0.9, and the Polynomial Mutation operator was applied with a probability of $1/n$ where $n$ is the number of decision variables. These operators were chosen for their ability to handle real-valued decision variables effectively.

\item \textbf{Constraint Handling}: The constraints were handled using a penalty function approach. Solutions violating the coupling coordination degree constraint ($D \geq 0.8$) or the carbon footprint ceiling were penalized proportionally to their degree of violation.

\end{itemize}

The evolution of the three objectives over generations is shown in Figure \ref{fig:convergence}. The coupling coordination degree ($D$) shows rapid improvement in the early stages and stabilizes around 0.84 after 200 generations. The government revenue exhibits a similar pattern, reaching a plateau at approximately 350 million USD. The carbon footprint initially fluctuates but gradually decreases and stabilizes around 54,000 tonnes CO$_2$ equivalent, demonstrating the algorithm's ability to balance multiple competing objectives.

\begin{figure}[htbp]
\centering
\includegraphics[width=18cm]{figures/evolution.png}
\caption{Mean Objective Values Evolution During the Optimization Process}
\label{fig:convergence}
\end{figure}

The final population's distribution in the objective space is visualized in Figure \ref{fig:scatter}, where each point represents a non-dominated solution. The scatter plot reveals clear trade-offs between the three objectives, with solutions clustering in distinct regions. The color gradient indicates the carbon footprint level, showing how solutions with higher coordination degrees and government revenues tend to have slightly higher carbon footprints, though all remain within the specified constraints.

\begin{figure}[htbp]
\centering
\includegraphics[width=16cm]{figures/sandian.png}
\caption{3D Scatter Plot of Non-dominated Solutions in the Final Population}
\label{fig:scatter}
\end{figure}

\subsection{Optimization Results and Investment Strategy}
Through the hierarchical multi-objective optimization process, we obtained a set of non-dominated solutions representing different trade-offs among the objectives. Based on the lexicographic ordering principle and our problem constraints, we identified the optimal solution with the following performance metrics:
\begin{itemize}
\item Coupling Coordination Degree ($D$): 0.8447
\item Government Revenue: 352.18 million USD
\item Carbon Footprint: 53,728.75 tonnes CO$_2$ equivalent
\end{itemize}

The corresponding optimal policy combination is presented in Table \ref{tab:optimal_solution}.

\begin{table}[htbp]
\centering
\caption{Optimal Policy Combination for Juneau's Sustainable Tourism Development}
\label{tab:optimal_solution}
\begin{tabular}{lll}
\toprule
\textbf{Decision Variable} & \textbf{Optimal Value} & \textbf{Unit} \
\midrule
Environmental Protection Investment & 18.21 & Million USD \
Infrastructure Investment & 59.37 & Million USD \
Tourism Market Promotion Investment & 1.52 & Million USD \
Community Project Investment & 15.23 & Million USD \
Tourist Per Capita Tourism Tax & 3.93 & USD \
Tourist Distribution Policy Intensity & 0.20 & Index Value \
Number of Tourists & 2,200 & Thousand People/Year \
Tourist Per Capita Consumption & 260 & USD/Person \
\bottomrule
\end{tabular}
\end{table}

Based on the optimization results, we propose an integrated investment strategy that creates reinforcing feedback mechanisms in the tourism system:

\begin{itemize}
\item \textbf{Infrastructure-Focused Investment}: The solution allocates the largest portion of the budget (59.37 million USD, 62.8%) to infrastructure improvement. This investment directly enhances tourism accessibility ($S_{3}$) and reduces congestion ($S_2$), creating a positive feedback loop that enables higher visitor capacity while maintaining service quality.

\item \textbf{Strategic Environmental Protection}: A significant investment of 18.21 million USD (19.3%) in environmental protection demonstrates the city's commitment to ecological preservation. This investment reduces carbon footprint and improves resident attitudes ($S_{1}$), ensuring the sustainability of natural attractions.

\item \textbf{Community Development}: The community project investment of 15.23 million USD (16.1%), combined with a modest distribution policy intensity (0.20), prioritizes local community benefits. This enhances resident disposable income ($S_{4}$) and strengthens social acceptance of tourism.

\item \textbf{Market Management}: The moderate tourism tax (3.93 USD per capita) and conservative market promotion investment (1.52 million USD, 1.8%) maintain tourism attractiveness while generating necessary revenue for sustainable development.
\end{itemize}

This investment strategy achieves the highest possible coupling coordination degree while satisfying all constraints. The high coordination degree of 0.8447 indicates a well-balanced development state among economic, social, and ecological subsystems, demonstrating how appropriate revenue allocation can promote sustainable tourism development.

\section{Model Adaptation to Nanjing}

To demonstrate the adaptability of our modeling approach, we apply the framework to Nanjing, China, a historic city facing overtourism challenges. As a cultural tourism destination with a population of over 8 million, Nanjing presents different characteristics from Juneau, allowing us to test the model's versatility.

\subsection{Model Adjustment}

The adaptation of our model requires several modifications to accommodate Nanjing's unique context:

\begin{itemize}
\item \textbf{Indicator Selection}: The glacier congestion index ($\text{Eco}_3$) was removed as it is specific to Juneau. The remaining nine indicators were retained as they are universal measures of tourism sustainability.

\item \textbf{System Integration}: The weights in SCCM were adjusted to reflect the changed composition of the ecological subsystem:
\begin{equation}
\begin{aligned}
U_E &= 0.6E_1 + 0.4E_2 \
U_S &= 0.25S_1 + 0.35S_2 + 0.15S_3 + 0.20S_4 + 0.10S_5 \
U_{Eco} &= 0.5\text{Eco}_1 + 0.5\text{Eco}_2
\end{aligned}
\end{equation}
\end{itemize}

The decision variables remain unchanged as they represent universal policy instruments, though their operational ranges were adjusted according to Nanjing's scale:

\begin{equation}
\left{
\begin{aligned}
20.0 \leq x_{env} \leq 70.0 & \quad \text{(Million USD)} \
150.0 \leq x_{infra} \leq 250.0 & \quad \text{(Million USD)} \
20.0 \leq x_{mkt} \leq 50.0 & \quad \text{(Million USD)} \
200.0 \leq x_{soc} \leq 250.0 & \quad \text{(Million USD)} \
0.0 \leq \alpha_{tax} \leq 5.0 & \quad \text{(USD)} \
0.2 \leq x_{div} \leq 0.5 & \quad \text{(Index Value)} \
90000 \leq N_{T} \leq 120000 & \quad \text{(Thousand People/Year)} \
1500 \leq x_{con} \leq 2300 & \quad \text{(USD/Person)}
\end{aligned}
\right.
\end{equation}

Based on regression analysis of Nanjing's historical data, the system dynamics equations were recalibrated. For example, the government revenue equation was updated to:

\begin{equation}
\text{E}{1} = \frac{1000N{T}(x_{con} + \alpha_{tax} \times 1327.1274)}{10^8} - 4401.0535
\end{equation}

The Hierarchical Optimization Model (HOM) retains its structure with the same three objectives but different parameters, demonstrating the framework's adaptability to various contexts while maintaining its core methodology.

\subsection{Optimization Results for Nanjing}

The optimization for Nanjing achieved a coupling coordination degree of 0.8848, demonstrating the model's effectiveness in a different context. The optimal policy combination is characterized by:

\begin{itemize}
\item \textbf{Maximum Environmental Protection}: Environmental investment reaches its upper limit (70M USD), reflecting the critical importance of environmental quality in urban tourism.

text
\item \textbf{Substantial Infrastructure Support}: A high infrastructure investment (197.7M USD) focuses on urban tourism facilities and transportation capacity.

\item \textbf{Active Market Promotion}: Nearly maximum market promotion investment (49.9M USD) suggests the importance of destination marketing in competitive urban tourism.

\item \textbf{Basic Social Programs}: Minimum social project investment (200M USD) indicates a focus on essential community support.

\item \textbf{Moderate Tourism Management}: A tourism tax of 4.45 USD and conservative distribution policy intensity (0.20) suggest a market-driven approach to tourist flow management.

\end{itemize}

This solution achieves a government revenue of 2,998.48M USD while maintaining carbon emissions at 3,098,827.61 tonnes CO$_2$ equivalent. The results demonstrate different priorities from Juneau, with a stronger emphasis on environmental protection and market promotion in the urban context. As shown in Figure \ref{fig:nanjing_scatter}, the final population of solutions exhibits clear trade-offs between the three objectives, with our selected solution representing an optimal balance according to the lexicographic ordering principle.

\begin{figure}[htbp]
\centering
\includegraphics[width=16cm]{figures/nanjing.png}
\caption{3D Scatter Plot of Non-dominated Solutions for Nanjing's Optimization}
\label{fig:nanjing_scatter}
\end{figure}

\subsection{Impact of Location Characteristics}

The comparative study between Juneau and Nanjing reveals how geographical characteristics significantly influence the relative importance of different measures in sustainable tourism management:

\begin{itemize}
\item \textbf{Tourism Resource Type}: In Juneau, where tourism depends heavily on natural attractions like glaciers, environmental protection investment becomes the primary concern, directly impacting both tourist satisfaction and ecological sustainability. Conversely, Nanjing's cultural-historical tourism necessitates greater emphasis on infrastructure capacity and preservation.

\item \textbf{Tourist Flow Pattern}: Juneau's cruise-dominated tourism creates significant seasonal fluctuations, making the distribution policy ($x_{div}$) crucial for peak-season management. In contrast, Nanjing's year-round tourism pattern shifts the focus to sustained infrastructure optimization and continuous flow management.

\item \textbf{Transportation Structure}: The singular dependence on cruise ships in Juneau results in concentrated tourist arrivals, requiring precise temporal control. Nanjing's diverse transportation network enables more flexible spatial distribution, as reflected in its higher optimal infrastructure investment ($x_{infra}$).
\end{itemize}

\subsection{Promoting Tourism Balance}

Our model incorporates the tourism accessibility index ($S_3$) and infrastructure investment ($x_{infra}$) to promote balanced tourism development:

\begin{itemize}
\item \textbf{Accessibility Enhancement}: The tourism accessibility index ($S_3$) in our model measures the ease of reaching different attractions. Through optimizing infrastructure investment and distribution policies, the model promotes higher accessibility for all attractions, including less-visited ones. This is reflected in Nanjing's optimization result where $S_3$ reaches [value], indicating improved access to diverse tourist locations.

\item \textbf{Infrastructure Support}: The optimal infrastructure investment of 197.7M USD can enhance the basic facilities and transportation networks connecting different attractions. The system dynamics equation for accessibility shows that improved infrastructure directly contributes to better tourist access across all sites:
\begin{equation}
S_{3} = 1.5081(\frac{N_{T} + 100.004}{0.000231623})^{0.429576}(1 - e^{-0.45747\frac{x_{infra}}{9.99294}})(1 + 0.0590587x_{div})
\end{equation}
\end{itemize}

These mechanisms demonstrate how our model naturally promotes tourism balance by incorporating accessibility measures and infrastructure support in its optimization framework.

\section{Sensitivity Analysis}

To validate our model's reliability and stability, we conducted three levels of sensitivity analysis targeting both the evaluation model (SCCM) and optimization model (HOM).

\subsection{Indicator Sensitivity in SCCM}
For the evaluation model, we performed a standardized sensitivity analysis on all ten indicators:

\begin{itemize}
\item \textbf{Analysis Method:} Each indicator was varied by ±15% from its baseline value while keeping others constant. The changes in coupling coordination degree (D) were recorded for each variation.

text
\item \textbf{Standardization Process:} All indicators were first normalized to [0,1] scale to ensure comparability. For positive indicators (E1, E2, S1, S3, S4, S5), we used the formula $(x-x_{min})/(x_{max}-x_{min})$; for negative indicators (S2, Eco1, Eco2), we used $(x_{max}-x)/(x_{max}-x_{min})$.

\item \textbf{Results Interpretation:} The sensitivity was quantified by the ratio of D's percentage change to indicator's percentage change. As shown in Figure \ref{fig:indicator_sensitivity}, steeper curves indicate higher sensitivity.

\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=14cm]{figures/sensitive 1.png}
\caption{Sensitivity of Coupling Coordination Degree to Individual Indicator Variations (±15%)}
\label{fig:indicator_sensitivity}
\end{figure}

\subsection{Weight Perturbation Analysis in HOM}
We then tested the optimization model's robustness through systematic weight perturbations:

\begin{itemize}
\item \textbf{Perturbation Method:} Random perturbations were applied to weights in each subsystem while maintaining their sum as 1. For example, at 20% perturbation level, each weight was randomly varied within ±20% of its original value, then renormalized.

text
\item \textbf{Evolution Analysis:} For each perturbation level (0\%, 10\%, ..., 70\%), we ran the NSGA-II algorithm for 400 generations with population size 200. Figure \ref{fig:weight_evolution} tracks the mean coordination degree across generations.

\item \textbf{Convergence Criteria:} The algorithm was considered converged when the mean D value change remained below 0.001 for 50 consecutive generations.

\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=14cm]{figures/sensitive 2.png}
\caption{Evolutionary Trajectories of Mean Coordination Degree under Different Weight Perturbation Levels}
\label{fig:weight_evolution}
\end{figure}

\subsection{Optimal Solution Stability Analysis}
Finally, we examined the stability of optimal solutions under weight perturbations:

\begin{itemize}
\item \textbf{Variable Selection:} Infrastructure investment (x_infra) and environmental protection investment (x_env) were chosen as key variables due to their high sensitivity in previous analyses.

text
\item \textbf{Solution Mapping:} All feasible solutions from different perturbation scenarios were plotted in the x\_env-x\_infra space. Colors indicate perturbation levels (0\%-70\%).

\item \textbf{Clustering Analysis:} As shown in Figure \ref{fig:solution_space}, optimal solutions cluster within x\_env [16.5-18.5M USD] and x\_infra [52-60M USD], demonstrating strong solution stability.

\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[width=10cm]{figures/sensitive3.png}
\caption{Distribution of Optimal Investment Solutions under Weight Perturbations with Local Magnification}
\label{fig:solution_space}
\end{figure}

The results reveal several key findings:
\begin{itemize}
\item The evaluation model (SCCM) shows highest sensitivity to economic indicators, followed by ecological indicators
\item The optimization model (HOM) maintains convergence even under 70% weight perturbations, demonstrating robust performance
\item The positive correlation between x_env and x_infra validates our model's ability to promote balanced development
\end{itemize}

% \subsection{How to cite?}
% bibliography cite use \cite{1,2,3}

% AI cite use \AIcite{AI1,AI2,AI3}

\begin{thebibliography}{99}
\bibitem{1} D.~E. KNUTH The \TeX{}book the American
Mathematical Society and Addison-Wesley
Publishing Company , 1984-1986.
\bibitem{2}Lamport, Leslie, \LaTeX{}: `` A Document Preparation System '',
Addison-Wesley Publishing Company, 1986.
\bibitem{3}\url{https://www.latexstudio.net/}
\end{thebibliography}
%%
%% Generate the Memorandum, if it's needed.
\memoto{Juneau Tourism Commission}
\memofrom{Sustainable Tourism Development Project}
\memosubject{Sustainable Tourism Recommendations}
\memodate{\today}
\memologo{\Large \textbf{Juneau}

\begin{memo}[Memorandum]
\noindent \textbf{To: Juneau Tourism Commission}\
\textbf{Date: January 27, 2025}\
Over the past months, we have been reflecting on how Juneau can continue growing its tourism industry while preserving the city’s environment and community well-being. \ldots

\noindent \textit{(Over the past months, we have been reflecting on how Juneau can continue growing its tourism industry while preserving the city’s environment and community well-being. To this end, we developed a relatively straightforward analytical framework that evaluates Juneau’s balance among economic growth, social needs, and ecological protection. Our findings suggest that, in the past few years, Juneau’s overall coordination in these areas has steadily improved—indicating that, with the right measures, it is indeed possible to increase tourism revenues while enhancing ecological stewardship and resident satisfaction.

Within this framework, we’ve observed that thoughtfully allocating annual budgets, along with moderate management of tourist numbers and flow, can effectively boost tourism revenue and improve the city’s balance. To help Juneau continue optimizing its tourism strategies, we’ve distilled the following key recommendations:

Strengthen Infrastructure
Allocate a substantial proportion of funding to roads, ports, and other essential facilities, aiming to prevent widespread congestion during peak seasons and minimize disruptions to residents’ daily routines.

Establish Dedicated Environmental Funds
Devote more resources to preserving and monitoring glaciers and surrounding ecosystems, including reducing pollution and emissions, thereby safeguarding the natural assets that make Juneau special.

Implement a Moderate Tourist Tax
Introduce a reasonable visitor fee that won’t undermine the city’s allure but will help fund infrastructure and environmental initiatives, while also discouraging excessive low-value tourism.

Invest in Community Projects
Ensure a portion of the annual budget goes toward public services and welfare improvements, so that local residents tangibly benefit from the tourism boom—helping maintain positive community sentiment.

Limit Marketing to High-Value Segments
Engage in measured destination promotion, focusing on creating higher-value experiences rather than simply attracting large numbers of visitors, thus reducing extra burden on infrastructure and the environment.

Adopt Basic Visitor Flow Controls
In especially popular areas, use straightforward methods such as timed entry or staggered admissions to distribute crowds more evenly, mitigating severe congestion at single attractions during peak hours.

In addition, we encourage ongoing data collection and monitoring of metrics such as traffic conditions, environmental indicators, and community satisfaction. By addressing any emerging issues promptly—and adjusting investments or policies where needed—Juneau can continue to enjoy strong tourism income without risking irreversible harm to its natural treasures or urban vitality.

We believe that with a more fine-tuned approach, Juneau can maintain its unique appeal in the eyes of global travelers, and preserve a “livable and visitable” balance even as its population and visitor numbers keep growing. Should the Commission have questions regarding these recommendations or require further assistance in implementing specific measures, we remain at your disposal. May Juneau’s future be marked by both sustainable economic growth and the enduring beauty and well-being of its environment and communities.)}

\bigskip

Sincerely,\
\textbf{Research Team | Sustainable Tourism Development Project}
\end{memo}

\begin{appendices}

\section{First appendix}

In addition, your report must include a letter to the Chief Financial Officer (CFO) of the Goodgrant Foundation, Mr. Alpha Chiang, that describes the optimal investment strategy, your modeling approach and major results, and a brief discussion of your proposed concept of a return-on-investment (ROI). This letter should be no more than two pages in length.

\begin{letter}{Dear, Mr. Alpha Chiang}

\lipsum[1-2]

\vspace{\parskip}

Sincerely yours,

Your friends

\end{letter}
Here are simulation programmes we used in our model as follow.\

\textbf{\textcolor[rgb]{0.98,0.00,0.00}{Input matlab source:}}
\lstinputlisting[language=Matlab]{./code/mcmthesis-matlab1.m}

\section{Second appendix}

some more text \textcolor[rgb]{0.98,0.00,0.00}{\textbf{Input C++ source:}}
\lstinputlisting[language=C++]{./code/mcmthesis-sudoku.cpp}

\end{appendices}

\AImatter

\begin{ReportAiUse}{9}
\bibitem{AI1}
ChatGPT\
Query1: Besides the COVID-19 pandemic, has the city of Juneau in Alaska experienced any particularly major events that would severely impact its tourism industry?''\\ Output: According to public sources, Juneau has not seen a single event comparable in severity to COVID-19 over the past two or three decades. While factors such as global economic recessions (like the 2008 financial crisis), fluctuations in the cruise industry, temporary transportation disruptions, localized natural events, and broader incidents (e.g., the 9/11 attacks) have occasionally affected tourism, none has caused a large-scale or prolonged impact on Juneau's visitor economy akin to the pandemic.''
\end{ReportAiUse}

\end{document}
%%
%% This work consists of these files mcmthesis.dtx,
%% figures/ and
%% code/,
%% and the derived files mcmthesis.cls,
%% mcmthesis-demo.tex,
%% README,
%% LICENSE,
%% mcmthesis.pdf and
%% mcmthesis-demo.pdf.
%%
%% End of file `mcmthesis-demo.tex'.
现在是这样 你看哪里有问题？