Introduction
Problem Background
朱诺市是阿拉斯加的一个热门旅游城市，在为当地旅游业创造巨大经济收益的同时对当地生态环境和居民的生活带来了巨大影响。为了维持朱诺市经济生态和居民的平衡发展，建立可持续性旅游发展评估模型尤为重要。
Juno City is a popular tourist city in Alaska, which has a huge impact on the local ecology and the lives of residents while generating huge economic benefits for the local tourism industry. In order to maintain the balanced development of the economy, ecology and residents of Juno City, it is particularly important to establish an evaluation model for sustainable tourism development.
Restatement of the Problem
对于给定的要求和任务，我们重申它们以帮助更好地定位我们的工作重点。
For the given requirements and tasks, we reiterate them to help better position our priorities.
Task1:构建可持续旅游模型：考虑游客数量、总收入、政策措施等因素，明确优化目标和约束条件，并制定支出计划以支持可持续发展
Task 1: Build a sustainable tourism model: Consider factors such as the number of tourists, total revenue, policy measures, etc., clarify optimization goals and constraints, and develop a spending plan to support sustainable development;
Task2:模型适应性分析：展示模型如何适用于其他受过度旅游影响的旅游目的地，并分析不同地点对措施选择的影响
Task2: Model Adaptability Analysis: Demonstrate how the model can be applied to other destinations affected by overtourism, and analyze the impact of different locations on the choice of measures;
Task3:提交备忘录：向朱诺市旅游委员会提交一页备忘录，概述预测结果、措施效果及优化建议。
Task3: Submit a memo: Submit a one-page memo to the Juno City Tourism Commission outlining the projected results, the effectiveness of the measures, and the recommendations for optimization.
Literature Review
针对可持续性旅游发展的研究，自联合国世界旅游组织(UNWTO)宣布2017年是“分水岭时刻”，正式将这一年定为“可持续旅游业促进发展国际年”，提出“使旅游业成为积极变革的催化剂”[1]以来，可持续性旅游发展已成为国际政府、从业人员和政策制定者之间争论的焦点领域。在这方面，以前的研究表明，旅游业不仅为各国提供财政援助，而且还提供了有吸引力的景观，并有助于建立该国的积极形象[2[3。最近的研究主要强调了旅游业在实现可持续发展目标的道路上的作用和重要性[4,5]。同时有研究指出尽管重大的环境破坏仍在继续[6]，但旅游业在可持续发展道路上已经取得了进展和动力[7]。值得注意的是，As humanity transitions from theHolocene to the Anthropocene [8]，由于栖息地丧失、生物多样性的威胁和气候变化，建立新的可持续性旅游发展评估模型以适应社会经济转变的需求，保护文化和环境多样性对于持续的生计发展和福祉越来越紧迫。
Since the United Nations World Tourism Organization (UNWTO) declared 2017 as a "watershed moment", the year has been officially designated as the "International Year of Sustainable Tourism for Development", proposing to "make tourism a catalyst for positive change" [1].Since then, sustainable tourism development has become a key area of debate among international governments, practitioners and policymakers. In this regard, previous studies have shown that tourism not only provides financial assistance to countries, but also provides attractive landscapes and contributes to the establishment of a positive image of the country [2][3]. Recent studies have focused on the role and importance of tourism on the road to achieving the Sustainable Development Goals [4, 5]. At the same time, studies have pointed out that although major environmental damage continues [6], the tourism industry has made progress and momentum on the road to sustainable development [7]. Notably, as humanity transitions from theHolocene to the Anthropocene[8], due to habitat loss, threats to biodiversity, and climate changeThe development of a new assessment model for sustainable tourism development to meet the needs of socio-economic transformation, and the preservation of cultural and environmental diversity is increasingly urgent for sustainable livelihood development and well-being.
Our Work
Our Work
Assumptions and Justifications
Considering those practical problems always contain many complex factors, first of all, we need to make reasonable assumptions to simplify the model, and each hypothesis is closely followed by its corresponding explanation:
Assumption 1:游客分布与时间段管理:我们忽略游客旅游淡季的影响，仅考虑朱诺市在特定旅游旺季接待的游客总流量。
Explanations:虽然游客数量在不同时间段分布可能不同，存在一定的灵活性，但由于本文影响模型的主要因素为环境和基础设施承载力，因此为了简化模型，我们以旅游旺季时游客数量为主要研究对象。
Assumption 2:隐性成本的量化:本文中隐性成本（包括对环境、基础设施和社会）为了简化模型，只考虑其中主要的影响因素。
Explanations:环境变化受到当地旅游带来的影响而外，还受到全球气候变化，极端天气影响等多种因素影响。因此，为了简化模型，我们只考虑由游客引起的主要影响因素，忽略掉数据中其它次要因素影响。
Assumption 3: 朱诺市的基础设施承载能力有限。
Explanations:朱诺市的基础设施(如水、电、垃圾处理)具有一定的承载能力，超过此能力将导致基础设施压力加剧，因此我们设定朱诺市基础设施承载能力有限，忽略旅游期间朱诺市可能设立的临时公共服务设施。
Notations
The key mathematical notations used in this paper are listed in Table 1:
Notations used in this paper
Symbol | Description | Unit |
| 代表朱诺市在特定期间内接待的游客数量，取值范围为[10000,20000]。 | Ten thousond |
| 对游客消费征税的比例，反映了市政府对游客消费征收的税率,取值范围为[0.05,1]， | -- |
| 基础设施压力（主要包括饮用水供应、交通、住房压力等） | -- |
| 环境影响（主要包括碳足迹） | -- |
| 居民满意度（受游客数量、基础设施压力和环境影响的综合影响） | -- |
| 游客带来的收入 | $ |
Data Description
在本模型中，数据是支撑模型运作的基础，帮助我们量化游客数量、收入、隐性成本以及相关约束条件。以下是我们使用的数据描述：
Given Data
利用题目中给出的参考文献[9]，我们收集得到了朱诺市游客数量，游客消费数据，以及总游客数量上限（来源于朱诺市为了维持当地生态平衡和居民正常生活颁布的政策）。
Additional data
由于题中没有给出关于隐形成本数据（包括碳足迹，基础设施压力等），通过查阅数据网站以及美国加州朱诺市官方数据，我们得到以下数据：
社会成本：从Destination Next[10]收集了朱诺市社会调查、居民满意度调查、投诉数据等数据。数据用于描述由于游客过多导致的社会压力，如房价上涨、噪音污染等。该数据集包括但不限于当地社区支持程度，居民对交通，住宿等的Perceived Performance。我们根据数据的相关和重要度进行了细分，囊括了当地居民交通压力，社区环境满意度等 ;
环境成本：从朱诺市政府官方网站[7]获取了朱诺市环境监测数据，此数据包括碳足迹 ;
基础设施成本：从朱诺经济发展委员会发布的数据[8]获取了朱诺市基础设施相关部门以及朱诺市的财政预算数据。其中包括交通等基础设施维护费用以及朱诺市基础设备承载能力 .
Data Preprocessing
在模型建立之前，我们对所有的数据进行了以下预处理：
数据清洗：为了确保所有数据完整，没有缺失值，去除异常值 ;
数据平滑：考虑到游客数量和隐性成本之间的波动，我们对一些数据进行平滑处理，以去除极端波动 ;
数据归一化：为了确保可比性和分析精度，我们将所有变量转换为统一的无量纲尺度，这是通过应用标准化公式实现的。
其中代表任何一个变量（游客数量、基础设施压力、环境影响、居民满意度）。
模型：可持续旅游发展模型
如果邮轮带来的游客量在可控范围内，则在不会破坏生态环境的情况下可以提高当地旅游收入，增强居民满意度。但是，当旅游带来的压力超过了朱诺市基础设施或者生态环境所能承受的范围，就会对当地生态环境以及居民正常生活带来破坏。因此，我们希望开发一个模型来估计在保证当地生态环境和居民正常生活的前提下，通过调整各种因素影响，实现对朱诺市可持续发展的优化。
可持续旅游发展模型建立
本模型的主要目标是以朱诺市可持续旅游发展最优为目标，建立可持续旅游发展的模型，通过调整税率以改变游客数量来实现提高收入，减小环境压力和基础设施压力，同时提高居民满意度的目的，同时以旅客、环境和基础设施最大承载量为约束条件，实现了对朱诺市可持续旅游发展优化。在此过程中具体目标可以简化为以下几个方面：
最大化旅游收入:考虑游客数量和税率对收入的影响 ;
最大化居民满意度:居民满意度与游客数量、基础设施压力、环境影响等因素相关 ;
最小化基础设施压力:基础设施压力与游客数量、资源消耗等因素相关 ;
最小化环境影响:环境影响与游客数量、碳排放等因素相关。
旅游带来的经济收入（I）
收入由游客数量和税率共同决定，关系式可表示为：
其中是每个游客的基础消费，是税率。本文中$。
Among them is the basic consumption of each tourist, which is the tax rate. $ in this article.
游客数量与税收的关系（T）
Relationship between the number of tourists and taxes (T).
游客数量随税率变化，通常可以使用指数衰减模型来描述：
The number of tourists varies with the tax rate and can often be described using an exponential decay model:
其中（万人）表示没有税率时最大游客数量，为税率对游客数量影响的衰减系数，是税率，本文中。
Among them (10,000 people) represents the maximum number of tourists when there is no tax rate, which is the attenuation coefficient of the impact of the tax rate on the number of tourists, which is the tax rate, in this article.
利用公式可以得出：随着税率增加，游客数量会逐渐下降，且下降速度会随税率的增加而加快。
Using the formula, it can be concluded that as the tax rate increases, the number of tourists will gradually decrease, and the rate of decline will accelerate as the tax rate increases.
基础设施压力（P）
Infrastructure Pressure (P).
基础设施交通压力可以与游客数量成二次函数关系[11]，因此可以通过一个二次方程来描述：
The traffic pressure of the infrastructure can be a quadratic function of the number of tourists [11], so it can be described by a quadratic equation:
其中为基础压力系数，我们通过最小二乘法拟合历史朱诺市基础设施交通压力数据估算得：。其中最大基础设施压力为29700。
Among them, the basic pressure coefficient is estimated by fitting the historical infrastructure traffic pressure data of Juno City by the least squares method: The maximum infrastructure pressure is 29,700.
旅客人数与基础设施压力的拟合曲线
Fitting curve of passenger numbers versus infrastructure pressures
环境影响（E）
Environmental impact (E).
环境影响可以于游客数量成三次函数关系[16]，随着游客数量的增加，环境负担（如碳排放、垃圾处理等）会急剧增加，因此可以使用以下三次方程描述：
The environmental impact can be a cubic function of the number of tourists [16], and as the number of tourists increases, the environmental burden (e.g., carbon emissions, garbage disposal, etc.) increases dramatically, so it can be described using the following cubic equation:
其中，是环境影响系数，我们通过最小二乘法拟合历史朱诺市碳排放数据与旅客人数关系估算得：。其中最大环境压力为952000。
Among them, is the environmental impact coefficient, which we estimate by fitting the relationship between historical Juneau carbon emission data and the number of tourists by fitting the least squares method: The maximum ambient pressure is 952,000.
游客人数与环境压力的拟合曲线
Fitting curve of tourist numbers versus environmental pressures
居民满足度（S）
Resident Satisfaction(s).
本文中通过主成分分析，得出居民满意度主要受三方面因素影响（游客数量，基础设施压力，环境影响），利用公式，可以描述居民满意度：
In this paper, through principal component analysis, it is concluded that residents' satisfaction is mainly affected by three factors (the number of tourists, infrastructure pressure, and environmental impact).Describe Resident Satisfaction:
其中是满意度模型的权重系数，为控制居民满意度衰减速度的参数。本文中。
Among them is the weight coefficient of the satisfaction model, which is the parameter that controls the decay rate of residents' satisfaction. in this article.
额外收入支出计划
Additional income expenditure plan
为了维持朱诺市可持续发展，探索最优政策，模型中将额外税收收入用于改善环境质量和基础设施建设，具体支出计划如下：
In order to maintain the sustainable development of the city of Juno and explore the optimal policies, the additional tax revenue will be used to improve environmental quality and infrastructure construction in the model, and the specific expenditure plan is as follows:
环境保护支出：利用税收和游客数量关系推导可知，环境保护资金与游客数量存在非线性关系，设定环境保护支出比例为0.2,则环境保护支出为：
Environmental protection expenditure: Using the relationship between tax and the number of tourists, it can be seen that there is a nonlinear relationship between environmental protection funds and the number of tourists, and the environmental protection expenditure is set to 0.2, then the environmental protection expenditure is：
基础设施建设支出：利用税收和游客数量关系推导可知，基础设施建设资金与游客数量存在非线性关系，设定基础设施建设支出比例为0.2,则环境保护支出为：
Infrastructure construction expenditure: Using the relationship between tax revenue and the number of tourists, it can be seen that there is a nonlinear relationship between infrastructure construction funds and the number of touristsIf the proportion of infrastructure construction expenditure is 0.2, the environmental protection expenditure is:
引入额外收入支出计划政策后，调整基础设施压力和环境压力分别为公式和公式：
After the introduction of the additional revenue expenditure plan policy, the adjustment of infrastructure pressure and environmental pressure are respectively formula and formula:
优化目标函数
Optimize the objective function
本文优化目标为：
The optimization objectives of this article are:
最大化旅游收入(通过调整税率控制游客数量)
Maximizing tourism revenue (controlling the number of tourists by adjusting the tax rate);
减少基础设施压力和环境影响
Reduce infrastructure stress and environmental impact;
保持较高的居民满意度。
Maintain a high level of resident satisfaction.
因此综合目标函数可以表达为：
Thus the composite objective function can be expressed as:
目标函数表示加权其中是各种目标因素的权重系数，表示不同因素对总目标的影响程度。本文中。
The objective function represents the weighted coefficients of various objective factors, which indicates the degree of influence of different factors on the overall objective. in this article.
基于模拟退火算法的模型求解
Model solution based on simulated annealing algorithm
为了求解出考虑朱诺市最大收入目标函数的最优解，我们选取模拟退火算法进行求解，通过不断随机扰动当前解，并根据目标函数的变化以最大化目标函数为指标来决定是否接收新的解，在不断迭代下，接收较差解的概率逐渐减小，从而可能跳出局部最优解，最终收敛到全局最优解。基本步骤如Figure 4:：
In order to solve the optimal solution considering the objective function of the maximum income of Juno City, we choose the simulated annealing algorithm to solve the problem, and the current solution is continuously disturbed randomly according to the change of the objective functionWith the maximization objective function as the index to decide whether to receive a new solution, the probability of receiving a worse solution gradually decreases under continuous iteration, so that it may jump out of the local optimal solution and finally converge to the global optimal solution. The basic steps are as shown in Figure 4::
模拟退化算法流程图
Flowchart of the simulated degradation algorithm
利用Matlab求解模型后，得到结果如下：
After using Matlab to solve the model, the results are as follows:
DATA | RESULT | Number of tourists N (ten thousand) | 110.5 | Objective function Z | 0.56 | Optimal income I | 35209.728 | Optimal infrastructure pressure P | 9039.51 | Optimal Environmental Impact E | 112699.01 | Optimal satisfaction S | 0.66 | Optimal tax rate K | 0.7703 |
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同时，为了探索额外收入用于支持环境保护和缓解基础设施压力策略对模型的影响，我们分别对使用政策和没有实施策略分别进行求解，得到的结果用于比较探索策略对模型带来的影响。
At the same time, in order to explore the impact of the additional revenue used to support environmental protection and alleviate the pressure on the infrastructure, we solved the strategy of use and the strategy of no implementation respectively, and the results obtained were used to compare the impact of the exploration strategy on the model.
利用Matlab求解模型得到结果如Figure 5:。
The results of the Matlab solution model are obtained as shown in Figure 5.
政策对可持续旅游发展模型产生的影响
The impact of policies on sustainable tourism development models
通过对比数据结果可以得出当我们实施政策后，产生了以下积极影响：
By comparing the results of the data, we can conclude that when we implemented the policy, we had the following positive impacts:
游客数量增加：实施政策后，游客数量增加了约0.91万（十万人），表明政策对吸引游客有积极作用
Increase in the number of tourists: After the implementation of the policy, the number of tourists increased by about 9,100 (100,000), indicating that the policy has a positive effect on attracting tourists;
目标函数值提高：目标函数值从0.54提高到0.56，说明政策有助于优化整体目标，可能包括经济、环境和社会等多个方面的综合效益
Increase in the value of the objective function: The increase in the value of the objective function from 0.54 to 0.56 indicates that the policy can help optimize the overall goal, which may include the combined benefits of economic, environmental and social aspects;
最优收入增加：实施政策后，最优收入增加了约183.015，表明政策对经济收入有显著的提升作用。
Optimal income increase: After the implementation of the policy, the optimal income increased by about 183.015, indicating that the policy has a significant effect on economic income.
基础设施压力减轻：实施政策后，基础设施压力减少了约1968.36，说明政策有助于合理分配和利用基础设施资源，减轻了基础设施的负担
Reduction of infrastructure pressure: After the implementation of the policy, the pressure on infrastructure was reduced by about 1968.36, indicating that the policy was conducive to the rational allocation and utilization of infrastructure resources and reduced the burden on infrastructure;
环境影响降低：实施政策后，环境影响减少了约63493.21，表明政策在环境保护方面发挥了积极作用，减少了对环境的负面影响
Reduction of environmental impact: After the implementation of the policy, the environmental impact was reduced by about 63493.21, indicating that the policy played an active role in environmental protection and reduced the negative impact on the environment;
居民满意度提高：实施政策后，满意度从0.62提高到0.66，说明政策提升了游客和相关利益方的满意度
Residents' satisfaction improved: After the implementation of the policy, the satisfaction rate increased from 0.62 to 0.66, indicating that the policy improved the satisfaction of tourists and stakeholders;
税率优化：实施政策后，税率从0.7756降低到0.7703，虽然变化不大，但表明政策在税收方面进行了优化，可能有助于减轻企业和个人的负担。
Tax rate optimization: After the implementation of the policy, the tax rate was reduced from 0.7756 to 0.7703, although the change is not large, but it indicates that the policy has been optimized in terms of taxation, which may help reduce the burden on enterprises and individuals.
