https://r2.erweima.ai/mathbot/image/1722929738137i3q3argk.xlsx

请利用以下数据，步骤1：多目标优化模型
筛选景点：最大化游览的景点数量和景点评分总和，同时满足时间和费用的约束条件，以及每个城市只选择一个景点的约束条件。
几何加权法：用于结合多个目标函数。
步骤2：旅行商问题模型（蚁群算法）
使用蚁群算法计算从选定城市的最短路径。结合该思路，解决以下问题：现有一名外国游客从广州入境，他想在 144 小时以内游玩尽可能多的城市，同时要求综合游玩体验最好（景点评分最高），请你规划他的游玩路线。需要结合游客的要求给出具体的游玩路线，包括总花费时间，门票和交通的总费用以及可以游玩的景点数量。他的要求有：
①遵循城市最佳景点游览原则（每个城市选一个评分最高的景点）； 
②城市之间的交通方式只选择高铁； 
只在“最令外国游客向往的 50 个城市”中选择要游玩的城市。



### Step 1: Multi-Objective Optimization Model

To plan the tourist's route, we need to maximize the number of attractions visited and the total attraction score while respecting the constraints on time, cost, and the requirement to choose only one attraction per city.

#### Geometric Weighted Method

1. **Formulate Objectives and Constraints**:
    - Objective 1: Maximize the number of attractions.
    - Objective 2: Maximize the total score of attractions.
    - Constraints:
      - Total time ≤ 144 hours.
      - Total cost ≤ budget (need budget information).
      - One attraction per city.
      - Transportation method: High-speed rail (only cities with high-speed rail connection).

2. **Geometric Weighted Method**:
    - Normalize the objectives.
    - Assign weights to each objective.
    - Combine objectives into a single objective function using geometric weighting.

### Step 2: Traveling Salesman Problem (TSP) Model using Ant Colony Optimization (ACO)

1. **Ant Colony Optimization**:
    - Initialize pheromones and ants.
    - Construct solutions based on pheromone trails and heuristic information.
    - Update pheromones.
    - Choose the best route.

### Implementation

We'll start with Step 1, where we select the cities and attractions. After that, we'll move to Step 2, where we optimize the travel route.

#### Extract and Prepare Data

Let's extract the relevant information and create the optimization model.

**Tourist's Requirements**:
1. Follow the principle of visiting the best-rated attraction in each city.
2. Only use high-speed rail for travel.
3. Choose from the top 50 cities most desired by foreign tourists.

We'll filter the data to include only cities with high-speed rail and then select the best-rated attraction in each city.

Let's proceed with these steps.### Step 1: Multi-Objective Optimization

#### Formulating the Optimization Problem

1. **Objective 1**: Maximize the number of attractions (\(n\)).
2. **Objective 2**: Maximize the total score of attractions (\(S\)).

#### Constraints:

- Total travel time (\(T\)) should be less than or equal to 144 hours.
- Total cost (\(C\)) should be within the budget (need budget details).
- One attraction per city.

#### Geometric Weighted Method

1. Normalize the objectives:
   \[
   n' = \frac{n}{n_{\text{max}}}, \quad S' = \frac{S}{S_{\text{max}}}
   \]
2. Combine the normalized objectives:
   \[
   Z = (n')^w \cdot (S')^{1-w}
   \]
   where \(w\) is the weight assigned to the number of attractions.

Let's implement the optimization using the above formulation.

### Step 2: Traveling Salesman Problem (TSP) Model using Ant Colony Optimization (ACO)

Next, we'll optimize the travel route using the Ant Colony Optimization (ACO) algorithm.

#### Implementing the ACO

1. Initialize pheromones and ants.
2. Construct solutions based on pheromone trails and heuristic information.
3. Update pheromones.
4. Choose the best route.

#### Data Preparation

We will create a distance matrix for the cities and proceed with the ACO implementation.

Let's start by calculating the distance matrix and proceed with the optimization.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like to continue with another approach or discuss something else? 

Here are some related questions to expand on this topic:

1. What are the specific constraints for time and budget for the trip?
2. How many cities are included in the top 50 most desired by foreign tourists?
3. What specific attractions are must-see for the tourist?
4. How do you prioritize between visiting more attractions versus higher-rated ones?
5. What are the preferred high-speed rail routes and schedules?
6. What other transportation options are available if high-speed rail is not feasible?
7. What is the tourist's starting point and final destination?
8. Are there any cities that should be avoided due to travel restrictions or other reasons?

**Tip**: When planning multi-city travel, always consider the local transportation schedules and possible delays to optimize the itinerary effectively.

Explore a detailed solution using multi-objective optimization and the traveling salesman problem (TSP) with ant colony optimization (ACO). Learn how to plan a tourist's route to maximize attractions visited and total score within time and budget constraints. Includes steps for geometric weighted methods and ACO implementation.

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