混合整数规划建模、求解TSP、VRP问题

Traveling Salesman Problem (TSP) and Vehicle Routing Problem (VRP) are two significant issues in the transportation industry, both requiring optimal path solutions to reduce transportation costs and improve resource efficiency. Mixed Integer Programming (MIP) is an effective mathematical modeling method for solving these problems, especially suitable for small-scale TSP and VRP challenges.

This article outlines the process of constructing MIP models using the Python library 'pulp' to address TSP and VRP issues. To get started, 'pulp' can be installed using the Python package manager pip with the command 'pip install pulp'.

For TSP problems, the article describes the following steps:

1. Importing necessary Python packages, including 'itertools', 'numpy', 'pandas', 'scipy', 'matplotlib', 'seaborn', 'pulp', and 'warnings'.
2. Generating sample data for TSP, using a random seed for consistent results, and creating a DataFrame with randomly positioned points.
3. Producing a distance matrix to represent the distances between points, displaying it as a heatmap for better visualization.
4. Plotting the distribution of points to visualize the locations, with the depot marked distinctly.
5. Constructing and solving the model by establishing the problem with 'pulp.LpProblem', defining variables and constraints, and setting up the objective function. The solution helps to eliminate sub-tours, ensuring a valid TSP solution.

The article provides a detailed guide on using 'pulp' to create MIP models for TSP problems, but it does not cover the VRP aspect in the summary provided. The use of 'pulp' demonstrates a practical approach to tackling optimization problems in transportation logistics.

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