https://github.com/lucidfrontier45/tsp_mip_example

Solve TSP as MIP with Rust
https://github.com/lucidfrontier45/tsp_mip_example

Last synced: about 4 hours ago
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Solve TSP as MIP with Rust

• Host: GitHub
• URL: https://github.com/lucidfrontier45/tsp_mip_example
• Owner: lucidfrontier45
• License: apache-2.0
• Created: 2024-09-17T10:07:04.000Z (about 2 months ago)
• Default Branch: main
• Last Pushed: 2024-09-18T04:58:17.000Z (about 2 months ago)
• Last Synced: 2024-09-18T14:15:24.065Z (about 2 months ago)
• Language: Rust
• Size: 18.6 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Example program to solve TSP as mixed integer programming

## How to run

The project is managed by uv.

You can use the following command to automatically download dependencies and run the main program.

```sh

uv run main.py berlin52.csv

```

CP-SAT is used as the default solver. You can use `--solver` option to choose other solvers e.g. 'highs' and 'scip'.

## Problem structure

- $i$ : index of city

- $d_{ij}$ : distance between cities $i$ and $j$

- $x_{ij}$ : binary decision variable, indicates if edge between $i$ and $j$ is used or not.

- $u_i$ : integer auxiliary variable, indicates thata $i$ is visited at $u_i$th order. 

- $D(x) = \sum_{i,j}d_{ij}x_{ij}$ : objective function, total distance

- $X_{i.} = \sum_j x_{ij} = 1$ : constraint, there must be one edge from $i$

- $X_{.j} = \sum_i x_{ij} = 1$ : constraint, there must be one edge to $j$

- if $x_{ij} = 1$ then $u_i - u_j = -1$ otherwise $u_i - u_j \leq M$, wher $M$ is a sufficiently large number. In this case, $M$ can be set to $N-1$ where $N$ is total number of cities. -> $u_i - u_j \leq (1-x_{ij})N -1$. This constraint, known as the Miller–Tucker–Zemlin (MTZ) formulation, is used for sub tour elimination.