belenfg / travelling-salesman-problem

A solution for TSP in php

Travelling Salesman Problem TSP

This project implements one way to solve the TSP for 32 cities without coming back to the start (Hamiltonian Path), which is an old problem about computing the shortest path for visiting all cities in a list without repeating any city.

The difficulty of the problem remains in the time of execution of this NP-Hard problem which is O(n!) and it gets not feasible with a brute force attack already for 20 cities.

There are solutions for best paths like:

Dynamic Programing O(n^2 * 2^n)

Branch and Bound (solves problems with 40 to 60 cities)

In this project the problem has been solved not with an exact solution, but with a faster computation based on the closest point to each city. This implementation in general returns a path 25% longer than the shortest path.

In this project are applied SOLID principles.

To add to this project remains: Exact solution with Branch and Bound Acceptance test which gives feedback about solve.php script with the real data.

Requirements

PHP 7.0

Composer

How to install

git clone https://github.com/befern/travelling-salesman-problem
composer install

Build Status

Run solver

In the project root:

php solve.php

Run tests

In the project root:

vendor/bin/phpunit

References

• Wikipedia - Travelling Salesman Problem
• Wikipedia - Branch And Bound
• Travelling Salesman Problem using Branch and Bound Approach

travelling-salesman-problem's Issues

Very bad results

Hello.
Tested your implementation of TCP algorithm.
It gives very bad results.
For example when we have usa map good result is 2578.
Your result is - 9086