# tsp_random Traveling Salesman Problem Solution by Sampling

tsp_random, a MATLAB program which reads a file of city-to-city distances, and then randomly samples a number of possible tours, to quickly seek a tour of lower length.

The user must prepare a file beforehand, containing the city-to-city distances. The program will request the name of this file, and then read it in as a matrix d. An example of such a file is:

```        0  3  4  2  7
3  0  4  6  3
4  4  0  5  8
2  6  5  0  6
7  3  8  6  0
```
The distance file d should be square, symmetric, and have a zero diagonal.

A tour of n cities can be represented as a permutation p on the integers 1 through n. The cost of the tour, that is, the length, is the sum

```        cost = sum ( 1 <= i <= n ) ( d(p(i),p(i+1)) )
```
where p(n+1) is understood to mean p(1).

In the sampling method, we simply generate sample_num permutations, each of which represents a tour, and return the permutation which has observed to have the shortest length. Since, except for small problems, there are typically an enormous number of possible tours, this method is unlikely to produce optimal results, but it may give some idea of the range of length of typical tours.

### Languages:

tsp_random is available in a MATLAB version.

### Related Data and Programs:

CHANGE_MAKING, a MATLAB library which considers the change making problem, in which a given sum is to be formed using coins of various denominations.

CITIES, a MATLAB library which handles various problems associated with a set of "cities" on a map.

COMBINATION_LOCK, a MATLAB program which simulates the process of determining the secret combination of a lock.

PARTITION_PROBLEM, a MATLAB library which seeks solutions of the partition problem, splitting a set of integers into two subsets with equal sum.

SATISFY, a MATLAB program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem.

SUBSET_SUM, a MATLAB library which seeks solutions of the subset sum problem.

TSP, a dataset directory which contains test data for the traveling salesperson problem;

tsp_brute, a MATLAB program which reads a file of city-to-city distances and solves the traveling salesperson problem, using brute force.

tsp_descent is a MATLAB program which is given a city-to-city distance map, chooses an initial tour at random, and then tries a number of simple variations, seeking to quickly find a tour of lower cost.

tsp_greedy, a MATLAB program which reads a file of city-to-city distances, picks a starting city, and then successively visits the nearest unvisited city.

### Reference:

1. Gerhard Reinelt,
TSPLIB - A Traveling Salesman Problem Library,
ORSA Journal on Computing,
Volume 3, Number 4, Fall 1991, pages 376-384.

### Source Code:

Last revised on 24 April 2019.