solve a travelling salesperson problem in matlab

The traveling salesperson problem (TSP) is a combinatorial optimization problem which asks for the shortest possible route that visits a given set of cities and returns to the starting city. There are several ways to formulate the TSP mathematically, but one common approach is to use dynamic programming.

In Matlab, you can use the built-in optimization toolbox to solve the TSP. Here's an example code that solves a small TSP instance:

main.m
% Define the distance matrix
dist = [
    0, 20, 30, 10;
    15, 0, 16, 4;
    3, 5, 0, 2;
    19, 6, 18, 0
];

n = size(dist, 1); % number of cities

% Define the optimization problem
f = reshape(dist, n^2, 1);
IntCon = 1:n;
Aeq = repmat({[1 zeros(1,n-1)]}, n, 1);
beq = ones(n,1);
lb = zeros(n^2,1);
ub = ones(n^2,1);
[sol, dist_min] = intlinprog(f, IntCon, [], [], Aeq, beq, lb, ub);

% Print the optimal tour and its length
tour = find(reshape(sol, n, n));
tour = [tour ; tour(1)];
fprintf('Optimal tour: %s\n', num2str(tour'));
fprintf('Length of tour: %f\n', dist_min);
576 chars
25 lines

The code defines the distance matrix dist, which represents the distances between cities. The optimization problem is then defined using the intlinprog function, which finds the optimal tour through an integer linear programming formulation. Finally, the optimal tour and its length are printed to the command window.

Note that this code is only suitable for small TSP instances, because it solves the problem exactly and the computational complexity grows exponentially with the number of cities. For larger instances, you may need to use heuristic algorithms (such as genetic algorithms or nearest neighbor algorithms) or other optimization techniques.