matlab邮递员问题代码

下面是一个matlab邮递员问题代码的示例：

function [min_distance, optimal_path] = tsp(points)
% TSP - Traveling Salesman Problem solver
%
% Syntax: [min_distance, optimal_path] = tsp(points)
%
% Inputs:
% points - an n-by-2 matrix where each row represents a point in the
% two-dimensional plane
%
% Outputs:
% min_distance - the minimum distance that a salesman must travel to visit
% all the points in the given order
% optimal_path - a vector representing the order in which the points should
% be visited to minimize the distance traveled
%
% Example:
% points = [0, 0; 3, 4; 1, 2; 4, 3];
% [min_distance, optimal_path] = tsp(points);
% disp([min_distance, optimal_path]);
%
% Reference:
% https://en.wikipedia.org/wiki/Travelling_salesman_problem

n = size(points, 1); % number of points
d = pdist(points); % pairwise distances between points
D = squareform(d); % distance matrix
D(D==0) = NaN; % remove self-loops

% Nearest neighbor heuristic
path = zeros(1, n);
path(1) = 1; % start at first point
for i = 2:n
[~, j] = nanmin(D(path(i-1), :));
path(i) = j;
end
path(n+1) = 1; % end at first point

% Two-opt heuristic
improvement = true;
while improvement
improvement = false;
for i = 1:n-2
for j = i+2:n
if (D(path(i), path(j)) + D(path(i+1), path(j+1))) ...
< (D(path(i), path(i+1)) + D(path(j), path(j+1)))
path(i+1:j) = fliplr(path(i+1:j));
improvement = true;
end
end
end
end

% Compute total distance
min_distance = sum(D(sub2ind([n,n], path(1:end-1), path(2:end))));

% Return optimal path
optimal_path = path;

end