matlab最优路径程序

以下是一个使用粒子群算法优化TSP最优路径的MATLAB程序示例：

% TSP城市坐标位置
cities = [0 0; 1 1; 2 2; 3 3; 4 4];

% 初始化粒子群算法参数
numParticles = 50; % 粒子数量
maxIterations = 100; % 最大迭代次数
c1 = 2; % 学习因子1
c2 = 2; % 学习因子2
w = 0.7; % 惯性权重

% 初始化粒子位置和速度
positions = zeros(numParticles, size(cities, 1));
velocities = zeros(numParticles, size(cities, 1));
for i = 1:numParticles
    positions(i, :) = randperm(size(cities, 1));
    velocities(i, :) = randperm(size(cities, 1));
end

% 初始化全局最优位置和适应度
globalBestPosition = positions(1, :);
globalBestFitness = tspFitness(positions(1, :), cities);

% 迭代优化
for iteration = 1:maxIterations
    % 更新粒子位置和速度
    for i = 1:numParticles
        % 更新速度
        velocities(i, :) = w * velocities(i, :) + c1 * rand(1, size(cities, 1)) .* (globalBestPosition - positions(i, :)) + c2 * rand(1, size(cities, 1)) .* (positions(i, :) - positions(i, :));
        
        % 更新位置
        [~, sortedIndices] = sort(velocities(i, :));
        positions(i, :) = positions(i, sortedIndices);
        
        % 更新个体最优位置和适应度
        fitness = tspFitness(positions(i, :), cities);
        if fitness < tspFitness(positions(i, :), cities)
            positions(i, :) = positions(i, :);
            fitness = tspFitness(positions(i, :), cities);
        end
        
        % 更新全局最优位置和适应度
        if fitness < globalBestFitness
            globalBestPosition = positions(i, :);
            globalBestFitness = fitness;
        end
    end
end

% 输出最优路径
optimalPath = cities(globalBestPosition, :);
disp('最优路径:');
disp(optimalPath);

% 计算最优路径长度
optimalPathLength = tspFitness(globalBestPosition, cities);
disp('最优路径长度:');
disp(optimalPathLength);

% 计算适应度函数
function fitness = tspFitness(position, cities)
    fitness = 0;
    for i = 1:size(position, 2)-1
        fitness = fitness + norm(cities(position(i), :) - cities(position(i+1), :));
    end
end