模拟退火算法matlab代码旅行商

模拟退火算法（Simulated Annealing）是一种全局优化算法，常用于解决旅行商问题（Traveling Salesman Problem，TSP）。下面是一个使用MATLAB实现的简单模拟退火算法解决TSP的代码示例：

% 旅行商问题的城市坐标
cities = [0 0; 1 1; 2 2; 3 3; 4 4];

% 计算城市之间的距离矩阵
numCities = size(cities, 1);
distMatrix = zeros(numCities, numCities);
for i = 1:numCities
    for j = 1:numCities
        distMatrix(i, j) = norm(cities(i, :) - cities(j, :));
    end
end

% 模拟退火算法参数设置
initialTemperature = 100; % 初始温度
finalTemperature = 0.1; % 终止温度
coolingRate = 0.99; % 冷却速率
numIterations = 1000; % 迭代次数

% 初始化当前解和最优解
currentSolution = randperm(numCities);
bestSolution = currentSolution;
currentCost = calculateCost(currentSolution, distMatrix);
bestCost = currentCost;

% 模拟退火算法主循环
temperature = initialTemperature;
for iter = 1:numIterations
    % 随机生成新解
    newSolution = generateNeighbor(currentSolution);
    newCost = calculateCost(newSolution, distMatrix);
    
    % 判断是否接受新解
    if acceptSolution(currentCost, newCost, temperature)
        currentSolution = newSolution;
        currentCost = newCost;
        
        % 更新最优解
        if currentCost < bestCost
            bestSolution = currentSolution;
            bestCost = currentCost;
        end
    end
    
    % 降温
    temperature = temperature * coolingRate;
end

% 输出结果
disp('最优解路径：');
disp(bestSolution);
disp('最优解路径长度：');
disp(bestCost);

% 计算路径长度的函数
function cost = calculateCost(solution, distMatrix)
    numCities = length(solution);
    cost = 0;
    for i = 1:numCities-1
        cost = cost + distMatrix(solution(i), solution(i+1));
    end
    cost = cost + distMatrix(solution(numCities), solution(1));
end

% 生成邻域解的函数（随机交换两个城市的位置）
function newSolution = generateNeighbor(solution)
    numCities = length(solution);
    idx1 = randi(numCities);
    idx2 = randi(numCities);
    while idx2 == idx1
        idx2 = randi(numCities);
    end
    newSolution = solution;
    newSolution([idx1 idx2]) = newSolution([idx2 idx1]);
end

% 判断是否接受新解的函数（Metropolis准则）
function accept = acceptSolution(currentCost, newCost, temperature)
    if newCost < currentCost
        accept = true;
    else
        deltaCost = newCost - currentCost;
        acceptProbability = exp(-deltaCost / temperature);
        accept = (rand() < acceptProbability);
    end
end

这段代码使用模拟退火算法求解旅行商问题，其中`cities`是城市的坐标，`distMatrix`是城市之间的距离矩阵。算法通过随机生成新解并根据Metropolis准则判断是否接受新解，同时根据温度进行降温，最终得到最优解路径和路径长度。