tsp旅行商三十个城市matlab模拟退火

以下是使用Matlab模拟退火算法解决TSP旅行商问题的示例代码：

% TSP旅行商问题的30个城市的坐标
cities = [0.4000    0.4439
          0.2439    0.1463
          0.1707    0.2293
          0.2293    0.7610
          0.5171    0.9414
          0.8732    0.6536
          0.6878    0.5219
          0.8488    0.3609
          0.6683    0.2536
          0.6195    0.2634
          0.3443    0.2634
          0.6878    0.5219
          0.5878    0.7122
          0.2232    0.9732
          0.1098    0.1720
          0.5171    0.9414
          0.8732    0.6536
          0.6878    0.5219
          0.8488    0.3609
          0.6683    0.2536
          0.6195    0.2634
          0.3443    0.2634
          0.6878    0.5219
          0.5878    0.7122
          0.2232    0.9732
          0.1098    0.1720
          0.5171    0.9414
          0.8732    0.6536
          0.6878    0.5219];

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

% 模拟退火算法求解TSP问题
nIterations = 10000;
temperature = 1;
coolingRate = 0.999;
currentSolution = randperm(nCities);
bestSolution = currentSolution;
for i = 1:nIterations
    % 随机交换两个城市的位置
    newSolution = currentSolution;
    idx = randperm(nCities, 2);
    newSolution(idx(1)) = currentSolution(idx(2));
    newSolution(idx(2)) = currentSolution(idx(1));
    
    % 计算新解的成本
    currentCost = 0;
    for j = 1:nCities-1
        currentCost = currentCost + distances(currentSolution(j), currentSolution(j+1));
    end
    currentCost = currentCost + distances(currentSolution(nCities), currentSolution(1));
    newCost = 0;
    for j = 1:nCities-1
        newCost = newCost + distances(newSolution(j), newSolution(j+1));
    end
    newCost = newCost + distances(newSolution(nCities), newSolution(1));
    
    % 判断是否接受新解
    if newCost < currentCost
        currentSolution = newSolution;
        if newCost < distances(bestSolution(nCities), bestSolution(1))
            bestSolution = newSolution;
        end
    else
        delta = newCost - currentCost;
        acceptanceProbability = exp(-delta/temperature);
        if rand() < acceptanceProbability
            currentSolution = newSolution;
        end
    end
    
    % 降温
    temperature = temperature * coolingRate;
end

% 输出最优解
disp(bestSolution);

% 绘制最优解的路径
figure;
plot(cities(:,1), cities(:,2), 'o');
hold on;
for i = 1:nCities-1
    plot(cities(bestSolution(i:i+1),1), cities(bestSolution(i:i+1),2), 'r');
end
plot(cities([bestSolution(nCities), bestSolution(1)],1), cities([bestSolution(nCities), bestSolution(1)],2), 'r');
title('TSP旅行商问题的最优路径');