30城市遗传算法matlab程序

很高兴能够帮助你！以下是一个基于遗传算法的 MATLAB 程序，用于解决旅行商问题（TSP）中的30个城市情况。

% 定义城市坐标
cityCoords = [...
    37 52; 49 49; 52 64; 20 26; 40 30; ...
    21 47; 17 63; 31 62; 52 33; 51 21; ...
    42 41; 31 32; 5 25; 12 42; 36 16; ...
    52 41; 27 23; 17 33; 13 13; 57 58; ...
    62 42; 42 57; 16 57; 8 52; 7 38; ...
    27 68; 30 48; 43 67; 58 48; 58 27];

% 定义遗传算法参数
populationSize = 100; % 种群大小
numGenerations = 500; % 迭代次数
mutationRate = 0.02; % 变异率

% 初始化种群
population = createPopulation(populationSize, size(cityCoords,1));

% 开始迭代
for generation = 1:numGenerations
    % 计算适应度
    fitness = calculateFitness(population, cityCoords);
    
    % 打印当前最优解
    [bestFitness, bestIndex] = min(fitness);
    bestSolution = population(bestIndex, :);
    fprintf('代数 %d: 最短路径 = %f\n', generation, bestFitness);
    
    % 选择下一代种群
    newPopulation = selection(population, fitness);
    
    % 交叉产生子代
    newPopulation = crossover(newPopulation);
    
    % 变异
    newPopulation = mutation(newPopulation, mutationRate);
    
    % 更新种群
    population = newPopulation;
end

% 绘制最优路径
figure;
bestSolution = [bestSolution, bestSolution(1)]; % 回到起点
plot(cityCoords(:,1), cityCoords(:,2), 'ko', 'MarkerSize', 10);
hold on;
plot(cityCoords(bestSolution,1), cityCoords(bestSolution,2), 'r-', 'LineWidth', 1.5);
title('最优路径');
xlabel('横坐标');
ylabel('纵坐标');

% 创建初始种群的函数
function population = createPopulation(populationSize, numCities)
    population = zeros(populationSize, numCities);
    for i = 1:populationSize
        population(i,:) = randperm(numCities);
    end
end

% 计算适应度的函数
function fitness = calculateFitness(population, cityCoords)
    numCities = size(cityCoords, 1);
    numIndividuals = size(population, 1);
    fitness = zeros(numIndividuals, 1);
    for i = 1:numIndividuals
        individual = population(i,:);
        totalDistance = 0;
        for j = 1:numCities-1
            cityA = individual(j);
            cityB = individual(j+1);
            distance = norm(cityCoords(cityA,:) - cityCoords(cityB,:));
            totalDistance = totalDistance + distance;
        end
        fitness(i) = 1 / totalDistance;
    end
end

% 选择操作的函数
function newPopulation = selection(population, fitness)
    numIndividuals = size(population, 1);
    numParents = round(numIndividuals/2);
    [~, sortedIndices] = sort(fitness, 'descend');
    selectedIndices = sortedIndices(1:numParents);
    newPopulation = population(selectedIndices,:);
end

% 交叉操作的函数
function newPopulation = crossover(population)
    numParents = size(population, 1);
    numOffsprings = size(population, 1) - numParents;
    shuffleIndices = randperm(numParents);
    parents = population(shuffleIndices,:);
    offsprings = zeros(numOffsprings, size(population, 2));
    for i = 1:numOffsprings
        parentA = parents(i,:);
        parentB = parents(i+numOffsprings,:);
        crossoverPoint = randi([1, size(population, 2)-1]);
        offspring = [parentA(1:crossoverPoint), parentB(crossoverPoint+1:end)];
        offsprings(i,:) = offspring;
    end
    newPopulation = [population; offsprings];
end

% 变异操作的函数
function newPopulation = mutation(population, mutationRate)
    numGenes = size(population, 2);
    numMutations = round(mutationRate * size(population, 1) * numGenes);
    newPopulation = population;
    for i = 1:numMutations
        individualIndex = randi(size(population, 1));
        geneIndexA = randi(numGenes);
        geneIndexB = randi(numGenes);
        newPopulation(individualIndex, [geneIndexA, geneIndexB]) = ...
            newPopulation(individualIndex, [geneIndexB, geneIndexA]);
    end
end

请注意，此程序仅提供了一种解决方法，并且可能不是最优解。你可以根据需要对其进行调整和优化。希望对你有所帮助！如有任何问题，请随时提出。