matlab遗传算法解决旅行商问题

在MATLAB中使用遗传算法（Genetic Algorithm, GA）解决旅行商问题是将GA应用到组合优化问题的经典案例之一。以下是一个简化的遗传算法TSP解决方案示例：

% 导入所需库
if ~isToolboxAvailable('optimization')
    error('Please install the Optimization Toolbox to run this code.');
end

% 假设城市数据与之前一样
cities = load('city_data.mat');

% 遗传算法参数设置
popSize = 50; % 种群大小
ngen = 100; % 代数
mutationRate = 0.05; % 变异率
crossoverRate = 0.8; % 交叉率
fitnessFcn = @(x) tspFitnessFunction(x, cities); % TSP适应度函数

% 初始化种群
population = zeros(popSize, size(cities, 1));

% 遗传算法核心循环
for gen = 1:ngen
    % 评估当前种群的适应度
    fitnessValues = arrayfun(fitnessFcn, population);
    
    % 选择操作
    parents = selectParents(population, fitnessValues);
    
    % 交叉操作
    children = crossover(parents, crossoverRate);
    
    % 变异操作
    mutatedChildren = mutate(children, mutationRate);
    
    % 合并新生成的个体
    population = [population; mutatedChildren];
    
    % 清除过大的种群
    population = population(1:end-size(population, 1)+1, :);
    
    % 检查是否找到最优解
    if isBestSolutionFound(population, fitnessValues)
        break;
    end
end

% 提取最优解
[bestFitness, bestSolution] = findMinfitness(population, fitnessValues);
fprintf('Optimal path: %s\n', mat2str(bestSolution, ','));
fprintf('Path length: %.2f km\n', tspFitnessFunction(bestSolution, cities));

% tspFitnessFunction 函数用于计算适应度（路径长度）
function fitness = tspFitnessFunction(solution, cities)
    path_length = tsp(cities(sub2ind(size(cities), solution, 1)));
    fitness = 1 / path_length; % 对于最小化问题，用倒数作为适应度
end

% 辅助函数
function selected = selectParents(population, fitnessValues)
    % 随机选择或按适应度排序选取父母
    % 可选的进化策略有轮盘赌选择、锦标赛选择等
end
function children = crossover(parents, crossoverRate)
    % 实现两点交叉或其他交叉方式
end
function mutatedChildren = mutate(children, mutationRate)
    % 实现单点变异等变异操作
end