多目标遗传算法 matlab代码

遗传算法是一种常用的优化算法，用于解决多目标优化问题。在Matlab中，可以使用多种方式实现多目标遗传算法。以下是一个简单的示例代码：

% 定义问题参数
nVar = 10; % 变量个数
nObj = 2; % 目标个数
VarSize = [1 nVar]; % 变量维度

% 定义遗传算法参数
MaxIt = 100; % 最大迭代次数
nPop = 50; % 种群大小
pc = 0.8; % 交叉概率
nc = 2*round(pc*nPop/2); % 交叉个体数
pm = 0.3; % 变异概率
nm = round(pm*nPop); % 变异个体数

% 初始化种群
empty_individual.Position = [];
empty_individual.Cost = [];
pop = repmat(empty_individual, nPop, 1);
for i = 1:nPop
    pop(i).Position = unifrnd(-5, 5, VarSize);
    pop(i).Cost = YourCostFunction(pop(i).Position); % 计算个体适应度值
end

% 进化循环
for it = 1:MaxIt
    % 生成子代种群
    offspring = repmat(empty_individual, nPop, 1);
    for k = 1:2:nPop
        % 选择父代个体
        p1 = TournamentSelection(pop);
        p2 = TournamentSelection(pop);

        % 交叉
        [offspring(k).Position, offspring(k+1).Position] = ...
            crossover(p1.Position, p2.Position);

        % 变异
        offspring(k).Position = mutate(offspring(k).Position);
        offspring(k+1).Position = mutate(offspring(k+1).Position);

        % 计算子代适应度值
        offspring(k).Cost = YourCostFunction(offspring(k).Position);
        offspring(k+1).Cost = YourCostFunction(offspring(k+1).Position);
    end

    % 合并父代和子代种群
    temp_pop = [pop; offspring];

    % 非支配排序
    fronts = NonDominatedSorting(temp_pop);

    % 计算拥挤度距离
    temp_pop = CalcCrowdingDistance(temp_pop, fronts);

    % 选择下一代种群
    pop = EnvironmentalSelection(temp_pop, nPop);
end

% 输出最优解
best_solution = pop(1);
disp(['Best Objective 1: ' num2str(best_solution.Cost(1))]);
disp(['Best Objective 2: ' num2str(best_solution.Cost(2))]);

% 定义交叉操作函数
function [child1, child2] = crossover(parent1, parent2)
    alpha = rand(size(parent1));
    child1 = alpha.*parent1 + (1-alpha).*parent2;
    child2 = alpha.*parent2 + (1-alpha).*parent1;
end

% 定义变异操作函数
function mutated = mutate(solution)
    sigma = 0.1*(max(solution)-min(solution)); % 变异幅度
    mutated = solution + sigma.*randn(size(solution));
end

% 定义计算适应度函数
function cost = YourCostFunction(solution)
    % 这里替换为你的目标函数计算方法，返回一个包含所有目标值的向量
    % cost = [obj1, obj2, ..., objN]
    % 例如：
    % cost = [solution(1)^2, solution(2)^2];
end

% 定义锦标赛选择操作函数
function winner = TournamentSelection(pop)
    k = 2; % 锦标赛规模
    nPop = size(pop, 1);
    indices = randperm(nPop, k);
    tournament_pop = pop(indices);
    [~, idx] = min([tournament_pop.Cost]); % 选择适应度最小的个体
    winner = tournament_pop(idx);
end

% 定义非支配排序函数
function fronts = NonDominatedSorting(pop)
    nPop = size(pop, 1);
    S = cell(nPop, 1);
    n = zeros(nPop, 1);
    rank = zeros(nPop, 1);
    
    for i = 1:nPop
        S{i} = [];
        n(i) = 0;
        for j = 1:nPop
            if i == j
                continue;
            end
            if dominates(pop(i), pop(j))
                S{i} = [S{i} j];
            elseif dominates(pop(j), pop(i))
                n(i) = n(i) + 1;
            end
        end
        if n(i) == 0
            rank(i) = 1;
        end
    end
    
    iFront = 1;
    fronts = {};
    while true
        if isempty(find(rank == iFront, 1))
            break;
        end
        front = find(rank == iFront);
        for i = front
            for j = S{i}
                n(j) = n(j) - 1;
                if n(j) == 0
                    rank(j) = iFront + 1;
                end
            end
        end
        fronts{iFront} = front;
        iFront = iFront + 1;
    end
end

% 定义支配关系判断函数
function result = dominates(solution1, solution2)
    cost1 = solution1.Cost;
    cost2 = solution2.Cost;
    result = all(cost1 <= cost2) && any(cost1 < cost2);
end

% 定义计算拥挤度距离函数
function pop = CalcCrowdingDistance(pop, fronts)
    nPop = size(pop, 1);
    nObj = numel(pop(1).Cost);
    
    for k = 1:numel(fronts)
        front = fronts{k};
        nFront = numel(front);
        
        % 初始化拥挤度距离
        for i = front
            pop(i).CrowdingDistance = 0;
        end
        
        % 计算每个目标的排序后数值
        for j = 1:nObj
            [~, idx] = sort([pop(front).Cost], 'ascend');
            pop(front(idx(1))).CrowdingDistance = inf;
            pop(front(idx(nFront))).CrowdingDistance = inf;
            
            for i = 2:nFront-1
                pop(front(idx(i))).CrowdingDistance = ...
                    pop(front(idx(i))).CrowdingDistance + ...
                    (pop(front(idx(i+1))).Cost(j) - pop(front(idx(i-1))).Cost(j)) / ...
                    (max([pop(front).Cost(j)]) - min([pop(front).Cost(j)]));
            end
        end
    end
end

% 定义环境选择操作函数
function pop = EnvironmentalSelection(pop, nPop)
    nObj = numel(pop(1).Cost);
    
    % 计算总的适应度值
    F = [pop.CrowdingDistance]';
    F(isinf(F)) = 0;
    total_fitness = sum(F);
    
    % 计算每个个体的选择概率
    p = F / total_fitness;
    
    % 按照选择概率选择个体
    pop = pop(RouletteWheelSelection(p, nPop));
end

% 定义轮盘赌选择操作函数
function idx = RouletteWheelSelection(p, n)
    c = cumsum(p);
    r = rand(n, 1);
    [~, idx] = histc(r, [0; c]);
end

以上代码实现了一个简单的多目标遗传算法，你可以根据自己的具体问题进行相应的修改和扩展。