matlab多目标规划代码GA

您好！对于多目标规划问题，可以使用遗传算法（Genetic Algorithm，GA）来求解。下面是一个简单的MATLAB多目标规划问题的GA代码示例：

% 定义目标函数
function f = objFunc(x)
    f(1) = x(1)^2 + x(2)^2;    f(2) = (x(1)-1)^2 + x(2)^2;
end

% 定义GA参数
nVar = 2; % 变量个数
nObj = 2; % 目标个数
varMin = -10; % 变量最小值
varMax = 10; % 变量最大值
nPop = 50; % 种群大小
maxGen = 100; % 最大迭代次数

% 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(varMin, varMax, 1, nVar);
    pop(i).cost = objFunc(pop(i).position);
end

% 进化循环
for gen = 1:maxGen
    % 生成子代种群
    offspring = [];
    for k = 1:nPop
        % 选择父代
        p1 = BinaryTournament(pop);
        p2 = BinaryTournament(pop);
        % 交叉
        c = Cross(p1, p2);
        % 变异
        c = Mutate(c, varMin, varMax);
        % 计算子代适应度
        c.cost = objFunc(c.position);
        % 添加到子代种群
        offspring = [offspring; c];
    end
    
    % 合并父代和子代种群
    combinedPop = [pop; offspring];
    
    % 非支配排序和拥挤度距离计算
    combinedPop = NonDominatedSorting(combinedPop);
    combinedPop = CalculateCrowdingDistance(combinedPop);
    
    % 选择下一代种群
    pop = EnvironmentalSelection(combinedPop, nPop);
end

% 输出最优解
bestIndividual = pop(1);
disp('最优解：');
disp(bestIndividual.position);
disp('最优目标函数值：');
disp(bestIndividual.cost);

% 二元锦标赛选择
function p = BinaryTournament(pop)
    nPop = numel(pop);
    i1 = randi([1, nPop]);
    i2 = randi([1, nPop]);
    if pop(i1).cost(1) < pop(i2).cost(1) || (pop(i1).cost(1) == pop(i2).cost(1) && pop(i1).cost(2) < pop(i2).cost(2))
        p = pop(i1);
    else
        p = pop(i2);
    end
end

% 单点交叉
function c = Cross(p1, p2)
    nVar = numel(p1.position);
    c.position = zeros(1, nVar);
    for i = 1:nVar
        if rand <= 0.5
            c.position(i) = p1.position(i);
        else
            c.position(i) = p2.position(i);
        end
    end
end

% 多项式变异
function c = Mutate(c, varMin, varMax)
    nVar = numel(c.position);
    for i = 1:nVar
        if rand <= 0.1
            c.position(i) = varMin + rand * (varMax - varMin);
        end
    end
end

% 非支配排序
function pop = NonDominatedSorting(pop)
    nPop = numel(pop);
    F = {};
    F{1} = [];
    nF = 1;
    for i = 1:nPop
        pop(i).dominationSet = [];
        pop(i).dominatedCount = 0;
        for j = 1:nPop
            if Dominates(pop(i), pop(j))
                pop(i).dominationSet = [pop(i).dominationSet, j];
            elseif Dominates(pop(j), pop(i))
                pop(i).dominatedCount = pop(i).dominatedCount + 1;
            end
        end
        
        if pop(i).dominatedCount == 0
            pop(i).rank = 1;
            F{1} = [F{1}, i];
        end
    end
    
    while ~isempty(F{nF})
        Q = [];
        for i = F{nF}
            for j = pop(i).dominationSet
                pop(j).dominatedCount = pop(j).dominatedCount - 1;
                if pop(j).dominatedCount == 0
                    pop(j).rank = nF + 1;
                    Q = [Q, j];
                end
            end
        end
        
        nF = nF + 1;
        F{nF} = Q;
    end
end

% 支配关系判断
function flag = Dominates(p1, p2)
    flag = all(p1.cost <= p2.cost) && any(p1.cost < p2.cost);
end

% 计算拥挤度距离
function pop = CalculateCrowdingDistance(pop)
    nPop = numel(pop);
    nObj = numel(pop(1).cost);
    for j = 1:nObj
        [sortedCost, sortedIndex] = sort([pop.cost], 'ascend');
        pop(sortedIndex(1)).distance = inf;
        pop(sortedIndex(nPop)).distance = inf;
        for i = 2:nPop-1
            pop(sortedIndex(i)).distance = pop(sortedIndex(i)).distance + (sortedCost(i+1) - sortedCost(i-1))/(sortedCost(nPop) - sortedCost(1));
        end
    end
end

% 环境选择
function pop = EnvironmentalSelection(pop, nPop)
    nObj = numel(pop(1).cost);
    [sortedRank, sortedIndex] = sort([pop.rank]);
    front = sortedIndex(sortedRank == 1);
    if numel(front) <= nPop
        pop = pop(front);
    else
        pop = [];
        for i = 1:numel(front)
            if numel(pop) == nPop
                break;
            end
            if numel(pop) + numel(front) - i + 1 <= nPop
                pop = [pop; pop(front(i))];
            else
                [sortedDistance, sortedIndex] = sort([pop(front(i)).distance], 'descend');
                pop = [pop; pop(front(i))];
                pop = [pop; pop(sortedIndex(1:nPop-numel(pop)))];
                break;
            end
        end
    end
end

这个例子中，目标函数为两个二次函数，遗传算法通过多次迭代来优化目标函数，并输出最优解及最优目标函数值。您可以根据自己的具体问题修改目标函数和遗传算法的参数，以适应您的多目标规划问题。

希望对您有帮助！如果有任何问题，请随时向我提问。