matlab多目标遗传算法代码

以下是一个简单的 Matlab 多目标遗传算法代码示例:

%% 多目标优化函数
function [y1, y2] = MO_func(x)
    y1 = sin(x(1));
    y2 = cos(x(2));
end

%% 多目标遗传算法主体
pop_size = 100; % 种群大小
n_var = 2; % 变量个数
n_obj = 2; % 目标个数
n_gen = 50; % 迭代次数

lower_bound = [-5, -5]; % 变量下界
upper_bound = [5, 5]; % 变量上界

pop = rand(pop_size, n_var) .* (upper_bound - lower_bound) + lower_bound; % 初始化种群
for i = 1:n_gen
    % 计算每个个体的适应度
    for j = 1:pop_size
        [y1(j), y2(j)] = MO_func(pop(j,:));
    end
    
    % 基于非支配排序的选择操作
    fronts = nondominated_sort([y1', y2']);
    new_pop = [];
    front_idx = 1;
    while size(new_pop, 1) + size(fronts{front_idx}, 1) <= pop_size
        new_pop = [new_pop; pop(fronts{front_idx}, :)];
        front_idx = front_idx + 1;
    end
    
    % 用拥挤度距离选择剩余的个体
    if size(new_pop, 1) < pop_size
        remaining = pop(setdiff(1:pop_size, fronts{1}), :);
        distances = crowding_distance([y1(fronts{1}), y2(fronts{1})]);
        [~, idx] = sort(distances, 'descend');
        new_pop = [new_pop; remaining(idx(1:pop_size-size(new_pop, 1)), :)];
    end
    
    % 基于交叉和变异的操作进行种群更新
    pop = crossover_mutation(new_pop);
end

%% 非支配排序
function fronts = nondominated_sort(obj_values)
    [n, m] = size(obj_values);
    fronts = cell(n, 1);
    S = cell(n, 1);
    n_dom = zeros(n, 1);
    rank = zeros(n, 1);
    
    for i = 1:n
        S{i} = [];
        n_dom(i) = 0;
        for j = 1:n
            if all(obj_values(i,:) <= obj_values(j,:)) && any(obj_values(i,:) < obj_values(j,:))
                S{i} = [S{i}, j];
            elseif all(obj_values(j,:) <= obj_values(i,:)) && any(obj_values(j,:) < obj_values(i,:))
                n_dom(i) = n_dom(i) + 1;
            end
        end
        
        if n_dom(i) == 0
            rank(i) = 1;
            fronts{1} = [fronts{1}, i];
        end
    end
    
    front_idx = 1;
    while ~isempty(fronts{front_idx})
        next_front = [];
        for i = fronts{front_idx}
            for j = S{i}
                n_dom(j) = n_dom(j) - 1;
                if n_dom(j) == 0
                    rank(j) = front_idx + 1;
                    next_front = [next_front, j];
                end
            end
        end
        
        front_idx = front_idx + 1;
        fronts{front_idx} = next_front;
    end
end

%% 拥挤度距离
function distances = crowding_distance(obj_values)
    [n, m] = size(obj_values);
    distances = zeros(n, 1);
    for i = 1:m
        [~, idx] = sort(obj_values(:,i));
        distances(idx(1)) = Inf;
        distances(idx(end)) = Inf;
        for j = 2:n-1
            distances(idx(j)) = distances(idx(j)) + (obj_values(idx(j+1),i) - obj_values(idx(j-1),i));
        end
    end
end

%% 交叉和变异
function new_pop = crossover_mutation(old_pop)
    [pop_size, n_var] = size(old_pop);
    new_pop = zeros(pop_size, n_var);
    for i = 1:pop_size
        parent1 = old_pop(randi(pop_size), :);
        parent2 = old_pop(randi(pop_size), :);
        child = crossover(parent1, parent2);
        child = mutation(child);
        new_pop(i, :) = child;
    end
end

function child = crossover(parent1, parent2)
    alpha = rand(1);
    child = alpha * parent1 + (1 - alpha) * parent2;
end

function child = mutation(parent)
    n_var = length(parent);
    child = parent;
    for i = 1:n_var
        if rand() < 0.1
            child(i) = rand() * (upper_bound(i) - lower_bound(i)) + lower_bound(i);
        end
    end
end

该代码实现了一个简单的二维多目标优化函数（sin 和 cos 函数），使用基于非支配排序和拥挤度距离的多目标遗传算法进行优化。你可以将 `MO_func` 函数替换为你自己的优化函数，并根据需要更改算法参数和操作。