nsga2的精英选择策略的matlab代码示例

以下是一个简单的NSGA-II算法的MATLAB实现示例，包括精英选择策略：

function [pop, fronts] = nsga2(pop_size, num_vars, num_objs, num_gens, ...
    lower_bounds, upper_bounds, crossover_prob, mutation_prob)

    % 初始化种群
    pop = initialize_pop(pop_size, num_vars, num_objs, lower_bounds, upper_bounds);

    for gen = 1:num_gens
        % 计算适应度值和支配关系
        [pop, fronts] = evaluate_pop(pop);

        % 选择精英个体
        elites = select_elites(pop, fronts, pop_size);

        % 生成下一代种群
        new_pop = generate_offspring(pop, elites, pop_size, crossover_prob, mutation_prob, ...
            lower_bounds, upper_bounds);

        % 合并当前种群和新种群
        pop = [pop; new_pop];

        % 前沿分层排序
        [pop, fronts] = evaluate_pop(pop);
        pop = select_parents(pop, fronts, pop_size);

        % 显示当前进化代数和最优解
        best_ind = get_best_individual(pop);
        fprintf('Generation %d: Best Fitness = %f\n', gen, best_ind.objs);
    end
end

function elites = select_elites(pop, fronts, pop_size)
    elites = [];

    % 从前沿层数低到高依次选取精英个体
    for i = 1:length(fronts)
        front = fronts{i};

        % 如果精英个体数量已经达到种群规模，停止选择
        if length(elites) + length(front) > pop_size
            break;
        end

        % 选择当前前沿中的所有个体作为精英
        elites = [elites; pop(front)];
    end

    % 如果精英个体数量不足种群规模，用拥挤度分配算法选择剩余个体
    if length(elites) < pop_size
        remaining_pop = pop(~ismember(pop, elites));
        remaining_pop = crowding_distance_sort(remaining_pop);
        elites = [elites; remaining_pop(1:pop_size - length(elites))];
    end
end

function sorted_pop = crowding_distance_sort(pop)
    % 计算每个个体的拥挤度
    num_objs = length(pop(1).objs);
    num_inds = length(pop);
    distances = zeros(num_inds, num_objs);
    for i = 1:num_objs
        [~, idx] = sort([pop.objs]);
        distances(idx(1), i) = Inf;
        distances(idx(end), i) = Inf;
        for j = 2:num_inds-1
            distances(idx(j), i) = distances(idx(j), i) + ...
                (pop(idx(j+1)).objs(i) - pop(idx(j-1)).objs(i)) / ...
                (max([pop.objs(i)]) - min([pop.objs(i)]));
        end
    end

    % 按照拥挤度排序
    cd = sum(distances, 2);
    [~, idx] = sort(cd, 'descend');
    sorted_pop = pop(idx);
end

其中，`select_elites`函数实现了NSGA-II的精英选择策略。它首先从前沿层数低到高依次选取前沿中的所有个体作为精英，直到精英个体数量达到种群规模。如果精英个体数量不足种群规模，它会用拥挤度分配算法选择剩余个体。`crowding_distance_sort`函数实现了拥挤度分配算法，用于计算每个个体的拥挤度，并按照拥挤度排序。