生产线平衡算法matlab,装配生产线任务平衡问题的遗传算法MATLAB源代码

以下是一个简单的基于遗传算法的装配生产线任务平衡问题的MATLAB源代码。这个算法旨在最小化每个工作站的空闲时间，同时保持任务的平衡。

% 初始化问题参数
num_jobs = 20; % 任务数量
num_stations = 4; % 工作站数量
processing_times = randi([1, 10], num_jobs, num_stations); % 随机生成处理时间

% 遗传算法参数
num_generations = 100; % 世代数量
population_size = 50; % 种群数量
mutation_rate = 0.01; % 变异率

% 初始化种群
population = zeros(population_size, num_jobs); % 每个染色体代表一个任务序列
for i = 1:population_size
    population(i, :) = randperm(num_jobs);
end

% 进化
for gen = 1:num_generations
    % 计算适应度
    fitness = zeros(population_size, 1); % 每个染色体的适应度
    for i = 1:population_size
        % 计算每个工作站的空闲时间
        station_times = zeros(1, num_stations);
        for j = 1:num_jobs
            station_times(1) = station_times(1) + processing_times(population(i, j), 1);
            for k = 2:num_stations
                station_times(k) = max(station_times(k), station_times(k-1)) + processing_times(population(i, j), k);
            end
        end
        % 计算适应度为最大空闲时间
        fitness(i) = max(station_times);
    end
    
    % 选择
    [~, idx] = sort(fitness); % 按适应度排序
    elite = population(idx(1:ceil(population_size/10)), :); % 保留前10%的精英
    parents = population(randperm(population_size, population_size-ceil(population_size/10)), :); % 随机选择90%的父代
    
    % 交叉
    children = zeros(size(parents)); % 子代数量等于父代数量
    for i = 1:2:population_size-ceil(population_size/10)
        p1 = parents(i, :);
        p2 = parents(i+1, :);
        pt = randi(num_jobs-1); % 随机选择交叉点
        c1 = [p1(1:pt), p2(pt+1:end)]; % 子代1
        c2 = [p2(1:pt), p1(pt+1:end)]; % 子代2
        children(i, :) = c1;
        children(i+1, :) = c2;
    end
    
    % 变异
    mutation_mask = rand(size(children)) < mutation_rate; % 随机生成变异掩码
    mutation_values = randi([1, num_jobs], size(children)); % 随机生成变异值
    children(mutation_mask) = mutation_values(mutation_mask); % 变异
    
    % 新种群
    population = [elite; children]; % 精英和子代组成新种群
end

% 输出结果
best_fitness = inf;
best_solution = zeros(1, num_jobs);
for i = 1:population_size
    % 计算每个工作站的空闲时间
    station_times = zeros(1, num_stations);
    for j = 1:num_jobs
        station_times(1) = station_times(1) + processing_times(population(i, j), 1);
        for k = 2:num_stations
            station_times(k) = max(station_times(k), station_times(k-1)) + processing_times(population(i, j), k);
        end
    end
    % 记录最佳解
    if max(station_times) < best_fitness
        best_fitness = max(station_times);
        best_solution = population(i, :);
    end
end
fprintf('最小化空闲时间为 %d\n', best_fitness);
disp('最佳任务序列为:');
disp(best_solution);