遗传模拟退火算法对流水车间调度优化,目标为最小化最大流程时间,输出甘特图和收敛图,matlab完整代码如何编写
时间: 2024-01-19 12:04:21 浏览: 50
这个问题的回答比较长,我尝试给出一个基础的框架供你参考,具体的实现需要根据实际情况进行调整和优化。
首先,我们需要定义问题的目标函数。在这个问题中,目标是最小化最大流程时间。因此,我们可以定义目标函数为最大流程时间的最小化,即:
```matlab
function [fitness, gantt_chart] = calculate_fitness(schedule, processing_time)
% schedule: 调度方案,每一行表示一台机器的调度顺序
% processing_time: 每个工件在每个机器上的加工时间,大小为 (num_jobs, num_machines)
% fitness: 目标函数值,即最大流程时间的最小化
% gantt_chart: 甘特图,大小为 (num_jobs, num_machines, 2),第三维度存储工件开始和结束的时间
num_jobs = size(processing_time, 1);
num_machines = size(processing_time, 2);
% 计算每个工件在每台机器上的开始时间和结束时间
start_time = zeros(num_jobs, num_machines);
end_time = zeros(num_jobs, num_machines);
for i = 1:num_machines
if i == 1
start_time(:, i) = 0;
else
start_time(:, i) = max(end_time(:, i-1));
end
end_time(:, i) = start_time(:, i) + processing_time(:, schedule(i));
end
% 计算每个工件的最大流程时间
max_flow_time = max(end_time, [], 2);
fitness = max(max_flow_time);
% 生成甘特图
gantt_chart = zeros(num_jobs, num_machines, 2);
for i = 1:num_machines
if i == 1
gantt_chart(:, i, 1) = 0;
else
gantt_chart(:, i, 1) = max(gantt_chart(:, i-1, 2));
end
gantt_chart(:, i, 2) = gantt_chart(:, i, 1) + processing_time(:, schedule(i));
end
end
```
接下来,我们需要定义遗传模拟退火算法的实现。这里我们采用遗传算法和模拟退火算法的混合策略,即首先使用遗传算法生成初始种群,然后使用模拟退火算法进行局部搜索。
```matlab
function [best_schedule, best_fitness, gantt_chart, convergence_curve] = GASA(processing_time, num_generations, population_size, mutation_rate, temperature, cooling_rate)
% processing_time: 每个工件在每个机器上的加工时间,大小为 (num_jobs, num_machines)
% num_generations: 遗传算法的迭代次数
% population_size: 种群大小
% mutation_rate: 变异率
% temperature: 初始温度
% cooling_rate: 冷却速率
% best_schedule: 最优调度方案
% best_fitness: 最优目标函数值
% gantt_chart: 最优调度方案对应的甘特图
% convergence_curve: 收敛曲线
num_jobs = size(processing_time, 1);
num_machines = size(processing_time, 2);
% 初始化种群
population = zeros(population_size, num_machines);
for i = 1:population_size
population(i, :) = randperm(num_jobs);
end
% 计算种群适应度
fitness = zeros(population_size, 1);
gantt_charts = zeros(population_size, num_jobs, num_machines, 2);
for i = 1:population_size
[fitness(i), gantt_charts(i,:,:,:)] = calculate_fitness(population(i,:), processing_time);
end
% 记录最优解和收敛曲线
best_fitness = min(fitness);
best_schedule = population(find(fitness == best_fitness, 1), :);
convergence_curve = zeros(num_generations, 1);
convergence_curve(1) = best_fitness;
% 遗传算法迭代
for i = 2:num_generations
% 选择
parent1 = tournament_selection(fitness);
parent2 = tournament_selection(fitness);
% 交叉
child = crossover(parent1, parent2);
% 变异
if rand() < mutation_rate
child = mutation(child);
end
% 替换最差个体
[worst_fitness, worst_index] = max(fitness);
[child_fitness, gantt_chart] = calculate_fitness(child, processing_time);
if child_fitness < worst_fitness
population(worst_index, :) = child;
fitness(worst_index) = child_fitness;
gantt_charts(worst_index,:,:,:) = gantt_chart;
end
% 更新最优解和收敛曲线
[best_fitness, best_index] = min(fitness);
best_schedule = population(best_index, :);
convergence_curve(i) = best_fitness;
end
% 模拟退火
current_schedule = best_schedule;
current_fitness = best_fitness;
current_temperature = temperature;
while current_temperature > 1e-6
% 随机生成相邻解
neighbor_schedule = generate_neighbor(current_schedule);
% 计算相邻解的适应度
[neighbor_fitness, neighbor_gantt_chart] = calculate_fitness(neighbor_schedule, processing_time);
% 判断是否接受相邻解
delta_fitness = neighbor_fitness - current_fitness;
if delta_fitness < 0 || rand() < exp(-delta_fitness/current_temperature)
current_schedule = neighbor_schedule;
current_fitness = neighbor_fitness;
gantt_chart = neighbor_gantt_chart;
end
% 降温
current_temperature = current_temperature * cooling_rate;
end
% 返回结果
best_schedule = current_schedule;
best_fitness = current_fitness;
gantt_chart = gantt_chart;
end
function parent = tournament_selection(fitness)
% 锦标赛选择,选择两个个体中适应度较好的一个
tournament_size = 2;
indices = randperm(length(fitness), tournament_size);
[~, index] = min(fitness(indices));
parent = indices(index);
end
function child = crossover(parent1, parent2)
% 交叉操作,采用部分映射交叉
num_jobs = length(parent1);
child = zeros(1, num_jobs);
% 随机选择交叉点
crossover_point1 = randi(num_jobs-1);
crossover_point2 = randi([crossover_point1+1, num_jobs]);
% 复制父代基因片段
child(crossover_point1:crossover_point2) = parent1(crossover_point1:crossover_point2);
% 映射父代2的基因到子代
for i = crossover_point1:crossover_point2
if ~ismember(parent2(i), child)
j = i;
while true
if child(j) == 0
child(j) = parent2(i);
break
else
j = find(parent1 == parent2(i));
end
end
end
end
end
function child = mutation(parent)
% 变异操作,采用交换操作
num_jobs = length(parent);
mutation_points = randperm(num_jobs, 2);
child = parent;
child(mutation_points) = parent(fliplr(mutation_points));
end
function neighbor = generate_neighbor(schedule)
% 随机生成相邻解,采用交换操作
num_jobs = length(schedule);
neighbor = schedule;
swap_points = randperm(num_jobs, 2);
neighbor(swap_points) = schedule(fliplr(swap_points));
end
```
最后,我们可以调用 `GASA` 函数来求解问题,并输出最优解和甘特图。
```matlab
% 生成随机的加工时间
num_jobs = 10;
num_machines = 3;
processing_time = rand(num_jobs, num_machines) * 10;
% 调用遗传模拟退火算法求解
num_generations = 100; % 遗传算法的迭代次数
population_size = 100; % 种群大小
mutation_rate = 0.1; % 变异率
temperature = 1000; % 初始温度
cooling_rate = 0.99; % 冷却速率
[best_schedule, best_fitness, gantt_chart, convergence_curve] = GASA(processing_time, num_generations, population_size, mutation_rate, temperature, cooling_rate);
% 输出结果
disp('Best schedule:');
disp(best_schedule);
disp('Best fitness:');
disp(best_fitness);
figure();
plot(convergence_curve);
xlabel('Generation');
ylabel('Fitness');
title('Convergence curve');
gantt(reshape(gantt_chart, [num_jobs*num_machines, 2]), 'ShowLabels', true);
```
这里我们使用了 `gantt` 函数来绘制甘特图,需要先下载并安装该函数库。
希望这个基础的框架能够帮助你完成流水车间调度优化问题的求解。
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