用遗传算法解决柔性车间调度问题（10器件，6车间）用Matlab实现

柔性车间调度问题是一个经典的优化问题，其中遗传算法是一种常见的优化算法之一。下面是一个基本的遗传算法实现柔性车间调度问题的示例，使用Matlab编写。

第一步是定义问题。在柔性车间调度问题中，我们需要安排一组作业在一组机器上运行，以最小化运行时间。每个作业可以在多个机器上运行，每个机器可以同时运行多个作业。我们需要定义以下参数：

- 器件数量
- 车间数量
- 作业数量
- 作业可运行的机器集合及对应的运行时间
- 所有机器可同时运行的最大作业数量

在这个例子中，我们使用10个器件和6个车间。

第二步是定义遗传算法的参数。我们需要定义以下参数：

- 种群大小
- 最大迭代次数
- 交叉概率
- 变异概率

在这个例子中，我们使用100个个体，最大迭代次数为1000，交叉概率为0.8，变异概率为0.1。

第三步是初始化种群。我们需要生成一组随机的个体，每个个体代表一组作业的调度方案。在这个例子中，我们使用随机排列算法生成初始种群。

第四步是评估个体适应度。我们需要计算每个个体的适应度，即该调度方案的运行时间。在这个例子中，我们使用作业流水线算法计算适应度。

第五步是选择。我们需要选择一组适应度高的个体作为下一代种群的父代。在这个例子中，我们使用轮盘赌选择算法选择父代。

第六步是交叉。我们需要使用交叉算法将父代个体组合成新的子代个体。在这个例子中，我们使用单点交叉算法。

第七步是变异。我们需要使用变异算法对子代个体进行变异，以增加种群的多样性。在这个例子中，我们使用随机重排变异算法。

最后，我们重复执行第四到第七步，直到达到最大迭代次数或找到最优解为止。

下面是一个Matlab代码示例，演示如何使用遗传算法解决柔性车间调度问题。

% Define problem parameters
nJobs = 10; % Number of jobs
nMachines = 6; % Number of machines
nOperations = 2; % Number of operations per job
machines = {[1 2 3], [1 2 3], [2 3 4], [2 3 4], [3 4 5], [3 4 5]}; % Machines that each operation can run on
times = {[4 5], [5 6], [4 6], [5 7], [6 8], [7 9]}; % Times for each operation on each machine
maxLoad = 2; % Maximum number of jobs that can run on each machine at the same time

% Define genetic algorithm parameters
popSize = 100; % Population size
maxIter = 1000; % Maximum number of iterations
crossProb = 0.8; % Crossover probability
mutProb = 0.1; % Mutation probability

% Initialize population
pop = zeros(nJobs, nOperations, popSize);
for i = 1:popSize
    pop(:,:,i) = randperm(nMachines, nJobs*nOperations);
end

% Evaluate fitness
fitness = zeros(popSize, 1);
for i = 1:popSize
    fitness(i) = pipelineFitness(pop(:,:,i), machines, times);
end

% Main loop
for iter = 1:maxIter
    % Selection
    parents = rouletteSelection(pop, fitness);

    % Crossover
    children = zeros(nJobs, nOperations, popSize);
    for i = 1:popSize/2
        [children(:,:,i*2-1), children(:,:,i*2)] = singlePointCrossover(parents(:,:,i*2-1), parents(:,:,i*2), crossProb);
    end

    % Mutation
    for i = 1:popSize
        if rand < mutProb
            children(:,:,i) = randomShuffleMutation(children(:,:,i));
        end
    end

    % Evaluate fitness
    for i = 1:popSize
        fitness(i) = pipelineFitness(children(:,:,i), machines, times);
    end

    % Replacement
    [pop, fitness] = elitistReplacement(pop, children, fitness);

    % Display progress
    [bestFitness, bestIdx] = min(fitness);
    bestSolution = pop(:,:,bestIdx);
    fprintf('Iteration %d, best fitness = %f\n', iter, bestFitness);
end

% Evaluate fitness using pipeline algorithm
function fitness = pipelineFitness(schedule, machines, times)
    nJobs = size(schedule, 1);
    nMachines = length(machines);
    nOperations = size(schedule, 2);

    % Calculate machine loads
    load = zeros(nMachines, 1);
    for i = 1:nJobs
        for j = 1:nOperations
            machine = machines{j}(schedule(i,j));
            load(machine) = load(machine) + 1;
        end
    end

    % Calculate makespan
    makespan = 0;
    for i = 1:nMachines
        if load(i) > makespan
            makespan = load(i);
        end
    end

    % Calculate flowtime
    flowtime = 0;
    for i = 1:nJobs
        startTimes = zeros(1, nOperations);
        endTimes = zeros(1, nOperations);
        for j = 1:nOperations
            machine = machines{j}(schedule(i,j));
            if j == 1
                startTimes(j) = 0;
            else
                startTimes(j) = endTimes(j-1);
            end
            endTimes(j) = startTimes(j) + times{j}(machine);
        end
        flowtime = flowtime + endTimes(nOperations);
    end

    % Calculate tardiness
    tardiness = 0;

    % Calculate fitness
    fitness = makespan + flowtime + tardiness;
end

% Roulette wheel selection
function parents = rouletteSelection(pop, fitness)
    nParents = size(pop, 3);
    parents = zeros(size(pop(:,:,1)), nParents);
    totalFitness = sum(fitness);
    if totalFitness == 0
        % Handle zero fitness case
        parents = pop(:,:,randperm(size(pop,3), nParents));
        return;
    end
    prob = fitness./totalFitness;
    cumProb = cumsum(prob);
    for i = 1:nParents
        r = rand;
        j = find(cumProb >= r, 1);
        parents(:,:,i) = pop(:,:,j);
    end
end

% Single point crossover
function [child1, child2] = singlePointCrossover(parent1, parent2, prob)
    nJobs = size(parent1, 1);
    nOperations = size(parent1, 2);
    if rand > prob
        child1 = parent1;
        child2 = parent2;
        return;
    end
    point = randi(nJobs-1);
    child1 = [parent1(1:point,:); parent2(point+1:end,:)];
    child2 = [parent2(1:point,:); parent1(point+1:end,:)];
end

% Random shuffle mutation
function child = randomShuffleMutation(parent)
    nJobs = size(parent, 1);
    nOperations = size(parent, 2);
    idx1 = randi(nJobs);
    idx2 = randi(nJobs);
    while idx2 == idx1
        idx2 = randi(nJobs);
    end
    child = parent;
    temp = child(idx1,:);
    child(idx1,:) = child(idx2,:);
    child(idx2,:) = temp;
end

% Elitist replacement
function [pop, fitness] = elitistReplacement(pop, children, fitness)
    nParents = size(pop, 3);
    nChildren = size(children, 3);
    totalPop = cat(3, pop, children);
    totalFitness = cat(1, fitness, zeros(nChildren, 1));
    [~, idx] = sort(totalFitness);
    pop = totalPop(:,:,idx(1:nParents));
    fitness = totalFitness(idx(1:nParents));
end