车辆调度问题matlab程序

车辆调度问题是一个经典的优化问题，其主要目标是将一组车辆分配到一系列任务中，使得任务完成时间最短、车辆的使用最优。针对这个问题，可以使用各种不同的优化算法进行求解，比如遗传算法、粒子群算法、蚁群算法等等。

以下是一个基于遗传算法的车辆调度问题的 MATLAB 程序：

% 车辆调度问题遗传算法求解程序

% 车辆和任务的数量
num_vehicles = 5;
num_tasks = 10;

% 距离矩阵，表示任意两个任务之间的距离
dist_matrix = rand(num_tasks, num_tasks);

% 初始化种群
pop_size = 50;
pop = zeros(pop_size, num_tasks);
for i = 1:pop_size
    pop(i, :) = randperm(num_tasks);
end

% 迭代次数和交叉率、变异率
num_generations = 100;
crossover_rate = 0.8;
mutation_rate = 0.2;

% 开始迭代
for i = 1:num_generations
    % 计算适应度，即每个个体的完成时间
    fitness = zeros(pop_size, 1);
    for j = 1:pop_size
        fitness(j) = calculate_fitness(pop(j, :), dist_matrix, num_vehicles);
    end
    
    % 选择操作，使用轮盘赌选择算法
    selected_pop = zeros(pop_size, num_tasks);
    for j = 1:pop_size
        selected_pop(j, :) = pop(roulette_wheel_selection(fitness), :);
    end
    
    % 交叉操作，使用基于顺序的交叉算子
    crossover_pop = zeros(pop_size, num_tasks);
    for j = 1:2:pop_size
        if rand() < crossover_rate
            [c1, c2] = sequential_crossover(selected_pop(j, :), selected_pop(j+1, :));
            crossover_pop(j, :) = c1;
            crossover_pop(j+1, :) = c2;
        else
            crossover_pop(j, :) = selected_pop(j, :);
            crossover_pop(j+1, :) = selected_pop(j+1, :);
        end
    end
    
    % 变异操作，使用交换变异算子
    mutate_pop = zeros(pop_size, num_tasks);
    for j = 1:pop_size
        if rand() < mutation_rate
            mutate_pop(j, :) = swap_mutation(crossover_pop(j, :));
        else
            mutate_pop(j, :) = crossover_pop(j, :);
        end
    end
    
    % 新种群
    pop = mutate_pop;
end

% 计算每个任务的完成时间
function completion_time = calculate_completion_time(schedule, dist_matrix)
    num_vehicles = size(schedule, 1);
    num_tasks = size(schedule, 2);
    current_time = zeros(num_vehicles, 1);
    completion_time = zeros(num_tasks, 1);
    for i = 1:num_tasks
        min_time = Inf;
        min_vehicle = 0;
        for j = 1:num_vehicles
            if current_time(j) + dist_matrix(schedule(j, i), i) < min_time
                min_time = current_time(j) + dist_matrix(schedule(j, i), i);
                min_vehicle = j;
            end
        end
        current_time(min_vehicle) = min_time;
        completion_time(i) = min_time;
    end
end

% 计算适应度，即完成时间
function fitness = calculate_fitness(schedule, dist_matrix, num_vehicles)
    completion_time = calculate_completion_time(reshape(schedule, [], num_vehicles)', dist_matrix);
    fitness = max(completion_time);
end

% 轮盘赌选择算法
function index = roulette_wheel_selection(fitness)
    total_fitness = sum(fitness);
    normalized_fitness = fitness / total_fitness;
    cumulative_fitness = cumsum(normalized_fitness);
    r = rand();
    index = find(cumulative_fitness >= r, 1);
end

% 基于顺序的交叉算子
function [child1, child2] = sequential_crossover(parent1, parent2)
    num_tasks = length(parent1);
    start = randi([1,num_tasks-1]);
    stop = randi([start+1,num_tasks]);
    child1 = zeros(1, num_tasks);
    child2 = zeros(1, num_tasks);
    child1(start:stop) = parent1(start:stop);
    child2(start:stop) = parent2(start:stop);
    index1 = stop + 1;
    index2 = stop + 1;
    while true
        if index1 > num_tasks
            index1 = 1;
        end
        if index2 > num_tasks
            index2 = 1;
        end
        if ~ismember(parent2(index1), child1)
            child1(index2) = parent2(index1);
            index2 = index2 + 1;
        end
        if ~ismember(parent1(index2), child2)
            child2(index1) = parent1(index2);
            index1 = index1 + 1;
        end
        if isequal(sort(child1), 1:num_tasks) && isequal(sort(child2), 1:num_tasks)
            break;
        end
    end
end

% 交换变异算子
function mutated_schedule = swap_mutation(schedule)
    num_tasks = length(schedule);
    indices = randperm(num_tasks, 2);
    mutated_schedule = schedule;
    mutated_schedule(indices(1)) = schedule(indices(2));
    mutated_schedule(indices(2)) = schedule(indices(1));
end

这个程序使用遗传算法求解车辆调度问题，其中包括了适应度函数、选择操作、交叉操作和变异操作等。具体来说，适应度函数计算每个个体的完成时间；选择操作使用轮盘赌选择算法；交叉操作使用基于顺序的交叉算子；变异操作使用交换变异算子。通过不断迭代，最终得到一组车辆分配方案，使得任务完成时间最短、车辆的使用最优。