利用遗传算法编写有多个货车的VRP问题的matlab代码

下面是利用遗传算法编写有多个货车的VRP问题的Matlab代码：

% VRP问题的遗传算法求解

% 初始化数据
num_customers = 50; % 客户数量
num_vehicles = 5; % 货车数量
capacity = 100; % 货车最大容量
demand = randi([1,10],num_customers,1); % 客户需求随机生成

% 计算距离矩阵
locations = rand(num_customers,2); % 客户位置随机生成
dist = zeros(num_customers+1,num_customers+1);
for i = 1:num_customers+1
    for j = 1:num_customers+1
        dist(i,j) = norm(locations(i,:)-locations(j,:));
    end
end

% 遗传算法参数
num_generations = 50;
population_size = 50;
mutation_rate = 0.05;

% 初始化种群
population = zeros(population_size,num_customers);
for i = 1:population_size
    population(i,:) = randperm(num_customers);
end

% 遗传算法主循环
for gen = 1:num_generations
    
    % 评估适应度
    fitness = zeros(population_size,1);
    for i = 1:population_size
        routes = decode(population(i,:),num_vehicles,demand,capacity);
        fitness(i) = evaluate(routes,dist);
    end
    
    % 选择父代
    [sorted_fitness,indices] = sort(fitness,'descend');
    parent_indices = indices(1:floor(population_size/2));
    
    % 交叉
    num_children = population_size - length(parent_indices);
    children = zeros(num_children,num_customers);
    for i = 1:num_children
        parent1 = parent_indices(randi(length(parent_indices)));
        parent2 = parent_indices(randi(length(parent_indices)));
        child = crossover(population(parent1,:),population(parent2,:));
        children(i,:) = mutate(child,mutation_rate);
    end
    
    % 更新种群
    new_population = [population(parent_indices,:); children];
    population = new_population;
    
    % 输出结果
    best_solution = decode(population(1,:),num_vehicles,demand,capacity);
    best_fitness = evaluate(best_solution,dist);
    fprintf('Generation %d: Best Fitness = %f\n',gen,best_fitness);
end

% 解码染色体，得到货车路径
function routes = decode(chromosome,num_vehicles,demand,capacity)
    num_customers = length(chromosome);
    routes = cell(num_vehicles,1);
    vehicle_loads = zeros(num_vehicles,1);
    vehicle_positions = ones(num_vehicles,1);
    for i = 1:num_customers
        customer = chromosome(i);
        assigned = false;
        for j = 1:num_vehicles
            if ~assigned && vehicle_loads(j)+demand(customer) <= capacity
                routes{j} = [routes{j} customer];
                vehicle_loads(j) = vehicle_loads(j) + demand(customer);
                assigned = true;
            end
        end
        if ~assigned
            error('Capacity exceeded');
        end
    end
end

% 计算路径长度
function length = route_length(route,dist)
    length = 0;
    for i = 1:length(route)-1
        length = length + dist(route(i),route(i+1));
    end
end

% 评估适应度
function fitness = evaluate(routes,dist)
    fitness = 0;
    for i = 1:length(routes)
        if ~isempty(routes{i})
            fitness = fitness + route_length([1 routes{i} 1],dist);
        end
    end
end

% 交叉
function child = crossover(parent1,parent2)
    num_customers = length(parent1);
    crossover_point = randi(num_customers-1);
    child = [parent1(1:crossover_point) parent2(crossover_point+1:end)];
end

% 变异
function child = mutate(parent,mutation_rate)
    num_customers = length(parent);
    if rand < mutation_rate
        indices = randsample(num_customers,2);
        child = parent;
        child(indices(1)) = parent(indices(2));
        child(indices(2)) = parent(indices(1));
    else
        child = parent;
    end
end

该代码实现了一个简单的遗传算法来解决有多个货车的VRP问题。该问题的目标是将一组客户分配给一组货车，使得每辆货车的总距离最小，同时满足每辆货车的容量限制。

首先，我们随机生成客户需求和位置，并计算距离矩阵。然后，我们使用遗传算法来搜索最佳解决方案。在每一代中，我们评估每个个体的适应度，选择父代进行交叉和变异，然后更新种群。最后，我们解码最佳个体，得到每辆货车的路径，并计算总距离。