利用遗传算法编写在matlab中解决VRP问题的代码

以下是使用遗传算法解决VRP问题的Matlab代码：

% VRP问题的遗传算法求解
clc;
clear;
close all;

% 初始化参数
pop_size = 50; % 种群大小
max_gen = 100; % 最大迭代次数
pc = 0.8; % 交叉概率
pm = 0.05; % 变异概率
city_num = 15; % 城市数量
truck_capacity = 100; % 货车容量
demand_range = [10, 30]; % 需求量范围
x_range = [0, 100]; % x坐标范围
y_range = [0, 100]; % y坐标范围
x = randi(x_range, 1, city_num); % x坐标
y = randi(y_range, 1, city_num); % y坐标
demand = randi(demand_range, 1, city_num); % 需求量

% 计算距离矩阵
dist = zeros(city_num);
for i = 1:city_num
    for j = 1:city_num
        dist(i, j) = sqrt((x(i)-x(j))^2 + (y(i)-y(j))^2);
    end
end

% 初始化种群
pop = zeros(pop_size, city_num+1);
for i = 1:pop_size
    pop(i, 1:city_num) = randperm(city_num);
    pop(i, city_num+1) = fitness(pop(i, 1:city_num), dist, demand, truck_capacity);
end

% 迭代优化
for gen = 1:max_gen
    % 计算适应度
    fitness_value = pop(:, city_num+1);
    [best_fitness, best_index] = min(fitness_value);
    average_fitness = mean(fitness_value);
    
    % 可视化
    plot(x(pop(best_index, 1:city_num)), y(pop(best_index, 1:city_num)), 'r-o');
    title(['Generation: ', num2str(gen), ', Best Distance: ', num2str(best_fitness)]);
    xlim(x_range);
    ylim(y_range);
    pause(0.01);
    
    % 选择
    fitness_prob = fitness_value / sum(fitness_value);
    cum_prob = cumsum(fitness_prob);
    new_pop = zeros(pop_size, city_num+1);
    for i = 1:pop_size
        index1 = find(rand() <= cum_prob, 1, 'first');
        index2 = find(rand() <= cum_prob, 1, 'first');
        parent1 = pop(index1, 1:city_num);
        parent2 = pop(index2, 1:city_num);
        
        % 交叉
        if rand() < pc
            [child1, child2] = crossover(parent1, parent2);
        else
            child1 = parent1;
            child2 = parent2;
        end
        
        % 变异
        if rand() < pm
            child1 = mutation(child1);
        end
        if rand() < pm
            child2 = mutation(child2);
        end
        
        % 计算适应度
        new_pop(i, 1:city_num) = child1;
        new_pop(i, city_num+1) = fitness(child1, dist, demand, truck_capacity);
        new_pop(i+1, 1:city_num) = child2;
        new_pop(i+1, city_num+1) = fitness(child2, dist, demand, truck_capacity);
    end
    
    % 更新种群
    pop = new_pop;
end

% 计算路径总长度
function d = fitness(path, dist, demand, capacity)
    num_trucks = 1;
    truck_load = 0;
    d = 0;
    for i = 1:length(path)-1
        j = path(i);
        k = path(i+1);
        d = d + dist(j, k);
        truck_load = truck_load + demand(k);
        if truck_load > capacity 
            num_trucks = num_trucks + 1;
            truck_load = demand(k);
        end
    end
end

% 交叉操作
function [child1, child2] = crossover(parent1, parent2)
    len = length(parent1);
    child1 = zeros(1, len);
    child2 = zeros(1, len);
    index1 = randi(len-1);
    index2 = randi([index1+1, len]);
    mask = zeros(1, len);
    mask(index1:index2) = 1;
    child1(mask==1) = parent1(index1:index2);
    child2(mask==1) = parent2(index1:index2);
    for i = 1:len
        if ~ismember(parent2(i), child1)
            empty_index = find(child1==0, 1, 'first');
            child1(empty_index) = parent2(i);
        end
        if ~ismember(parent1(i), child2)
            empty_index = find(child2==0, 1, 'first');
            child2(empty_index) = parent1(i);
        end
    end
end

% 变异操作
function mutant = mutation(individual)
    len = length(individual);
    index1 = randi(len);
    index2 = randi(len);
    mutant = individual;
    mutant(index1) = individual(index2);
    mutant(index2) = individual(index1);
end

使用该代码，您可以解决具有以下参数的VRP问题：

- 城市数量：15
- 货车容量：100
- 需求量范围：10-30
- x坐标范围：0-100
- y坐标范围：0-100

请注意，这仅是一个示例，您可以根据自己的需求更改参数。