VRP在matlab的代码

以下是一个简单的VRP问题解决方案的MATLAB代码：

clc
clear
close all

% 定义数据
n = 10; % 客户数量
m = 4; % 车辆数量
Q = 10; % 车辆容量
x = [0 1 1 2 4 5 6 7 8 9 3]; % 客户横坐标
y = [0 1 2 1 2 3 2 3 2 1 0]; % 客户纵坐标
c = zeros(n+1,n+1); % 距离矩阵
for i = 1:n+1
    for j = 1:n+1
        c(i,j) = sqrt((x(i)-x(j))^2+(y(i)-y(j))^2);
    end
end
c(1,:) = [];
c(:,1) = [];
d = randi([1,3],1,n); % 客户需求

% 定义模型
cvx_solver sedumi
cvx_begin
    variable x(n+1,n+1,m) binary % 定义决策变量
    minimize sum(sum(c.*x(:,:,1)))+sum(sum(c.*x(:,:,2)))+sum(sum(c.*x(:,:,3)))+sum(sum(c.*x(:,:,4))) % 目标函数
    subject to
        sum(x(1,:,1)) == 0; % 起点不是终点
        sum(x(:,1,1)) == 0; % 终点不是起点
        sum(x(:,1,1)) == sum(x(1,:,1)); % 一辆车只能出发一次
        sum(x(:,1,2)) == sum(x(1,:,2));
        sum(x(:,1,3)) == sum(x(1,:,3));
        sum(x(:,1,4)) == sum(x(1,:,4));
        for i = 1:n
            sum(x(i,:,1)) == sum(x(:,i,1));
            sum(x(i,:,2)) == sum(x(:,i,2));
            sum(x(i,:,3)) == sum(x(:,i,3));
            sum(x(i,:,4)) == sum(x(:,i,4));
            sum(x(i,:,1))+sum(x(:,i,1)) == 2*(sum(x(i,:,2))+sum(x(:,i,2))+sum(x(i,:,3))+sum(x(:,i,3))+sum(x(i,:,4))+sum(x(:,i,4)));
            sum(x(i,:,1)) <= 1;
            sum(x(:,i,1)) <= 1;
            sum(d(i)*x(i,:,1)) <= Q;
            sum(d(i)*x(:,i,1)) <= Q;
            sum(d(i)*x(i,:,2)) <= Q;
            sum(d(i)*x(:,i,2)) <= Q;
            sum(d(i)*x(i,:,3)) <= Q;
            sum(d(i)*x(:,i,3)) <= Q;
            sum(d(i)*x(i,:,4)) <= Q;
            sum(d(i)*x(:,i,4)) <= Q;
        end
cvx_end

% 可视化
figure(1)
plot(x,y,'r*')
hold on
for i = 1:n+1
    for j = 1:n+1
        for k = 1:m
            if x(i,j,k) == 1
                plot([x(i),x(j)],[y(i),y(j)],'b')
            end
        end
    end
end
title('VRP车辆路径规划')
xlabel('横坐标')
ylabel('纵坐标')

这段代码使用了CVX工具箱进行求解，可以通过调整数据和模型来解决不同规模的VRP问题。