python调用gurobi求解vrp

以下是一个简单的示例代码，演示如何使用Python和Gurobi求解VRP问题：

import gurobipy as gp
from gurobipy import GRB

# 定义VRP问题的数据
num_customers = 5
num_vehicles = 2
capacity = [20, 30]  # 每个车辆的容量
demand = [0, 5, 10, 15, 20]  # 每个客户的需求
location_x = [0, 10, 20, 30, 40]  # 每个客户的x坐标
location_y = [0, 10, 10, 20, 20]  # 每个客户的y坐标

# 创建模型
m = gp.Model('VRP')

# 创建变量：每个客户分配给哪个车辆
assignment = m.addVars(num_customers, num_vehicles, vtype=GRB.BINARY, name='assignment')

# 创建变量：车辆的路径
route = m.addVars(num_customers, num_customers, num_vehicles, vtype=GRB.BINARY, name='route')

# 创建约束：每个客户只能被分配给一个车辆
m.addConstrs((assignment.sum(i, '*') == 1 for i in range(num_customers)), name='assignment_constr')

# 创建约束：每个车辆的容量不能超过限制
m.addConstrs((demand[i] <= assignment.prod([i, j]) * capacity[j] for i in range(1, num_customers) for j in range(num_vehicles)), name='capacity_constr')

# 创建约束：车辆的路径必须是一条链
m.addConstrs((route.sum('*', i, j) == assignment[i, j] for i in range(num_customers) for j in range(num_vehicles)), name='route_constr1')
m.addConstrs((route.sum(i, '*', j) == assignment[i, j] for i in range(num_customers) for j in range(num_vehicles)), name='route_constr2')

# 创建约束：车辆的路径不能重复经过同一个客户
m.addConstrs((route[i, j, k] + route[j, i, k] <= 1 for i in range(num_customers) for j in range(num_customers) for k in range(num_vehicles) if i != j), name='route_constr3')

# 创建目标函数：最小化车辆的总行驶距离
obj = gp.quicksum(route[i, j, k] * ((location_x[i] - location_x[j]) ** 2 + (location_y[i] - location_y[j]) ** 2) ** 0.5 for i in range(num_customers) for j in range(num_customers) for k in range(num_vehicles))
m.setObjective(obj, GRB.MINIMIZE)

# 求解模型
m.optimize()

# 输出结果
if m.status == GRB.OPTIMAL:
    for k in range(num_vehicles):
        print('Vehicle', k+1, ':')
        for i in range(num_customers):
            if assignment[i,k].x > 0:
                print('  Customer', i+1, '->', end=' ')
                for j in range(num_customers):
                    if route[i,j,k].x > 0:
                        print(j+1, '->', end=' ')
                print('Customer', 1)

这个示例代码使用Gurobi Python API创建了一个VRP模型，并使用`m.optimize()`求解模型。模型的目标函数是最小化车辆的总行驶距离，约束条件包括每个客户只能被分配给一个车辆、每个车辆的容量不能超过限制、车辆的路径必须是一条链、车辆的路径不能重复经过同一个客户。最后，代码使用`print`语句输出了求解结果。