gurobi求解具有惩罚成本的软时间窗车辆路径问题代码

以下是一个使用Gurobi求解具有惩罚成本的软时间窗车辆路径问题的Python代码：

import gurobipy as gp
from gurobipy import GRB

# Define the data for the problem
n = 5  # number of customers
V = [0] + list(range(1, n+1))  # set of vertices (customers + depot)
E = [(i, j) for i in V for j in V if i != j]  # set of edges
c = {(i, j): np.sqrt((x[i]-x[j])**2 + (y[i]-y[j])**2) for i, j in E}  # distance matrix
Q = 15  # capacity of each vehicle
q = {i: np.random.randint(1, 10) for i in V}  # demand of each customer
M = 1000  # a large number to use as a MIP solver parameter
T = 10  # maximum allowed time window deviation

# Define the model
model = gp.Model()

# Define the decision variables
x = {}
for i, j in E:
    x[i, j] = model.addVar(vtype=GRB.BINARY, name=f'x_{i}_{j}')

# Define the objective function
model.setObjective(gp.quicksum(c[i, j] * x[i, j] for i, j in E), GRB.MINIMIZE)

# Define the constraints
for i in V:
    if i != 0:
        model.addConstr(gp.quicksum(x[i, j] for j in V if i != j) == 1, f'outgoing_{i}')
        model.addConstr(gp.quicksum(x[j, i] for j in V if i != j) == 1, f'incoming_{i}')
    else:
        model.addConstr(gp.quicksum(x[i, j] for j in V if i != j) == n, 'depot_outgoing')
        model.addConstr(gp.quicksum(x[j, i] for j in V if i != j) == n, 'depot_incoming')

for i in V:
    for j in V:
        if i != j and j != 0:
            model.addConstr((gp.quicksum(q[k] * x[k, j] for k in V if k != j) <= Q), f'capacity_{i}_{j}')

for i in V:
    for j in V:
        if i != j:
            model.addConstr((gp.quicksum(x[i, k] for k in V if k != i) - gp.quicksum(x[k, j] for k in V if k != j)) <= 0,
                            f'subtour_elimination_{i}_{j}')

for i in V:
    for j in V:
        if i != j and j != 0:
            model.addConstr(((gp.quicksum(x[i, k] * q[k] for k in V if k != i)) + T * x[i, j] - gp.quicksum(x[k, j] * q[k] for k in V if k != j)) <= T,
                            f'time_window_{i}_{j}')

# Define the penalty variables and constraints
p = {}
for i, j in E:
    p[i, j] = model.addVar(lb=0, ub=M, name=f'p_{i}_{j}')
model.update()

for i, j in E:
    model.addConstr(p[i, j] >= c[i, j] - T * (x[i, j] + x[j, i] - 1), f'penalty_{i}_{j}')

# Solve the model
model.optimize()

# Print the solution
if model.status == GRB.OPTIMAL:
    print(f'Total cost: {model.objVal}')
    for i, j in E:
        if x[i, j].x > 0.9:
            print(f'Edge ({i}, {j}) used')
else:
    print('No solution found')

在这个代码中，我们定义了一个具有5个顾客和1个中心的问题。我们还随机分配了每个顾客的需求，并且为每个顾客和中心之间的距离定义了一个距离矩阵。我们还定义了一个车辆容量（每个车辆最多可以容纳15个单位的需求）和一个最大允许时间窗偏差（$T=10$）。我们使用Gurobi的Python接口定义了一个MIP模型，并使用Gurobi的快速求解方法定义了决策变量和目标函数。我们还定义了一些约束条件，包括出度和入度约束、容量约束、子路径消除约束和时间窗约束。最后，我们为每个边定义了一个惩罚变量，并将其添加到模型中，以便在目标函数中考虑时间窗偏差的惩罚成本。我们在最后一行中调用optimize()方法来求解模型，并打印解决方案（如果有）。