Question

我正在尝试用来解决10个客户和5个仓库的多仓库车辆路径问题。当添加子行程约束时，求解器不再在合理的时间内找到最优解。当我在一定时间后停止求解器并检索最佳解时，他返回了不可行的解（连续变量，而整数是必需的）。我如何才能找到到目前为止找到的最佳可行解决方案，或者还有其他方法可以解决我的问题？我知道堆栈上也有类似的问题，但是它解决了gurobi求解器的问题。

在这里您可以找到部分代码以及10秒后他给我的输出。

# Definition of the route variables:
route_vars = plp.LpVariable.dicts("Route",(Places,Places,Trucks),0,None,plp.LpInteger)

# constraint 7: No subtours
for i in Places:
    for j in Places:
        for k in Trucks:
            if i != j:
                prob += u[i]-u[j] + (15)*route_vars[i][j][k] <= 14       


# Solve the problem
prob.solve(plp.PULP_CBC_CMD(maxSeconds=10))
print("status:", plp.LpStatus[prob.status])
print("optimal solution to the problem: ", plp.value(prob.objective))

# Print Results
for i in Places:
    for k in Trucks:
        for j in Places:
            if plp.value(route_vars[i][j][k]) != 0:
                print(plp.value(route_vars[i][j][k]), 'Truck ',k + 1, " from Place ",i+1, " to place ",j+1)

运行10秒后的输出：

status: Not Solved
optimal solution to the problem:  348.1102769976801
0.066666667 Truck  7  from Place  1  to place  11
0.93333333 Truck  8  from Place  1  to place  11
0.066666667 Truck  4  from Place  2  to place  6
0.93333333 Truck  7  from Place  2  to place  6
0.066666667 Truck  2  from Place  3  to place  7
0.93333333 Truck  8  from Place  3  to place  7
0.93333333 Truck  1  from Place  4  to place  5
0.033333333 Truck  3  from Place  4  to place  5
0.033333333 Truck  3  from Place  4  to place  9
0.93333333 Truck  1  from Place  5  to place  9
0.033333333 Truck  3  from Place  5  to place  4
0.033333333 Truck  4  from Place  5  to place  9
0.066666667 Truck  4  from Place  6  to place  2
0.93333333 Truck  7  from Place  6  to place  2
0.066666667 Truck  2  from Place  7  to place  3
0.93333333 Truck  8  from Place  7  to place  3
0.066666667 Truck  2  from Place  8  to place  10
0.93333333 Truck  8  from Place  8  to place  10
0.93333333 Truck  1  from Place  9  to place  4
0.033333333 Truck  3  from Place  9  to place  4
0.033333333 Truck  4  from Place  9  to place  5
0.066666667 Truck  2  from Place  10  to place  8
0.93333333 Truck  8  from Place  10  to place  8
0.066666667 Truck  7  from Place  11  to place  1
0.93333333 Truck  8  from Place  11  to place  1

如您所见，它给了我一个不可行的解决方案。

Answer 1

没有子行程的Miller-Tucker-Zemlin约束定义不正确。约束应该看起来像这样，其中N是客户数，D是仓库数。

# constraint 8: No subtours (Miller Tucker Zemlin)
for i in range(0,N):
    for j in range(0,N):
        for k in Trucks:
            if j != i:
                prob += u[i]-u[j] + (N+D+1)*route_vars[i][j][k] <= N+D

获得在时间限制后找到的最佳可行解决方案-纸浆

1 个答案: