Google OR-Tools 装箱问题：努力添加约束，以便装在箱中的所有物品必须具有相同的交付目的地

Question

正如标题所示，我正在使用 Google OR-Tools 来解决装箱问题。我想要求装在给定卡车中的所有订单都具有相同的交货目的地。以下是我尝试实现这一点，但似乎没有用：

# x[i, j] = 1 if item i is packed in bin j

x = {}
for i in data['orders']:
    for j in data['trucks']:
        x[(i, j)] = solver.IntVar(0, 1, 'x_%i_%i' % (i, j))

data['trucks'] = [0, 1, 2, 3, ...]
data['orders'] = [0, 1, 2, 3, ...]
data['delivery_county_id'] = [8, 8, 8, 1, 3, 2, ...]

from itertools import groupby

# Checks if all elements of list are equal
def all_equal(iterable):
    g = groupby(iterable)
    return next(g, True) and not next(g, False)

for j in data['trucks']:
    solver.Add( all_equal ( [ x[(i, j)] * data['delivery_county_id'][i] for i in data['orders'] if x[(i, j)] == 1 ] ) == True )

奇怪的是，我在执行代码时没有收到任何错误，但我的约束没有得到遵守。我不确定为什么会这样。任何帮助或建议将不胜感激！

Answer 1

我没有有效的 Python 安装，但这是在 c# 中完成的方式：

       public void initModel(CpModel model)
        {
            // Make up some data for the counties of the orders
            deliveryCountyId = new int[nOrders];
            for (int order = 0; order < nOrders; order++)
            {
                deliveryCountyId[order] = order % nCounties;
            }

            // Boolean variables for item shipped by truck
            x = new IntVar[nOrders, nTrucks];
            for (int order = 0; order < nOrders; order++)
            {
                for (int truck = 0; truck < nTrucks; truck++)
                {
                    x[order, truck] = model.NewBoolVar($"Item {order} (county {deliveryCountyId[order]}) in truck {truck}");
                }
            }

            // Boolean variables for truck carrying an item for county
            y = new IntVar[nTrucks, nCounties];
            for (int truck = 0; truck < nTrucks; truck++)
            {
                for (int county = 0; county < nCounties; county++)
                {
                    y[truck, county] = model.NewBoolVar($"Truck {truck} has item for county {county}");
                }
            }

            // Each item must be shipped by exactly one truck
            for (int order = 0; order < nOrders; order++)
            {
                List<IntVar> trucksForThisItem = new List<IntVar>();
                for (int truck = 0; truck < nTrucks; truck++)
                {
                    trucksForThisItem.Add(x[order, truck]);
                }
                model.Add(LinearExpr.Sum(trucksForThisItem) == 1);
            }

            // Compute which counties are in each truck
            for (int truck = 0; truck < nTrucks; truck++)
            {
                for (int county = 0; county < nCounties; county++)
                {
                    List<IntVar> ordersForCountyAndTruck = new List<IntVar>();
                    {
                        for (int order = 0; order < nOrders; order++)
                        {
                            if (deliveryCountyId[order] == county)
                            {
                                ordersForCountyAndTruck.Add(x[order, truck]);
                            }
                        }
                    }
                    if (ordersForCountyAndTruck.Count > 0)
                    {
                        model.AddMaxEquality(y[truck, county], ordersForCountyAndTruck);
                    }
                    else
                    {
                        model.Add(y[truck, county] == 0);
                    }
                }
            }

            // Each truck may carry items for only one county
            for (int truck = 0; truck < nTrucks; truck++)
            {
                List<IntVar> countiesPerTruck = new List<IntVar>();
                for (int county = 0; county < nCounties; county++)
                {
                    countiesPerTruck.Add(y[truck, county]);
                }
                model.Add(LinearExpr.Sum(countiesPerTruck) <= 1);
            }
        }
    }

您可以轻松地用 Python 表达等效的方法调用。

Answer 2

我使用了 Google-ortool 的 CP-SAT 求解器（python）。请看下面的代码，我添加了所需的约束

import random
from ortools.sat.python import cp_model as cp

trucks = list(range(1, 9))
orders = list(range(1, 51))
delivery_county_id = [random.randint(1, 8) for _ in orders]

order_country = list(zip(orders, delivery_county_id))

model = cp.CpModel()

dv_order_truck = {}
for ord_cntry in order_country:
    for trck in trucks:
        dv_order_truck[(ord_cntry, trck)] = model.NewBoolVar("")
        
# one order in one truck only
for ord_cntry in order_country:
    model.Add(sum(dv_order_truck[(ord_cntry, trck)] for trck in trucks) == 1)
    
# all orders packed into a given truck have the same delivery destination
dv_truck_country = {}
for trck in trucks:
    for cntry in set(delivery_county_id):
        dv_truck_country[trck, cntry] = model.NewBoolVar("")
       
for trck in trucks:
    for cntry in set(delivery_county_id):
        orders_inTruck_cntry = [v for k,v in dv_order_truck.items() if k[1] == trck and k[0][1] == cntry]
        model.AddMaxEquality(dv_truck_country[trck, cntry], orders_inTruck_cntry)
        
for trck in trucks:
    model.Add(sum(dv_truck_country[trck, cntry] for cntry in set(delivery_county_id)) == 1)
    
solver = cp.CpSolver()
solver.Solve(model)

# inspect the solution
solution = [(ord_cntry, trck) for ord_cntry in order_country for trck in trucks if solver.Value(dv_order_truck[(ord_cntry, trck)]) > 0]
sorted(solution, key = lambda x : x[0][1],reverse=True)