问约束优化:只适用于继续选择的第二项的条件？
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Stack Overflow用户

提问于 2022-08-26 03:32:31

回答 1查看 53关注 0票数 0

我有一个约束优化问题(特别是OR工具)。我正努力将不同运输供应商发送包裹的成本降到最低。它们中的每一个都有一定的维度约束，但一些航运供应商可以选择发送多个包裹，而且对于第二项产品，他们的价格更低。。

如何合并约束(或目标)？对选定的第一个项目收取一个价格，对所有其他项目收取不同的价格?如果有任何方法使其分层，奖金点-例如，为所选的第一个项目设置一个价格，通过第5项的另一个价格，以及对项目6+.的第三个价格。

以下是我的一些代码供参考--如果有什么事情看不见/您将如何改进，请告诉我：

def cost_optimisation()：

# Instantiate solver
solver = pywraplp.Solver.CreateSolver('SCIP')

# Get data
data = get_model_data()

### VARIABLES ###

# whether a courier can ship a parcel (T or F depending on whether the courier is eligible to ship the parcel)
parcel_by_courier = {}
for parcel_num in data['parcel_range']:
    for courier_num in data['courier_range']:
        parcel_by_courier[parcel_num, courier_num] = solver.BoolVar(f"parcel_{parcel_num}_courier_{courier_num}")

# the total number of parcels shipped by a courier
all_courier_sums = {}
for courier_num in data['courier_range']:
    all_courier_sums[courier_num] = solver.IntVar(0, len(data['parcel_range']), f"{data['courier_names'][courier_num]}_total_parcels_shipped")

print('Number of variables =', solver.NumVariables(), '\n')

### CONSTRAINTS ###

# add constraint that all parcels have to be shipped
for parcel_num in data['parcel_range']:
    solver.Add(sum(parcel_by_courier[parcel_num, courier_num] for courier_num in data['courier_range']) == 1)

# add weight & dimension constraints
for parcel_num in data['parcel_range']:
    for courier_num in data['courier_range']:
        solver.Add(parcel_by_courier[parcel_num, courier_num] * data['parcel_weights'][parcel_num] <= parcel_by_courier[parcel_num, courier_num] * data['courier_weights'][courier_num])
        solver.Add(parcel_by_courier[parcel_num, courier_num] * data['parcel_largest_dimensions'][parcel_num] <= parcel_by_courier[parcel_num, courier_num] * data['courier_largest_dimensions'][courier_num])

# add a constraint that couriers can only ship >1 parcel IF "further_item_allowed" = True
for courier_num in data['courier_range']:
    solver.Add(sum(parcel_by_courier[parcel_num, courier_num] for parcel_num in data['parcel_range']) <= 1 if data['courier_further_item_allowed'][courier_num] is False else sum(parcel_by_courier[parcel_num, courier_num] for parcel_num in data['parcel_range']) >= 0)

print('Number of constraints =', solver.NumConstraints(), '\n')

### OBJECTIVE ###

# Calculate costs for the objective and run the solver

total_base_item_cost = []

for courier_num in data['courier_range']:
    for parcel_num in data['parcel_range']:
        if all_courier_sums[courier_num] >= 2:
            if ???:
                total_base_item_cost.append(data['courier_first_item_pence'][courier_num] * parcel_by_courier[parcel_num, courier_num])
            else:
                total_base_item_cost.append(data['courier_further_item_pence'][courier_num] * parcel_by_courier[parcel_num, courier_num])
        else:
            total_base_item_cost.append(data['courier_first_item_pence'][courier_num] * parcel_by_courier[parcel_num, courier_num])

total_cost = sum(total_base_item_cost)

solver.Minimize(total_cost)
status = solver.Solve()

(很明显，???是我开始失去它的地方)

python

optimization

or-tools

回答 1

Stack Overflow用户

发布于 2022-08-26 05:41:53

测试IntVar值的结构，如if语句中的

if all_courier_sums[courier_num] >= 2:

都不管用。IntVar的值不是在求解器之外定义的，它只是一个容器，它的值将在解决方案期间确定。

首先，添加一个约束以强制all_courier_sums[courier_num]等于该信使的parcel_by_courier之和。

for courier_num in data['courier_range']:
    solver.Add(Sum(parcel_by_courier[parcel_num, courier_num] for parcel_num in data['parcel_range']) == all_courier_sums[courier_num])

为每个信使定义一个变量courier_cost[courier_num]。

然后，您可以为每个快递员创建一个成本公式，如下所示：

for courier_num in data['courier_range']:
    p1 = data['courier_first_item_pence'][courier_num]
    p2 = data['courier_further_item_pence'][courier_num]
    c1 = solver.IntVar(0, len(data['parcel_range']) * max_cost_per_parcel)
    solver.Add(c1 == (p1 * all_courier_sums[courier_num]))
    qty2 = solver.IntVar(0, len(data['parcel_range']))
    solver.AddMaxEquality(qty2, [0, (all_courier_sums[courier_num] - 1)])
    c2 = solver.IntVar(0, len(data['parcel_range']) * max_cost_per_parcel)
    solver.Add(c2 == ((p2 - p1) * qty2)
    solver.Add(courier_cost[courier_num] == c1 + c2)