针对特定约束循环遍历 PuLP 嵌套变量

Question

我有以下约束：

sum of (between p = 0 to p = 2) of X_sap <= A_sa

我的类是：

# s
site_classes = [1, 2]
# a
age_classes = [1, 2, 3]
# p
period_classes = [0, 1, 2]

age_areas = {1: {'age_range': '0to10', 1: 3000, 2: 8000},
             2: {'age_range': '11to20', 1: 6000, 2: 4000},
             3: {'age_range': '21to30', 1: 9000, 2: 7000}}

我的sap定义如下：

sap = []
for s in site_classes:
    for a in age_classes:
        for p in period_classes:
            sap.append(f'{s}_{a}_{p}')

以下是我创建 X_sap 的方式：

x_vars = lp.LpVariable.dicts("X", sap, lowBound=0, cat='Continuous')

这是我创建区域限制的方式

area_c_dict = {}
for s in site_classes:
    for a in age_classes:
        for p in period_classes:
            area_c_dict[f'{s}_{a}_{p}'] = age_areas[a][s]

我正在努力生成以这种方式输出的约束

X110 + X111 + X112 <= 3,000
X120 + X121 + X122 <= 6,000
X130 + X131 + X132 <= 9,000
X210 + X211 + X212 <= 8,000
X220 + X221 + X222 <= 4,000
X230 + X231 + X232 <= 7,000

我输出的变量是

area_c_dict = {'1_1_0': 3000, '1_1_1': 3000, '1_1_2': 3000, '1_2_0': 6000, '1_2_1': 6000, '1_2_2': 6000, '1_3_0': 9000, '1_3_1': 9000, '1_3_2': 9000, '2_1_0': 8000, '2_1_1': 8000, '2_1_2': 8000, '2_2_0': 4000, '2_2_1': 4000, '2_2_2': 4000, '2_3_0': 7000, '2_3_1': 7000, '2_3_2': 7000}


x_vars = {'1_1_0': X_1_1_0, '1_1_1': X_1_1_1, '1_1_2': X_1_1_2, '1_2_0': X_1_2_0, '1_2_1': X_1_2_1, '1_2_2': X_1_2_2, '1_3_0': X_1_3_0, '1_3_1': X_1_3_1, '1_3_2': X_1_3_2, '2_1_0': X_2_1_0, '2_1_1': X_2_1_1, '2_1_2': X_2_1_2, '2_2_0': X_2_2_0, '2_2_1': X_2_2_1, '2_2_2': X_2_2_2, '2_3_0': X_2_3_0, '2_3_1': X_2_3_1, '2_3_2': X_2_3_2}

如能提供任何帮助，我将不胜感激。我不确定如何在不破坏

的情况下循环遍历我的 x_vars

Answer 1

首先，像这样创建决策变量：

x_vars = lp.LpVariable.dicts("X", [(s,a,p) for s in site_classes for a in age_classes for p in period_classes] , lowBound=0, cat='Continuous')

然后使用 pulp 库中的 lpSum 函数进行约束：

for s in site_classes:
    for a in age_classes:
        prob += lp.lpSum(x_vars[(s,a,p)] for p in period_classes) <= age_areas[a][s]

prob 变量是 LpProblem class

的实例

演示如何为要在其他约束中使用的变量之和定义决策变量

定义一个自由变量

sum_var = lp.LpVariable.dicts("sum_of_variables", [(s,a) for s in site_classes for a in age_classes] , cat='Continuous')

现在为您的自由变量添加一个定义。

for s in site_classes:
    for a in age_classes:
        prob += lp.lpSum(x_vars[(s,a,p)] for p in period_classes) == sum_var[(s,a)]

现在您可以在约束中使用您的自由变量

for s in site_classes:
    for a in age_classes:
        prob += sum_var[(s,a)] <= age_areas[a][s]

这种方法可以提高线性程序的可读性，并且更容易增加模型的复杂性

针对特定约束循环遍历 PuLP 嵌套变量

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