提问人：Ali E 提问时间：11/9/2023 更新时间：11/9/2023 访问量：16
如何产生所需数量的纸浆。Python中的LpVariable（如x11、x12、x21、x22等）并将它们存储在字典中？
How to generate desired number of pulp.LpVariable in Python (such as x11, x12, x21, x22 and so on) and store them in a dictionary?
问：
我想定义一定数量的数学 x 变量。我使用术语“数学 x 变量”，因为这些是我想用 Python 变量表示的数学变量。我需要这些 x 值，以便稍后在 LP（线性规划）问题中使用。
在 Python PuLP 库中，我们可以这样生成多个 x 变量：
x = {i: LpVariable(name=f"x{i}", lowBound=0) for i in range(1, 5)}
然后当我们使用时，我们得到字典：print(x)
{1： x1， 2： x2， 3： x3， 4： x4}
其中每个 x 值（如 x1、x2 等）都是类型。pulp.pulp.LpVariable
但是我想要一个代码来生成 x 的多个分支。我可以用它来生成我想要的尽可能多的分支。
我想将所有 x 值（例如 x11、x12、x21、x22...）存储在字典中。
这是我写的解决方案：
# Defining the decision variables
# Here, we create a nested dictionary to store the x variables
# Using a dictionary also allows us to store the indice values
x = {i:
{j:
{k:
{l:
LpVariable(name=f"x{i}{j}{k}{l}", lowBound=0, cat="Integer")
for l in range(1, 3) }
for k in range(1, 4) }
for j in range(1, 4) }
for i in range(1, 3) }
此解决方案打印为：
{1: {1: {1: {1: x1111, 2: x1112},
2: {1: x1121, 2: x1122},
3: {1: x1131, 2: x1132}},
2: {1: {1: x1211, 2: x1212},
2: {1: x1221, 2: x1222},
3: {1: x1231, 2: x1232}},
3: {1: {1: x1311, 2: x1312},
2: {1: x1321, 2: x1322},
3: {1: x1331, 2: x1332}}},
2: {1: {1: {1: x2111, 2: x2112},
2: {1: x2121, 2: x2122},
3: {1: x2131, 2: x2132}},
2: {1: {1: x2211, 2: x2212},
2: {1: x2221, 2: x2222},
3: {1: x2231, 2: x2232}},
3: {1: {1: x2311, 2: x2312},
2: {1: x2321, 2: x2322},
3: {1: x2331, 2: x2332}}}}
这就是我想要的。现在的问题是，我想自动完成同样的工作。因此，让我们用这样的函数来假设;
def generate_nested_variables(dimension_number, dimension_ranges)
这将生成具有所需范围的所需数量的维度（嵌套）。所以说
def generate_nested_variables(2, [3,5])
会打印出这个：
{1: {1: x11, 2: x12, 3: x13, 4: x14, 5: x15},
2: {1: x21, 2: x22, 3: x23, 4: x24, 5: x25},
3: {1: x31, 2: x32, 3: x33, 4: x34, 5: x35}}
答：
0赞
AirSquid
11/9/2023
#1
这看起来真的像是你试图以艰难的方式进行多维约束。
您应该分别为多个约束设置索引集，然后使用该功能来构造变量 - 这要容易得多，而且您不必为字符串标记而烦恼。然后，以后按多维索引中的项目索引变量要容易得多。我不确定你会如何在你的例子中做到这一点。.dicts()pulp
这里有一些想法。如果你在我的个人资料中搜索类似的东西，我相信你会找到其他人。LpVariable.dicts
法典：
import pulp as pl
from itertools import product
# some indexing sets (or dimensions)
d1 = [4, 5, 6]
d2_size = 4
d2 = list(range(1, d2_size + 1))
d3 = ['red', 'green', 'blue']
d123 = list(product(d1, d2, d3))
# declare the LP
prob = pl.LpProblem('example')
# make some variables
x = pl.LpVariable.dicts('x', indices=d1)
y = pl.LpVariable.dicts('y', indices=[(i, j) for i in d1 for j in d2])
z = pl.LpVariable.dicts('z', indices = d123)
# some example constraints
prob += x[4] >= 3.4
# sum over d2 dimension for each i in d1
for i in d1:
prob += sum(y[i, j] for j in d2) >= 1.2
# sum over all the greens in z
greens = [(i, j, k) for i, j, k in d123 if k=='green']
prob += sum(z[green] for green in greens) <= 4
print(prob)
输出：
example:
MINIMIZE
None
SUBJECT TO
_C1: x_4 >= 3.4
_C2: y_(4,_1) + y_(4,_2) + y_(4,_3) + y_(4,_4) >= 1.2
_C3: y_(5,_1) + y_(5,_2) + y_(5,_3) + y_(5,_4) >= 1.2
_C4: y_(6,_1) + y_(6,_2) + y_(6,_3) + y_(6,_4) >= 1.2
_C5: z_(4,_1,_'green') + z_(4,_2,_'green') + z_(4,_3,_'green')
+ z_(4,_4,_'green') + z_(5,_1,_'green') + z_(5,_2,_'green')
+ z_(5,_3,_'green') + z_(5,_4,_'green') + z_(6,_1,_'green')
+ z_(6,_2,_'green') + z_(6,_3,_'green') + z_(6,_4,_'green') <= 4
VARIABLES
x_4 free Continuous
y_(4,_1) free Continuous
y_(4,_2) free Continuous
y_(4,_3) free Continuous
y_(4,_4) free Continuous
y_(5,_1) free Continuous
y_(5,_2) free Continuous
y_(5,_3) free Continuous
y_(5,_4) free Continuous
y_(6,_1) free Continuous
y_(6,_2) free Continuous
y_(6,_3) free Continuous
y_(6,_4) free Continuous
z_(4,_1,_'green') free Continuous
z_(4,_2,_'green') free Continuous
z_(4,_3,_'green') free Continuous
z_(4,_4,_'green') free Continuous
z_(5,_1,_'green') free Continuous
z_(5,_2,_'green') free Continuous
z_(5,_3,_'green') free Continuous
z_(5,_4,_'green') free Continuous
z_(6,_1,_'green') free Continuous
z_(6,_2,_'green') free Continuous
z_(6,_3,_'green') free Continuous
z_(6,_4,_'green') free Continuous
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