如何自動化 PuLP 中的變量定義

Question

我正在嘗試自動化PuLP 中的模型定義。 現在，我有以下模型：

import pulp as pl

" Cost parameters"
p1 = 200  # Cost per unit 1
p2 = 300  # Cost per unit 2

" VARIABLES"
k0101 = pl.LpVariable("k0101", 0, 1, pl.LpInteger) 
k0102 = pl.LpVariable("k0102", 0, 1, pl.LpInteger) 

k0201 = pl.LpVariable("k0201", 0, 1, pl.LpInteger) 
k0202 = pl.LpVariable("k0202", 0, 1, pl.LpInteger) 

###### DEMAND
x010101 = pl.LpVariable("x010101", lowBound = 0) 
x010102 = pl.LpVariable("x010102", lowBound = 0) 
x010103 = pl.LpVariable("x010103", lowBound = 0) 
x010104 = pl.LpVariable("x010104", lowBound = 0) 

x010201 = pl.LpVariable("x010201", lowBound = 0)
x010202 = pl.LpVariable("x010202", lowBound = 0)
x010203 = pl.LpVariable("x010203", lowBound = 0)
x010204 = pl.LpVariable("x010204", lowBound = 0)

x020101 = pl.LpVariable("x020101", lowBound = 0) 
x020102 = pl.LpVariable("x020102", lowBound = 0) 
x020103 = pl.LpVariable("x020103", lowBound = 0) 
x020104 = pl.LpVariable("x020104", lowBound = 0)

x020201 = pl.LpVariable("x020201", lowBound = 0) 
x020202 = pl.LpVariable("x020202", lowBound = 0) 
x020203 = pl.LpVariable("x020203", lowBound = 0) 
x020204 = pl.LpVariable("x020204", lowBound = 0) 

# Problem
z = pl.LpProblem("optimizator", pl.LpMinimize)

"OBJECTIVE FUNCTION"
z += ((p1) * (x010101 + x010102 + x010103 + x010104) + (p1) * (x010201 + x010202 + x010203 + x010204) + (p2) * (x020101 + x020102 + x020103 + x020104) + (p2) * (x020201 + x020202 + x020203 + x020204) + (p1) * (x010101 + x010102 + x010103 + x010104) + (p1) * (x010201 + x010202 + x010203 + x010204) + (p2) * (x020101 + x020102 + x020103 + x020104) + (p2) * (x020201 + x020202 + x020203 + x020204))

" CONSTRAINTS "
z += x010101 + x020101 >= 15 * k0101

" SOLUTION "
print(z)
estado = z.solve()
print(pl.LpStatus[estado]) 

"TOTAL COST:"
print(pl.value(z.objective))

我想簡化這個變量定義，以便能夠在更簡單的描述中定義更多變量。

現在有人如何將我的變量和參數定義為字典，並在目標函數和約束中考慮？

Answer 1

這將有助於更多地解釋問題。 現在寫的目標函數有重復的術語，很難從概念上理解你想要最小化的東西。

話雖如此，您可以使用 lpSum 來表示變量 * cost 的總和。

# create the variables
k_variable_names = ('k0101', 'k0102', 'k0201', 'k0202')
k_variables = {var: pl.LpVariable(var, cat=pl.LpBinary)
               for var in k_variable_names}

x_variables_names = ('x010101' ...)
x_variables = {var: pl.LpVariable(var, lowBound=0)
               for var in x_variable_names}

# objective function
z += (
  lpSum([var * 2 * p1 for var_name, var in x_variables.items() if 'x010' in var_name]) +
  lpSum([var * 2 * p2 for var_name, var in x_variables.items() if 'x020' in var_name])

)