python - 使用 scipy.optimize.linprog 进行线性规划返回优化失败

Question

我正在尝试使用 linprog 来优化以下问题 (uploaded in Google Drive) 。数据集本身已上传here

到目前为止，我已经用 Python 编写了以下实现:

import pandas as pd
import numpy as np

df = pd.read_csv('Supplier Specs.csv')
from scipy.optimize import linprog

def fromPandas(dataframe, colName):
    return dataframe[[colName]].values.reshape(1,11)[0]

## A_ub * x <= b_ub
## A_eq * x == b_eq

A_eq = [1.0]*11
u_eq = [600.0] # demand

## reading the actual numbers from the pandas dataframe and then converting them to vectors

BAR = fromPandas(df, 'Brix / Acid Ratio')
acid = fromPandas(df, 'Acid (%)')
astringency = fromPandas(df, 'Astringency (1-10 Scale)')
color = fromPandas(df, 'Color (1-10 Scale)')
price = fromPandas(df, 'Price (per 1K Gallons)')
shipping = fromPandas(df, 'Shipping (per 1K Gallons)')
upperBounds = fromPandas(df, 'Qty Available (1,000 Gallons)')

lowerBounds = [0]*len(upperBounds) # list with length 11 and value 0
lowerBounds[2] = 0.4*u_eq[0] # adding the Florida tax bound

bnds = [(0,0)]*len(upperBounds) # bounds
for i in range(0,len(upperBounds)):
    bnds[i] = (lowerBounds[i], upperBounds[i])

c = price + shipping # objective function coefficients

print("------------------------------------- Debugging Output ------------------------------------- \n")
print("Objective function coefficients: ", c)
print("Bounds: ", bnds)
print("Equality coefficients: ", A_eq)
print("BAR coefficients: ", BAR)
print("Astringency coefficients: ", astringency)
print("Color coefficients: ", color)
print("Acid coefficients: ", acid)
print("\n")

A_ub = [BAR, acid, astringency, color, -BAR, -acid, -astringency, -color] # coefficients for inequalities
b_ub = np.array([12.5, 1.0, 4.0, 5.5, -11.5, -0.75, 0, -4.5]) # limits for the inequalities

b_ub = b_ub * u_eq[0] # scaling the limits with the demand

xOptimized = linprog(c, A_ub, b_ub, [A_eq], u_eq, bounds=(bnds))

print(xOptimized) # the amounts of juice which we need to buy from each supplier

优化方法返回找不到可行的起点。我相信我在使用该方法时犯了一个主要错误，但到目前为止我无法理解它。

有什么帮助吗？

提前致谢!

编辑:目标函数的期望值为371724

预期解向量 [0,0,240,0,15.8,0,0,0,126.3,109.7,108.2]

Answer 1

这确实是我的一个不成熟的猜测。 [A_eq] 当然是 1xn 的二维。当您删除所有负面约束时，您的脚本原则上可以工作，这表明了示例。

A_ub = [BAR, acid, astringency, color, -BAR, -acid, -astringency, -color] # coefficients for inequalities
b_ub = np.array([12.5, 1.0, 4.0, 5.5, -11.5, -0.75, 0, -4.5]) # limits for the inequalities

这似乎是问题的症结所在。由于 A_ub * x <= b_ub，您寻找解决方案
BAR * x <= 12.5
和
-BAR * x <= -11.5，即
11.5 <= 酒吧 * x <= 12.5这显然无法产生任何结果。您实际上正在寻找

A_ub = [BAR, acid, astringency, color, -BAR, -acid, -astringency, -color] # coefficients for inequalities
b_ub = np.array([12.5, 1.0, 4.0, 5.5, 11.5, 0.75, 0, 4.5]) # limits for the inequalities

现在收敛了，但给出的结果与您现在在编辑中发布的预期解决方案不同。显然，您必须重新评估您的不等式参数，而您在问题中没有指定这些参数。