约束线性优化设置

Question

我正在为以下设置而苦苦挣扎。

我的数据如下：

Group   ID  Wt       Coeff      Coeff*Wt
------  --- ------   -------    -------
Group1  A   10.00%   1.00000     0.100 
Group1  B   10.00%   1.00000     0.100 
Group1  C   10.00%   3.00005     0.300 
Group2  D   10.00%   1.00000     0.100 
Group2  E   10.00%   1.00000     0.100 
Group2  F   10.00%   1.00000     0.100 
Group2  G   10.00%   7.80016     0.780 
Group3  H   10.00%   7.80485     0.780 
Group3  I   10.00%   1.00000     0.100 
Group3  J   10.00%   0.39529     0.040 



Objective function: Fmin = mimimize(sum of weights * coeff)

我需要实现以下约束：

Sum of Weights*Coeff of Group1 = 20% of total minimized fmin
Sum of Weights*Coeff of Group1 = 45% of total minimized fmin
Sum of Weights*Coeff of Group1 = 35% of total minimized fmin

以及以下边界条件：

Weights <=10% and Weights > 0.30%

和

Sum of weights = 100%

我正在尝试使用以下代码来完成此操作。

我不知道为什么这不起作用：

from scipy.optimize import linprog

c = [ 1.0000 ,1.0000 ,3.0001 ,1.0000 ,1.0000 ,1.0000 ,7.8002 ,7.8049 ,1.0000 ,0.3953 ]

groupPerID = ['Group1','Group1','Group1','Group2','Group2','Group2','Group2','Group3','Group3','Group3']

groupList = ['Group1','Group2','Group3']

groupUpperBound = [0.20,0.45,0.40]

A_eq_list = []
A_eq_list.append([1]*len(c))

b_eq_list = [1]

for idx,currentGroup in enumerate(groupList):

    matches = [i for i in range(len(groupPerID)) if groupPerID[i] == currentGroup]

    currentGroupUB = groupUpperBound[idx]

    x_list = [float(-1*currentGroupUB*coeff) for coeff in c]

    for idx in matches:
        x_list[idx] = float((1-currentGroupUB)*c[idx])

    A_eq_list.append(x_list)

b_eq_list.extend([0]*len(groupUpperBound))
res = linprog(c, A_eq=A_eq_list, b_eq=b_eq_list,bounds =(0.003,0.1),options={'tol':0.05})
print(res)

谁能指出我犯了什么错误？

Answer 1

所以我在 scipy 包装器 symfit 中实现了它，它负责所有样板代码。它现在可以工作了，除了我还没有在权重上实现你的界限。但是，我认为这些都是错误的，如您的问题所述，因为满足所有权重总和为 1 的约束的唯一方法是将它们全部设置为上限 0.1。除此之外，这是我的尝试：

from symfit import parameters, Minimize, Variable, Eq
import numpy as np

# Make 10 weight parameters w_i to optimize
weights = parameters(','.join('w_{}'.format(i) for i in range(1, 11)))
c = np.array([1.0000, 1.0000, 3.0001, 1.0000, 1.0000, 1.0000, 7.8002, 7.8049, 1.0000, 0.3953])
f = Variable()

for w_i in weights:
    w_i.min = 0.003
    w_i.max = 1.0
    w_i.value = 0.1

sum_of_group_1 = sum(c_i * w_i for c_i, w_i in zip(c, weights)[0:3])
sum_of_group_2 = sum(c_i * w_i for c_i, w_i in zip(c, weights)[3:7])
sum_of_group_3 = sum(c_i * w_i for c_i, w_i in zip(c, weights)[7:10])
# Function to minimize
model = {f: sum_of_group_1 + sum_of_group_2 + sum_of_group_3}

constraints = [
    Eq(0.20 * sum_of_group_1, 0.45 * sum_of_group_2),
    Eq(0.20 * sum_of_group_1, 0.35 * sum_of_group_3),
    Eq(sum(weights), 1)
]

fit = Minimize(model, constraints=constraints)
fit.eval_jacobian = None  # Workaround needed because f is just a scalar, not an array
fit_result = fit.execute()

print(fit_result)
print(sum(fit_result.value(w) for w in weights)) # >>> 1.0

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