约束线性优化设置

Question

我正在为下面的设置而挣扎。在

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：

^{pr2}$

以及以下边界条件：

Weights <=10% and Weights > 0.30%

以及

Sum of weights = 100%

我试着用下面的代码来完成这个。在

我不知道为什么这样不行：

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)

有人能指出我犯了什么错误吗？在

Answer 1

所以我在我的scipy包装器symfit中实现了它，它负责所有的锅炉板代码。它现在起作用了，除了我还没有实现你对权重的限制。但是，我认为这些都是错误的，正如你的问题所说，因为满足所有权重之和应为1的约束的唯一方法是将它们全部设置为0.1的上限。除此之外，我的尝试是：

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

您可以在文档here中阅读更多内容。在