为什么我用 scipy.optimize 得不到我想要的值。 （线性规划问题）

Question

import numpy as np
from scipy.optimize import linprog

b_ub = [74, 40, 36]
b_eq = [20, 45, 30]
A = np.array([[7, 3, 6], [4, 8, 2], [1, 5, 9]])
m, n = A.shape
c = list(np.reshape(A, n * m))  # Convert matrix A to list c.
A_ub = np.zeros([m, m * n])
for i in np.arange(0, m,
                   1):  # Filling in the matrix of conditions-inequalities.
    for j in np.arange(0, n * m, 1):
        if i * n <= j <= n + i * n - 1:
            A_ub[i, j] = 1
A_eq = np.zeros([m, m * n])
for i in np.arange(0, m, 1):  # Filling in the matrix of conditions-equalities
    k = 0
    for j in np.arange(0, n * m, 1):
        if j == k * n + i:
            A_eq[i, j] = 1
            k = k + 1
print(linprog(c, A_ub, b_ub, A_eq, b_eq))

我明白了

而不是

Answer 1

我认为这是默认解算器造成的。交换求解器给出了您要寻找的解决方案。请参阅 docs 并评估使用每个求解器的权衡以确定您要使用的内容。

print(linprog(c, A_ub, b_ub, A_eq, b_eq, method='highs-ds'))

           con: array([0., 0., 0.])
 crossover_nit: 0
           fun: 215.0
       message: 'Optimization terminated successfully.'
           nit: 3
         slack: array([29., 10., 16.])
        status: 0
       success: True
             x: array([ 0., 45.,  0.,  0.,  0., 30., 20.,  0.,  0.])