python - Gekko 中的双重不等式约束

Question

我有一个优化问题，其中某些不等式约束可以为 0 或大于某个值。例如，在下面的代码中，qtde 和 c1 是列表，pp 是二维 numpy 数组。

import numpy as np
from gekko import GEKKO

qtde = [7, 2, 2, 12, 2, 7, 1.5, 8, 4, 16, 2, 1, 3, 0.2, 3, 1, 1, 10, 8, 5, 3, 2.5, 5, 2.5, 10, 3, 1, 6, 12, 2, 6, 1, 4, 1, 2, 10, 1, 1, 1, 1]
c1 = [26.0, 150.0, 300.0, 110.0, 400.0, 500.0, 200.0, 200.0, 27.0, 150.0, 50.0, 200.0, 75.0, 0.0, 250.0, 22.8, 300.0, 22.8, 22.8, 150.0, 300.0, 150.0, 100.0, 100.0, 1000.0, 150.0, 150.0, 200.0, 31.2, 100.0, 100.0, 50.0, 23.0, 300.0, 200.0, 300.0, 0.0, 300.0, 30.0, 26.0, 300.0, 300.0, 250.0, 100.0, 100.0, 200.0, 400.0, 21.2, 200.0, 500.0, 0.0]

mm = [[4,0,0,0,0,0,0,0,0,0,9,0,0,0,0,0,5,0,2,0,0,0,7,0,0,0,6,0,0,0,8,0,0,0,0,0,0,0,0,0,3,0,1,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,13,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,14,0,0,0,0,0,0,0,0,0,0,0,0,0,11,0,10,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,19,0,0,0,0,0,0,17,15,0,0,16,0,0,18,0,0,0,0,0,0,0,0,0,0],
[26,0,0,0,0,0,0,0,0,0,27,0,0,0,0,0,0,0,21,0,0,0,25,0,0,0,23,0,0,0,22,0,0,0,0,0,0,0,0,0,24,0,20,0,0,0,0,0,0,0,0],
[29,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,34,0,0,0,0,0,0,0,30,0,0,31,0,0,0,0,0,0,0,32,0,0,33,0,28,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,37,0,0,0,36,0,0,0,38,0,0,0,39,0,0,0,0,0,0,0,0,0,0,0,35,0,0,0,0,0,0,0,0],
[42,0,0,0,0,0,0,0,0,0,48,0,0,0,0,0,44,0,43,0,0,0,49,0,0,0,46,0,0,0,47,0,0,0,0,0,0,0,0,0,45,0,41,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,54,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,53,0,0,0,52,0,0,0,0,0,0,0,0,0,51,0,50,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,56,0,0,0,59,0,0,0,57,0,0,0,58,0,0,0,0,0,0,0,0,0,0,0,55,0,0,0,0,0,0,0,0],
[69,0,0,0,0,0,0,0,0,0,68,0,0,0,0,0,61,0,0,0,0,0,64,0,0,0,63,0,0,0,65,0,0,0,0,0,0,67,0,0,62,0,66,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,71,0,70,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,78,0,0,0,0,0,77,0,0,0,0,0,73,0,0,0,76,0,0,0,75,0,0,0,0,0,0,0,0,0,74,0,72,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,80,0,0,0,79,0,0,0,82,0,0,0,0,0,0,0,0,0,83,0,81,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,86,0,0,0,84,0,0,0,0,0,0,0,0,0,85,0,87,0,0,0,0,0,0,0,0],
[93,0,0,0,0,0,0,0,0,0,95,0,0,0,0,0,94,0,92,0,0,0,90,0,0,0,91,0,0,0,96,0,0,0,0,0,0,0,0,0,89,0,88,0,0,0,0,0,0,0,0],
[104,0,0,0,0,0,0,0,0,0,100,0,0,0,0,0,99,0,98,0,0,0,103,0,0,0,101,0,0,0,102,0,0,0,0,0,0,0,0,0,0,0,97,0,0,0,0,0,0,0,0],
[112,0,0,0,0,0,0,0,0,0,108,0,0,0,0,0,110,0,107,0,0,0,111,0,0,0,109,0,0,0,113,0,0,0,0,0,0,0,0,0,106,0,105,0,0,0,0,0,0,0,0],
[114,0,0,0,0,0,0,0,0,0,116,0,0,0,0,0,117,0,119,0,0,0,115,0,0,0,118,0,0,0,120,0,0,0,0,0,0,0,0,0,121,0,122,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,123,0,0,0,0,0,0,0,0],
[0,129,0,0,0,0,126,0,0,0,0,0,0,128,0,0,0,0,0,0,0,0,0,0,0,0,0,127,125,0,0,0,0,0,0,0,0,0,0,130,0,0,0,0,0,124,0,131,0,0,0],
[0,133,0,0,0,0,136,0,0,0,0,0,0,135,0,0,0,0,0,0,0,0,0,0,0,0,0,132,0,0,0,0,0,0,0,0,0,0,134,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,138,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,137,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,139,0,0,0,0,0,0,0,0,0,0,0,0,140,0,0,0,0,0,0,0,0,0,0,0,0,0,141],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,142,0,143,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,144,0,0,0,150,0,146,0,149,0,0,0,0,0,0,152,0,0,0,145,0,0,0,0,147,0,0,151,0,0,0,0,0,148],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,154,0,0,0,0,0,153,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,155,0,0,0,157,0,0,156,0,0,0,158,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,160,0,0,0,0,0,0,0,0,0,0,0,0,0,159,0],
[0,0,0,0,0,0,0,0,0,0,0,161,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,164,0,0,163,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,162,0],
[0,0,165,0,0,0,0,0,0,166,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,167,169,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,170,0,0,0,0,0,0,0,0,0,0,168,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,173,0,0,0,0,0,0,175,177,0,0,171,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,176,0,0,0,0,0,0,0,0,0,0,0,0,174,172,0],
[0,0,0,0,0,0,0,0,0,0,0,0,180,0,0,178,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,179,0],
[0,0,0,0,182,184,0,186,0,0,0,183,185,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,181,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,190,191,0,0,187,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,189,0,0,0,0,0,0,0,0,0,0,0,0,0,188,0],
[0,0,193,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,192,0,0,0,0],
[0,0,197,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,196,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,195,0,0,194,0,0,0,0],
[0,0,0,0,0,0,0,0,0,199,0,0,0,0,201,0,0,0,0,0,0,0,200,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,198,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,203,0,0,0,0,204,0,0,0,0,0,0,0,0,0,0,0,0,0,0,202,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,205,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]]

mm = np.array(mm)
#
pp = [[5.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,7.90,0.00,0.00,0.00,0.00,0.00,5.49,0.00,2.89,0.00,0.00,0.00,5.98,0.00,0.00,0.00,5.94,0.00,0.00,0.00,6.21,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,3.55,0.00,2.89,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,5.70,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,3.61,0.00,0.00,0.00,5.80,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,3.15,0.00,3.15,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,15.95,0.00,0.00,0.00,0.00,0.00,0.00,14.00,11.95,0.00,0.00,12.36,0.00,0.00,14.18,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[3.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,3.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,2.20,0.00,0.00,0.00,2.80,0.00,0.00,0.00,2.29,0.00,0.00,0.00,2.27,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,2.61,0.00,2.20,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[3.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,9.76,0.00,0.00,0.00,0.00,0.00,0.00,0.00,5.70,0.00,0.00,6.47,0.00,0.00,0.00,0.00,0.00,0.00,0.00,7.47,0.00,0.00,8.51,0.00,3.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,10.50,0.00,0.00,0.00,0.00,0.00,0.00,0.00,9.52,0.00,0.00,0.00,9.10,0.00,0.00,0.00,9.57,0.00,0.00,0.00,9.62,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,9.10,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[6.75,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,9.50,0.00,0.00,0.00,0.00,0.00,7.98,0.00,6.99,0.00,0.00,0.00,11.05,0.00,0.00,0.00,8.55,0.00,0.00,0.00,8.88,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,8.27,0.00,6.75,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,11.20,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,10.95,0.00,0.00,0.00,9.75,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,9.63,0.00,9.16,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,3.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,1.69,0.00,0.00,0.00,1.98,0.00,0.00,0.00,1.77,0.00,0.00,0.00,1.96,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,1.69,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[10.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,7.10,0.00,0.00,0.00,0.00,0.00,1.59,0.00,0.00,0.00,0.00,0.00,1.95,0.00,0.00,0.00,1.74,0.00,0.00,0.00,2.09,0.00,0.00,0.00,0.00,0.00,0.00,6.43,0.00,0.00,1.70,0.00,2.83,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,9.93,0.00,9.93,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,18.40,0.00,0.00,0.00,0.00,0.00,14.49,0.00,0.00,0.00,0.00,0.00,12.89,0.00,0.00,0.00,14.36,0.00,0.00,0.00,13.76,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,13.48,0.00,11.91,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,9.39,0.00,0.00,0.00,7.97,0.00,0.00,0.00,9.57,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,10.24,0.00,9.49,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,33.35,0.00,0.00,0.00,14.80,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,18.00,0.00,72.90,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[5.70,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,6.00,0.00,0.00,0.00,0.00,0.00,5.78,0.00,4.50,0.00,0.00,0.00,3.90,0.00,0.00,0.00,4.06,0.00,0.00,0.00,6.46,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,3.55,0.00,3.55,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[4.50,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,3.60,0.00,0.00,0.00,0.00,0.00,3.19,0.00,2.69,0.00,0.00,0.00,4.12,0.00,0.00,0.00,3.75,0.00,0.00,0.00,4.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,2.69,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[5.70,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,3.80,0.00,0.00,0.00,0.00,0.00,4.65,0.00,3.69,0.00,0.00,0.00,5.42,0.00,0.00,0.00,4.50,0.00,0.00,0.00,6.40,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,3.55,0.00,3.55,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[4.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,5.40,0.00,0.00,0.00,0.00,0.00,5.49,0.00,6.60,0.00,0.00,0.00,4.33,0.00,0.00,0.00,6.38,0.00,0.00,0.00,6.92,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,7.09,0.00,8.68,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,8.68,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,18.99,0.00,0.00,0.00,0.00,16.98,0.00,0.00,0.00,0.00,0.00,0.00,17.80,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,17.20,16.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,28.58,0.00,0.00,0.00,0.00,0.00,13.99,0.00,30.45,0.00,0.00,0.00],
[0.00,9.49,0.00,0.00,0.00,0.00,34.98,0.00,0.00,0.00,0.00,0.00,0.00,18.90,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,8.77,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,15.90,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,47.90,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,38.39,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,89.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,91.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,92.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,66.89,0.00,79.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,27.30,0.00,0.00,0.00,36.90,0.00,29.50,0.00,36.00,0.00,0.00,0.00,0.00,0.00,0.00,49.90,0.00,0.00,0.00,28.90,0.00,0.00,0.00,0.00,31.99,0.00,0.00,42.00,0.00,0.00,0.00,0.00,0.00,33.50],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,65.00,0.00,0.00,0.00,0.00,0.00,23.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,12.89,0.00,0.00,0.00,13.99,0.00,0.00,13.90,0.00,0.00,0.00,14.32,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,16.50,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,15.57,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,36.75,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,58.73,0.00,0.00,53.43,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,51.85,0.00],
[0.00,0.00,5.39,0.00,0.00,0.00,0.00,0.00,0.00,6.90,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,12.36,14.63,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,18.76,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,12.90,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,86.00,0.00,0.00,0.00,0.00,0.00,0.00,89.90,97.30,0.00,0.00,81.60,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,96.70,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,89.00,83.77,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,64.28,0.00,0.00,49.46,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,52.34,0.00],
[0.00,0.00,0.00,0.00,79.90,89.00,0.00,124.00,0.00,0.00,0.00,85.00,104.47,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,67.20,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,91.00,91.11,0.00,0.00,73.61,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,81.50,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,80.60,0.00],
[0.00,0.00,2.47,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,2.44,0.00,0.00,0.00,0.00],
[0.00,0.00,28.44,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,15.90,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,15.10,0.00,0.00,13.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,22.00,0.00,0.00,0.00,0.00,31.92,0.00,0.00,0.00,0.00,0.00,0.00,0.00,28.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,22.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,8.55,0.00,0.00,0.00,0.00,62.70,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,8.30,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00],
[0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,62.70,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00]]
pp = np.array(pp)
#c1 = [26.0, 150.0, 300.0, 110.0, 400.0, 500.0, 200.0, 200.0, 27.0, 150.0, 50.0, 200.0, 75.0, 0.0, 250.0, 22.8, 300.0, 22.8, 22.8, 150.0, 300.0, 150.0, 100.0, 100.0, 1000.0, 150.0, 150.0, 200.0, 31.2, 100.0, 100.0, 50.0, 23.0, 300.0, 200.0, 300.0, 0.0, 300.0, 30.0, 26.0, 300.0, 300.0, 250.0, 100.0, 100.0, 200.0, 400.0, 21.2, 200.0, 500.0, 0.0]

m = GEKKO()
ni = 40
nj = 51

x = [[m.Var(lb=0,integer=True) for j in range(nj)] for i in range(ni)]

s = 0
expr = []
for i in range(ni):
    for j in range(nj):
        s += x[i][j]

for i in range(ni):
    expr.append(sum(x[i]))


for i in range(ni):
    for j in range(nj):
        if mm[i][j] == 0:
            m.Equation(x[i][j] == 0)



for i in range(ni):
    m.Equation(sum([x[i][j] for j in range(nj)]) >= qtde[i])



b = m.Array(m.Var,nj,integer=True,lb=0,ub=1)
iv = [None]*nj
for j in range(nj):
    iv[j] = m.sum([pp[i][j]*x[i][j] for i in range(ni)])
    m.Equation(iv[j] >= b[j]*c1[j])
    m.Equation((1 - b[j])*iv[j] == 0)

m.Obj(m.sum(expr))


m.options.SOLVER=1  # switch to APOPT
m.solver_options = ['minlp_gap_tol 1.0e-1',\
                    'minlp_maximum_iterations 10000',\
                    'minlp_max_iter_with_int_sol 1000',\
                    'minlp_branch_method 1',\
                    'minlp_integer_leaves 2']

m.solve()    

编辑:我按照 John Hedengren(如下)的建议更改了最后一个约束的写法。但是，随着二进制变量的插入，代码现在在开始任何迭代之前返回错误。如何防止这种情况发生？

Answer 1

您可以使用二进制变量(0=设备关闭，1=设备打开并高于阈值)和等式:

b = m.Array(m.Var,nj,integer=True,lb=0,ub=1)
iv = [None]*nj

for j in range(nj):
    iv[j] = m.sum([pp[i][j]*x[i][j] for i in range(ni)])
    m.Equation(iv[j] >= b[j]*c1[j])
    m.Equation((1-b[j])*iv[j] <= 0)

m.options.SOLVER = 1  # Change to MINLP solver

您可以将求和拆分为中间变量 iv，因为它用于两个方程。另一个建议是使用 m.sum() 而不是 sum。使用 Gekko 求和通常会更快。还有其他方法可以解决这个问题，但这可能是最可靠的。我无法验证此解决方案，因为您的脚本缺少一些输入。它有助于在以后的帖子中将问题减少到 Minimal and Reproducible example以便验证解决方案。关于 logical conditions in optimization problems 有更多信息.

回复编辑

MINLP 无法快速收敛，因为有 nj x ni = 2040 个二进制变量。这是 2^2040 潜在的解决方案。您可以调整求解器设置以帮助其找到至少一个可行的解决方案。

m.options.SOLVER=3
m.solve()  # sometimes it helps to solve with IPOPT first

m.options.SOLVER=1  # switch to APOPT
m.solver_options = ['minlp_gap_tol 1.0e-2',\
                    'minlp_maximum_iterations 10000',\
                    'minlp_max_iter_with_int_sol 500',\
                    'minlp_branch_method 1',\
                    'minlp_integer_leaves 2']
m.solve()

APOPT website 上有关于求解器选项的附加说明.

回复编辑

第一次 MINLP 迭代的错误是因为问题不可行。如果切换到求解器选项 minlp_as_nlp 1，那么您可以看到第一个 NLP 问题无法收敛。如果您切换到 m.options.SOLVER=3，您还可以使用 IPOPT 求解器看到这一点。

EXIT: Converged to a point of local infeasibility.
Problem may be infeasible.

如果您使用 m=GEKKO(remote=False) 在本地求解，并在求解命令之前使用 m.open_folder() 打开运行文件夹，那么您可以看到infeasibilities.txt 文件将帮助您识别不可行的方程。我怀疑不可行是因为方程 m.Equation(m.sum([x[i][j] for j in range(nj)]) >= qtde[i]) 和m.Equation(x[i][j] == 0)。您还可以尝试使用 m.options.COLDSTART=2 来识别不可行的问题。 exercise 18 in the Gekko tutorials 中提供了有关应用程序故障排除的其他帮助。 .