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Double inequality constraint in Gekko - python

I have an optimization problem in which some inequalities constraints can either be 0 or greater than a certain value. For example, in the code below, qtde and c1 are lists and pp is a 2d numpy array.
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()
Edit: I have changed the writing of the last constraint as suggested by John Hedengren (bellow). However, with the insertion of the binary variable, the code now returns an error before starting any iterations. How can this be prevented?

You can use a binary variable (0=equipment off, 1=equipment on and above threshold) and equation as:
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
You can split out the summation into an intermediate variable iv because it is used in two equations. Another recommendation is to use m.sum() instead of sum. Using the Gekko summation is typically faster. There are also other ways to pose the problem but this may be the most reliable. I can't verify this solution because your script is missing some inputs. It helps on future posts to reduce the problem to a Minimal and Reproducible example so that solutions can be verified. There is additional information on logical conditions in optimization problems.
Response to Edit
The MINLP does not converge quickly because there are nj x ni = 2040 binary variables. That is 2^2040 potential solutions. You can adjust solver settings to help it find at least one feasible solution.
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()
There is additional description on the solver options on the APOPT website.
Response to Edit
The error on the first MINLP iteration is because the problem is not feasible. If you switch to solver option minlp_as_nlp 1 then you can see the first NLP problem fail to converge. You can also see this with the IPOPT solver if you switch to m.options.SOLVER=3.
EXIT: Converged to a point of local infeasibility.
Problem may be infeasible.
If you solve locally with m=GEKKO(remote=False) and open the run folder before the solve command with m.open_folder() then you can see the infeasibilities.txt file that will help you identify the infeasible equation. I suspect that the infeasibility is because of the equations m.Equation(m.sum([x[i][j] for j in range(nj)]) >= qtde[i]) and m.Equation(x[i][j] == 0). You can also try to identify an infeasible problem with m.options.COLDSTART=2. There is additional help on troubleshooting applications in exercise 18 in the Gekko tutorials.

Related

The output of result are 3 arrays that are 2 dimensional with lengths that are getting decremented by one. I want to write a code that gets the ending index value last_incs, max value maxs and the minimum values mins. It should iterate through all the rows of each of the 2nd dimensional array, for example the result output for [-3,-1,-2,1] is array([array([ 0., 0., 0., 25.]),array([ 0,0, 33.33333333]), array([ 0., 50.]),array([100.])], dtype=object). The maximum values corresponding to each of these sub arrays are as follows: [25.0, 33.33333333333333, 50.0, 100.0] which is shown in the Expected Outputs below in Max:. How would I be able to do this?
import numpy as np
def run(*args):
result = np.array([np.array([((arr[i:] > 0).cumsum()/ np.arange(1, len(arr[i:])+1) * 100) for i in range(len(arr))],dtype=object) for arr in args], dtype=object)
#print(result)
last_inc = result[-1]
maxs = np.max(result)
mins = np.min(result)
run(np.array([12,12,-3,-1,2,1]), np.array([-3,-1,-2,1]), np.array([12,-12]))
Expected Output:
last incs: [array([66.66666666666666, 60.0, 50.0, 66.66666666666666, 100.0, 100.0],
dtype=object)
array([25.0, 33.33333333333333, 50.0, 100.0], dtype=object)
array([50.0, 0.0], dtype=object)]]
mins: [array([50.0, 33.33333333333333, 0.0, 0.0, 100.0, 100.0], dtype=object)
array([0.0, 0.0, 0.0, 100.0], dtype=object)
array([50.0, 0.0], dtype=object)]
maxs: [array([100.0, 100.0, 50.0, 66.66666666666666, 100.0, 100.0], dtype=object)
array([25.0, 33.33333333333333, 50.0, 100.0], dtype=object)
array([100.0, 0.0], dtype=object)]

The following code gets your needed outputs, use it in your function:
size = np.empty(0)
for i in result:
size = np.append(size, np.size(i))
results_arrays = np.empty(0)
for i in np.hstack(result).T:
last_incs = np.float64(np.vstack(i)[-1])
maxs = np.max(np.vstack(i))
mins = np.min(np.vstack(i))
results_arrays = np.append(results_arrays, np.array([last_incs, maxs, mins]))
last_incs = np.array_split(results_arrays[0::3], np.cumsum(size, axis=0).astype(int), axis=0)[:-1]
maxs = np.array_split(results_arrays[1::3], np.cumsum(size, axis=0).astype(int), axis=0)[:-1]
mins = np.array_split(results_arrays[2::3], np.cumsum(size, axis=0).astype(int), axis=0)[:-1]

I have a dictionary with:
inds = [0, 3, 7, 3, 3, 5, 1]
vals = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0]
d = {'inds': inds, 'vals': vals}
print(d) will get me: {'inds': [0, 3, 7, 3, 3, 5, 1], 'vals': [1.0, 2.0, 3.0, 4.0, 5.0, 6.0,
7.0]}
As you can see, inds(keys) are not ordered, there are dupes, and there are missing ones: range is 0 to 7 but there are only 0,1,3,5,7 distinct integers. I want to write a function that takes the dictionary (d) and decompresses this into a full vector like shown below. For any repeated indices (3 in this case), I'd like to sum the corresponding values, and for the missing indices, want 0.0.
# ind: 0 1 2 3* 4 5 6 7
x == [1.0, 7.0, 0.0, 11.0, 0.0, 6.0, 0.0, 3.0]
Trying to write a function that returns me a final list... something like this:
def decompressor (d, n=None):
final_list=[]
for i in final_list:
final_list.append()
return(final_list)
# final_list.index: 0 1 2 3* 4 5 6 7
# final_list = [1.0, 7.0, 0.0, 11.0, 0.0, 6.0, 0.0, 3.0]

Try it,
xyz = [0.0 for x in range(max(inds)+1)]
for i in range(max(inds)):
if xyz[inds[i]] != 0.0:
xyz[inds[i]] += vals[i]
else:
xyz[inds[i]] = vals[i]

Some things are still not clear to me but supposing you are trying to make a list in which the maximum index is the one you can find in your inds list, and you want a list as a result you can do something like this:
inds = [0, 3, 7, 3, 3, 5, 1]
vals = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0]
#initialize a list of zeroes with lenght max index
res=[float(0)]*(max(inds)+1)
#[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
#Loop indexes and values in pairs
for i, v in zip(inds, vals):
#Add the value to the corresponding index
res[i] += v
print (res)
#[1.0, 7.0, 0.0, 11.0, 0.0, 6.0, 0.0, 3.0]

inds = [0, 3, 7, 3, 3, 5, 1]
vals = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0]
first you have to initialise the dictionary , ranging from min to max value in the inds list
max_id = max(inds)
min_id = min(inds)
my_dict={}
i = min_id
while i <= max_id:
my_dict[i] = 0.0
i = i+1
for i in range(len(inds)):
my_dict[inds[i]] += vals[i]
my_dict = {0: 1.0, 1: 7.0, 2: 0, 3: 11.0, 4: 0, 5: 6.0, 6: 0, 7: 3.0}

I have been trying to test the numpy.gradient function recently. However, it's behavior is little bit strange for me. I have created an array with random variables and then applied the numpy.gradient over it, but the values seems crazy and irrelevant. But when using numpy.diff the values are correct.
So, after viewing the documentation of numpy.gradient, I see that it uses distance=1 over the desired dimension.
This is what I mean:
import numpy as np;
a= np.array([10, 15, 13, 24, 15, 36, 17, 28, 39]);
np.gradient(a)
"""
Got this: array([ 5. , 1.5, 4.5, 1. , 6. , 1. , -4. , 11. , 11. ])
"""
np.diff(a)
"""
Got this: array([ 5, -2, 11, -9, 21, -19, 11, 11])
"""
I don't understand how the values in first result came. If the default distance is supposed to be 1, then I should have got the same results as numpy.diff.
Could anyone explain what distance means here. Is it relative to the array index or to the value in the array? If it depends on the value, then does that mean that numpy.gradient could not be used with images since values of neighbor pixels have no fixed value differences?

# load image
img = np.array([[21.0, 20.0, 22.0, 24.0, 18.0, 11.0, 23.0],
[21.0, 20.0, 22.0, 24.0, 18.0, 11.0, 23.0],
[21.0, 20.0, 22.0, 24.0, 18.0, 11.0, 23.0],
[21.0, 20.0, 22.0, 99.0, 18.0, 11.0, 23.0],
[21.0, 20.0, 22.0, 24.0, 18.0, 11.0, 23.0],
[21.0, 20.0, 22.0, 24.0, 18.0, 11.0, 23.0],
[21.0, 20.0, 22.0, 24.0, 18.0, 11.0, 23.0]])
print "image =", img
# compute gradient of image
gx, gy = np.gradient(img)
print "gx =", gx
print "gy =", gy
# plotting
plt.close("all")
plt.figure()
plt.suptitle("Image, and it gradient along each axis")
ax = plt.subplot("131")
ax.axis("off")
ax.imshow(img)
ax.set_title("image")
ax = plt.subplot("132")
ax.axis("off")
ax.imshow(gx)
ax.set_title("gx")
ax = plt.subplot("133")
ax.axis("off")
ax.imshow(gy)
ax.set_title("gy")
plt.show()

Central differences in the interior and first differences at the boundaries.
15 - 10
13 - 10 / 2
24 - 15 / 2
...
39 - 28

For the boundary points, np.gradient uses the formulas
f'(x) = [f(x+h)-f(x)]/h for the left endpoint, and
f'(x) = [f(x)-f(x-h)]/h for the right endpoint.
For the interior points, it uses the formula
f'(x) = [f(x+h)-f(x-h)]/2h
The second approach is more accurate - O(h^2) vs O(h). Thus at the second data point, np.gradient estimates the derivative as (13-10)/2 = 1.5.
I made a video explaining the mathematics: https://www.youtube.com/watch?v=NvP7iZhXqJQ

I have two arrays with the following values:
>>> x = [24.0, 13.0, 12.0, 22.0, 21.0, 10.0, 9.0, 12.0, 7.0, 14.0, 18.0,
... 1.0, 18.0, 15.0, 13.0, 13.0, 12.0, 19.0, 13.0]
>>> y = [10.0, 9.0, 22.0, 7.0, 4.0, 7.0, 56.0, 5.0, 24.0, 25.0, 11.0, 2.0,
... 9.0, 1.0, 9.0, 12.0, 9.0, 4.0, 2.0]
I used the scipy library to calculate r-squared:
>>> from scipy.interpolate import polyfit
>>> p1 = polyfit(x, y, 1)
When I run the code below:
>>> yfit = p1[0] * x + p1[1]
>>> yfit
array([], dtype=float64)
The yfit array is empty. I don't understand why.

The problem is you are performing scalar addition with an empty list.
The reason you have an empty list is because you try to perform scalar multiplication with a python list rather than with a numpy.array. The scalar is converted to an integer, 0, and creates a zero length list.
We'll explore this below, but to fix it you just need your data in numpy arrays instead of in lists. Either create it originally, or convert the lists to arrays:
>>> x = numpy.array([24.0, 13.0, 12.0, 22.0, 21.0, 10.0, 9.0, 12.0, 7.0, 14.0,
... 18.0, 1.0, 18.0, 15.0, 13.0, 13.0, 12.0, 19.0, 13.0]
An explanation of what was going on follows:
Let's unpack the expression yfit = p1[0] * x + p1[1].
The component parts are:
>>> p1[0]
-0.58791208791208893
p1[0] isn't a float however, it's a numpy data type:
>>> type(p1[0])
<class 'numpy.float64'>
x is as given above.
>>> p1[1]
20.230769230769241
Similar to p1[0], the type of p1[1] is also numpy.float64:
>>> type(p1[0])
<class 'numpy.float64'>
Multiplying a list by a non-integer interpolates the number to be an integer, so p1[0] which is -0.58791208791208893 becomes 0:
>>> p1[0] * x
[]
as
>>> 0 * [1, 2, 3]
[]
Finally you are adding the empty list to p[1], which is a numpy.float64.
This doesn't try to append the value to the empty list. It performs scalar addition, i.e. it adds 20.230769230769241 to each entry in the list.
However, since the list is empty there is no effect, other than it returns an empty numpy array with the type numpy.float64:
>>> [] + p1[1]
array([], dtype=float64)
An example of a scalar addition having an effect:
>>> [10, 20, 30] + p1[1]
array([ 30.23076923, 40.23076923, 50.23076923])

I am really new to programming and I am a bit in over my head here with this whole minimize business, so it might just be a simple mistake, but when I try to run my code below, it simply returns the x0 values that I put in to start.
What I'm trying to do:
I have two "functions" that are made up of points, f(x) and h(x). f(X) can be thought of a measured curve, and h(x) is a reference curve. I am trying to use the least squares to find the horizontal shift, x scale, and y scale terms that will best fit the reference curve to the measured results.
I am using the interpolate function to fit a spline to the reference data so the spline can be used to find intermediate values along the curve.
Here is my code:
import numpy
from scipy import optimize
from scipy import interpolate
def f(x):
vals = {1: 0.35, 17: 0.45, 33: 0.67, 49: 0.8, 65: 0.73, 81: 0.65, 97: 0.51, 113: 0.27, 129: 0.01, 145: -0.1,
161: -0.19, 177: -0.21, 193: -0.2, 209: -0.23, 225: -0.24, 241: -0.25, 257: -0.23, 273: -0.26, 289: -0.28,
305: -0.22, 321: -0.24, 337: -0.12, 353: 0.14}
return vals[x]
def h(x):
vals = {1: -0.2, 17: -0.2, 33: -0.2, 49: -0.2, 65: -0.2, 81: -0.2, 97: -0.2, 113: -0.2, 129: -0.1, 145: 0.1,
161: 0.32, 177: 0.4, 193: 0.7, 209: 0.81, 225: 0.7, 241: 0.6, 257: 0.5, 273: 0.3, 289: 0, 305: -0.1,
321: -0.2, 337: -0.2, 353: -0.2}
return vals[x]
x1 = []
y1 = []
for i in range(1, 365, 16):
x1.append(i)
y1.append(h(i))
tck = interpolate.splrep(x1, y1)
fun = lambda x: ((1 / 22.8125 * numpy.sum(
(f(i) - (x[0] * interpolate.splev((x[1] * (i + x[2]) + 0.5), tck)) - 0.5) ** 2 for i in range(1, 365, 16))) ** (
1 / 2))
bnds = ((0.3, 1.5), (0.3, 1.5), (0, 150))
res = optimize.minimize(fun, (1, 1, 0), method='SLSQP', bounds=bnds)
print res.x
Again, when I run this I simply get [1.0, 1.0, 0.0] for res.x. Any thoughts?
Thank you!

1 / 2 in Python2 without from __future__ import division is equal to 0, and this seems to be what's causing your problem. After replacement with 0.5 or 1./2, I get
[ 3.00000000e-01 1.14967789e+00 7.48854782e-04]
for res.x.