def test_max_problem():
"""
This function will test a maximization problem
"""
# Definimos y resolvemos problema con scipy
c_max_obj = [-3, -5]
A_max_obj = [[1, 0], [0, 2], [3, 2]]
b_max_obj = [4, 12, 18]
max_obj = -1 * linprog(c_max_obj, A_ub=A_max_obj, b_ub=b_max_obj).fun
coeff_obj = linprog(c_max_obj, A_ub=A_max_obj, b_ub=b_max_obj).x
# Definimos y resolvemos problema con nuestro paquete
n_var_approx = 2
n_cons_approx = 3
matrix_max_approx = create_matrix(n_var_approx, n_cons_approx)
constrain(matrix_max_approx, '1,0,L,4')
constrain(matrix_max_approx, '0,2,L,12')
constrain(matrix_max_approx, '3,2,L,18')
obj(matrix_max_approx, '3,5,0')
problem_approx = maxz(matrix_max_approx)
max_approx = problem_approx['max']
problem_approx.pop('max')
coeff_approx = np.array(list(problem_approx.values()))
assert max_approx == approx(max_obj)
assert coeff_obj == approx(coeff_approx)
def test_min_problem():
"""
This function will test a minimization problem
"""
# Definimos y resolvemos problema con scipy
c_min_obj = [-1, -3]
A_min_obj = [[1, 1], [-1, 2]]
b_min_obj = [6, 8]
min_obj = linprog(c_min_obj, A_ub=A_min_obj, b_ub=b_min_obj).fun
coeff_obj = linprog(c_min_obj, A_ub=A_min_obj, b_ub=b_min_obj).x
# Definimos y resolvemos problema con nuestro paquete
n_var_approx = 2
n_cons_approx = 2
matrix_min_approx = create_matrix(n_var_approx, n_cons_approx)
constrain(matrix_min_approx, '1,1,L,6')
constrain(matrix_min_approx, '-1,2,L,8')
obj(matrix_min_approx, '-1,-3,0')
problem_approx = minz(matrix_min_approx)
min_approx = problem_approx['min']
problem_approx.pop('min')
coeff_approx = np.array(list(problem_approx.values()))
assert min_approx == approx(min_obj)
assert coeff_obj == approx(coeff_approx)
def test_net_problem():
"""
This function will test a minimum cost network flow problem
"""
# Definimos y resolvemos problema con scipy
c_net_obj = [2, 4, 9, 3, 1, 3, 2]
A_ub_net_obj = [[1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0]]
b_ub_net_obj = [10, 80]
A_eq_net_obj = [[1, 1, 1, 0, 0, 0, 0], [-1, 0, 0, 1, 0, 0, 0],
[0, -1, 0, -1, 1, 0, 0], [0, 0, -1, 0, 0, 1, -1],
[0, 0, 0, 0, -1, -1, 1]]
b_eq_net_obj = [50, 40, 0, -30, -60]
net_obj = linprog(c_net_obj,
A_ub=A_ub_net_obj,
b_ub=b_ub_net_obj,
A_eq=A_eq_net_obj,
b_eq=b_eq_net_obj).fun
net_coeff_obj = linprog(c_net_obj,
A_ub=A_ub_net_obj,
b_ub=b_ub_net_obj,
A_eq=A_eq_net_obj,
b_eq=b_eq_net_obj).x
# Definimos y resolvemos problema con nuestro paquete
n_var_approx = 7
n_cons_approx = 7
matrix_net_approx = create_matrix(n_var_approx, n_cons_approx)
constrain(matrix_net_approx, '1,1,1,0,0,0,0,E,50')
constrain(matrix_net_approx, '-1,0,0,1,0,0,0,E,40')
constrain(matrix_net_approx, '0,-1,0,-1,1,0,0,E,0')
constrain(matrix_net_approx, '0,0,-1,0,0,1,-1,E,-30')
constrain(matrix_net_approx, '0,0,0,0,-1,-1,1,E,-60')
constrain(matrix_net_approx, '1,0,0,0,0,0,0,L,10')
constrain(matrix_net_approx, '0,0,0,0,1,0,0,L,80')
obj(matrix_net_approx, '2,4,9,3,1,3,2,0')
problem_approx = minz(matrix_net_approx)
net_approx = problem_approx['min']
problem_approx.pop('min')
net_coeff_approx = np.array(list(problem_approx.values()))
assert net_obj == approx(net_approx)
assert np.round(net_coeff_obj, 0) == approx(net_coeff_approx)
6.828, 84.55, 80.55, 86.10, 54.30, 18.86, 80.63, 54.07,
63.94, 89.28, 64.89, 87.44, 13.06, 31.29, 63.10, 75.33,
21.06, 61.33, 1.093, 91.08
],
[
85.33, 57.98, 42.51, 53.95, 10.49, 32.74, 43.28, 51.52,
89.99, 43.97, 46.69, 44.05, 85.91, 19.12, 23.85, 58.82,
71.23, 8.885, 18.81, 87.44
]]
b_max_obj = [
79.72, 68.64, 1.240, 34.53, 43.64, 3.692, 44.21, 94.85, 39.16, 38.43,
57.08, 19.63, 70.07, 32.45, 15.32, 49.46, 54.54, 24.96, 11.98, 1.772,
50.61, 94.20, 97.49, 34.16, 6.26, 70.31, 79.18, 44.51, 53.22, 50.65
]
max_obj_1 = -1 * linprog(c_max_obj_1, A_ub=A_max_obj_1,
b_ub=b_max_obj_1).fun
coeff_obj_1 = linprog(c_max_obj_1, A_ub=A_max_obj_1, b_ub=b_max_obj_1).x
# Paquete mex
matrix_max_approx_1 = create_matrix(20, 30)
max_approx_1, coeff_approx_1 = profiling_memory_example(
matrix_max_approx_1)
print("El valor objetivo obtenido con scipy es: ", max_obj_1)
print("El valor aproximado obtenido con mex es: ", max_approx_1)
print("Los coeficientes objetivos obtenidos con scipy son: ", coeff_obj_1)
print("Los coeficientes aproximados obtenidos con mex son: ",
coeff_approx_1)
assert max_approx_1 == approx(max_obj)
assert np.round(coeff_obj, 2) == approx(np.round(coeff_obj, 2))
def profiling_memory_example(aux=True):
"""
Problema a resolver de optimización con el método Simplex
"""
matrix = create_matrix(20, 30)
#Restricciones 1-5:
matrix = constrain(
matrix,
'90.09,50.61,45.03,16.83,26.92,36.29,51.61,2.450,25.15,30.22,81.78,2.444,34.71,57.17,41.14,92.00,69.17,26.77,38.44,25.35,L,79.72',
True)
matrix = constrain(
matrix,
'69.62,6.235,18.95,4.843,12.34,82.56,83.65,11.18,29.91,34.66,79.32,64.11,95.56,70.83,69.77,93.99,10.83,17.88,78.04,87.34,L,68.64',
True)
matrix = constrain(
matrix,
'27.58,31.56,72.90,95.74,69.19,84.21,58.42,18.88,72.27,85.58,60.66,51.78,46.34,30.96,5.505,11.68,84.84,81.16,3.668,65.52,L,1.240',
True)
matrix = constrain(
matrix,
'28.91,98.28,80.47,78.34,48.34,40.00,92.46,93.44,93.79,46.63,50.50,30.32,71.96,52.57,46.29,67.03,71.13,82.94,4.676,5.110,L,34.53',
True)
matrix = constrain(
matrix,
'10.16,9.828,11.24,53.81,23.53,16.98,94.65,55.01,96.43,5.556,54.05,40.95,35.37,14.02,32.04,71.37,29.52,24.35,71.32,46.73,L,43.64',
True)
#Restricciones 6-10:
matrix = constrain(
matrix,
'70.56,93.54,27.93,95.94,91.23,8.491,78.54,7.435,85.27,32.27,97.65,34.44,97.45,77.70,86.22,3.460,52.49,59.86,6.446,20.77,L,3.692',
True)
matrix = constrain(
matrix,
'30.93,40.11,9.917,22.34,2.947,8.553,85.74,31.01,4.919,12.60,3.358,89.39,50.05,25.59,13.33,75.14,57.81,14.29,88.59,24.34,L,44.21',
True)
matrix = constrain(
matrix,
'7.511,72.81,19.49,55.05,86.04,36.84,7.233,67.59,92.62,24.06,15.87,45.52,75.98,71.86,64.45,15.81,57.22,84.86,28.66,7.867,L,94.85',
True)
matrix = constrain(
matrix,
'62.27,38.88,82.58,84.71,68.00,97.57,36.58,11.57,73.91,75.40,65.75,7.540,52.08,96.61,9.278,60.24,59.22,6.214,63.88,68.99,L,39.16',
True)
matrix = constrain(
matrix,
'73.05,10.49,93.23,91.39,63.19,47.53,20.71,14.26,51.71,71.02,11.87,61.36,97.72,70.67,28.40,73.55,33.02,81.46,67.22,85.30,L,38.43',
True)
#Restricciones 11-15:
matrix = constrain(
matrix,
'93.49,28.98,23.75,48.18,73.61,18.85,15.89,90.90,71.75,80.48,97.08,88.23,86.15,57.57,78.16,40.38,19.41,75.39,54.97,38.35,L,57.08',
True)
matrix = constrain(
matrix,
'84.61,42.17,56.76,23.61,66.47,13.86,36.55,37.61,39.77,2.123,92.07,21.21,85.36,27.84,81.87,34.29,55.51,71.08,81.14,41.18,L,19.63',
True)
matrix = constrain(
matrix,
'66.07,71.30,29.57,3.874,45.04,98.19,92.92,18.87,44.20,17.36,36.33,45.50,17.97,67.95,62.03,32.55,50.91,47.08,85.63,36.12,L,70.07',
True)
matrix = constrain(
matrix,
'63.66,7.173,29.93,31.48,64.60,72.68,2.754,16.71,79.55,4.050,95.43,31.18,61.87,68.41,3.567,21.61,45.96,3.881,40.50,91.86,L,32.45',
True)
matrix = constrain(
matrix,
'67.60,7.276,78.37,96.71,79.11,21.35,78.86,23.26,63.76,43.93,59.46,78.19,70.34,92.42,58.98,95.50,84.86,76.11,13.00,60.67,L,15.32',
True)
#Restricciones 16-20:
matrix = constrain(
matrix,
'12.17,45.38,51.97,93.29,97.74,58.34,71.99,26.91,26.85,74.88,69.95,43.51,8.723,38.97,74.16,81.20,77.52,20.84,46.12,16.24,L,49.46',
True)
matrix = constrain(
matrix,
'85.82,3.365,53.87,41.57,37.04,97.64,16.76,90.16,50.49,76.92,85.17,57.76,29.29,12.79,93.86,59.50,84.81,43.91,6.931,14.25,L,54.54',
True)
matrix = constrain(
matrix,
'72.94,37.67,28.00,33.56,71.22,73.32,33.33,27.54,71.75,61.17,39.68,38.85,79.89,92.34,31.80,10.18,78.30,6.469,41.89,50.98,L,24.96',
True)
matrix = constrain(
matrix,
'80.03,67.82,37.00,51.50,17.85,10.91,26.95,65.79,18.51,84.34,3.196,72.33,48.76,8.459,53.13,18.23,9.679,2.543,48.12,52.09,L,11.98',
True)
matrix = constrain(
matrix,
'28.10,98.61,1.938,94.54,98.78,18.29,26.88,91.15,9.967,5.279,99.44,79.94,82.80,30.05,85.13,8.410,83.47,15.45,46.43,56.54,L,1.772',
True)
#Restricciones 21-25:
matrix = constrain(
matrix,
'92.44,92.82,95.87,78.14,93.72,55.82,92.28,64.95,94.39,91.63,20.11,32.16,10.08,23.98,9.257,71.39,48.74,60.76,96.93,56.57,L,50.61',
True)
matrix = constrain(
matrix,
'22.14,72.51,48.51,98.13,90.25,85.24,1.804,28.47,45.93,36.05,35.43,7.104,70.67,97.69,74.87,39.72,13.98,58.00,2.024,85.30,L,94.20',
True)
matrix = constrain(
matrix,
'72.16,93.13,45.85,76.06,22.53,36.16,81.15,92.51,97.12,67.37,37.37,69.21,72.32,63.23,92.90,61.86,11.42,34.15,49.78,6.688,L,97.49',
True)
matrix = constrain(
matrix,
'58.39,34.12,77.96,5.433,83.02,84.14,59.82,22.39,70.75,19.67,24.53,41.00,56.24,89.32,14.63,77.15,34.12,34.28,55.17,31.45,L,34.16',
True)
matrix = constrain(
matrix,
'20.15,1.416,74.34,23.20,8.632,71.47,32.10,59.23,91.44,37.58,23.29,39.11,19.54,3.000,2.319,43.50,35.17,66.78,40.41,50.82,L,6.26',
True)
#Restricciones 26-30:
matrix = constrain(
matrix,
'54.65,70.46,46.30,66.92,27.45,25.48,81.67,96.67,42.57,43.22,43.29,60.58,19.07,27.73,92.63,60.94,84.33,8.800,78.62,17.94,L,70.31',
True)
matrix = constrain(
matrix,
'83.10,98.45,22.09,36.01,39.99,6.380,28.27,10.69,57.29,63.19,44.42,51.00,15.57,11.27,63.56,17.54,40.71,47.53,27.81,27.66,L,79.18',
True)
matrix = constrain(
matrix,
'22.20,29.98,87.02,25.26,47.23,55.22,83.70,88.56,67.82,6.36,66.62,3.853,47.37,97.22,83.37,89.41,61.79,96.26,91.11,79.89,L,44.51',
True)
matrix = constrain(
matrix,
'6.828,84.55,80.55,86.10,54.30,18.86,80.63,54.07,63.94,89.28,64.89,87.44,13.06,31.29,63.10,75.33,21.06,61.33,1.093,91.08,L,53.22',
True)
matrix = constrain(
matrix,
'85.33,57.98,42.51,53.95,10.49,32.74,43.28,51.52,89.99,43.97,46.69,44.05,85.91,19.12,23.85,58.82,71.23,8.885,18.81,87.44,L,50.65',
True)
#Función objetivo:
matrix = obj(
matrix,
'52.16,45.51,69.09,84.88,38.73,84.47,97.50,61.32,16.27,36.42,77.24,36.91,62.85,50.77,81.22,66.94,31.10,45.05,37.68,40.76,0',
True)
problem_approx_1 = maxz(matrix)
max_approx_1 = problem_approx_1['max']
problem_approx_1.pop('max')
coeff_approx_1 = np.array(list(problem_approx_1.values()))
return max_approx_1, coeff_approx_1
import numpy as np from scipy.optimize import linprog from pytest import approx from mex.simplex.simplex_networks import create_matrix, pivots_col, pivots_row, find_negative_col, find_negative_row, find_pivot_col, find_pivot_row, pivot from mex.simplex.problem_definition import add_cons, constrain, add_obj, obj, maxz, minz from memory_profiler import profile from guppy import hpy hp = hpy() hp.setrelheap() matrix_max_approx_1 = create_matrix(7, 7) constrain(matrix_max_approx_1, '1,1,1,0,0,0,0,E,50') constrain(matrix_max_approx_1, '-1,0,0,1,0,0,0,E,40') constrain(matrix_max_approx_1, '0,-1,0,-1,1,0,0,E,0') constrain(matrix_max_approx_1, '0,0,-1,0,0,1,-1,E,-30') constrain(matrix_max_approx_1, '0,0,0,0,-1,-1,1,E,-60') constrain(matrix_max_approx_1, '1,0,0,0,0,0,0,L,10') constrain(matrix_max_approx_1, '0,0,0,0,1,0,0,L,80') obj(matrix_max_approx_1, '2,4,9,3,1,3,2,0') problem_approx_1 = minz(matrix_max_approx_1) h = hp.heap() print(h)
import numpy as np from scipy.optimize import linprog from pytest import approx from mex.simplex.simplex_networks import create_matrix, pivots_col, pivots_row, find_negative_col, find_negative_row, find_pivot_col, find_pivot_row, pivot from mex.simplex.problem_definition import add_cons, constrain, add_obj, obj, maxz, minz from memory_profiler import profile from guppy import hpy hp = hpy() hp.setrelheap() matrix_max_approx_1 = create_matrix(2, 2) constrain(matrix_max_approx_1, '1,1,L,6') constrain(matrix_max_approx_1, '-1,2,L,8') obj(matrix_max_approx_1, '-1,-3,0') problem_approx_1 = minz(matrix_max_approx_1) h = hp.heap() print(h)