def test_compare_two_phase_to_bigm(self):
'''Greater than and equality constraints from pg 1 of [8]_.'''
c = [3, 5]
A_ub = [
[0, 1],
]
b_ub = [6]
A_eq = [
[3, 2],
]
b_eq = [18]
A_lb = [
[3, 5],
]
b_lb = [2]
res = simplex(c=c,
A_ub=A_ub,
b_ub=b_ub,
A_eq=A_eq,
b_eq=b_eq,
A_lb=A_lb,
b_lb=b_lb)
# Round to match given solution
xres = [round(x0, 6) for x0 in res['x']]
x = [2, 6]
fopt = 36
self.assertEqual(x, xres)
self.assertEqual(fopt, res['fopt'])
def test_dual_with_A_ub_and_A_lb(self):
'''Try a dual with multiple kinds of constraints from [10]_.'''
c = [-1, -2]
A_ub = [
[4, 3],
]
b_ub = [12]
A_lb = [
[1, 3],
[2, 1],
]
b_lb = [6, 4]
res = simplex(
c=c,
A_ub=A_ub,
b_ub=b_ub,
A_lb=A_lb,
b_lb=b_lb,
)
# Make sure primal checks out
x = [6 / 5, 8 / 5]
s = [12 / 5, 0, 0]
fopt = 22 / 5
self.assertEqual(x, res['x'])
self.assertEqual(s, [round(s0, 8) for s0 in res['slack']])
self.assertEqual(fopt, -1 * res['fopt'])
# Check dual
u = [0, 3 / 5, 1 / 5]
self.assertEqual(u, res['dual'])
def test_1994_UG_exam(self):
'''Example problem from [3]_.'''
c = [20 - 10 * 13 / 60 - 2 * 20 / 60, 30 - 10 * 19 / 60 - 2 * 29 / 60]
A_ub = [
[13, 19],
[20, 29],
]
b_ub = [40 * 60, 35 * 60]
A_lb = [
[1, 0],
]
b_lb = [10]
res = simplex(
c=c,
A_ub=A_ub,
b_ub=b_ub,
A_lb=A_lb,
b_lb=b_lb,
)
# Need to get rounded to match given exam solution
xres = [round(x0, 2) for x0 in res['x']]
fres = round(sum([c0 * x0 for c0, x0 in zip(c, xres)]), 1)
x = [10, 65.52]
fopt = 1866.5
self.assertEqual(x, xres)
self.assertEqual(fopt, fres)
def test_symmetric_dual(self):
'''Extract dual solution from tableau when prob has A_ub only.
Uses example prob from pg 1 of [9]_.
'''
c = [2, 3]
A_ub = [
[-1, 1],
[1, -2],
[3, 4],
]
b_ub = [3, 2, 26]
res = simplex(c=c, A_ub=A_ub, b_ub=b_ub)
# Make sure primal solution is correct
x = [2, 5]
s = [0, 10, 0]
fopt = 19
self.assertEqual(x, res['x'])
self.assertEqual(s, res['slack'])
self.assertEqual(fopt, res['fopt'])
# Round to resolve small differences
dig = 8
ures = [round(u0, dig) for u0 in res['dual']]
u = [round(1 / 7, dig), 0, round(5 / 7, dig)]
self.assertEqual(u, ures)
def test_1988_UG_exam(self):
'''Example problem from [3]_.'''
c = [-4, -5, -6]
A_ub = [
[1, -1, 0],
]
b_ub = [5]
A_eq = [
[-1, -1, 1],
]
b_eq = [0]
A_lb = [
[1, 1, 0],
[7, 12, 0],
]
b_lb = [11, 35]
res = simplex(c=c,
A_ub=A_ub,
b_ub=b_ub,
A_eq=A_eq,
b_eq=b_eq,
A_lb=A_lb,
b_lb=b_lb)
xres = [round(x0, 6) for x0 in res['x']]
x = [8, 3, 11]
fopt = 113
self.assertEqual(x, xres)
self.assertEqual(fopt, -1 * res['fopt'])
def test_test_compare_two_phase_to_bigm2(self):
'''Greater than and equality constraints from pg 5 of [8]_.'''
c = [3, 2]
A_ub = [
[0, 1],
]
b_ub = [6]
A_eq = [
[3, 2],
]
b_eq = [18]
A_lb = [
[1, 1],
]
b_lb = [2]
res = simplex(c=c,
A_ub=A_ub,
b_ub=b_ub,
A_eq=A_eq,
b_eq=b_eq,
A_lb=A_lb,
b_lb=b_lb)
x = [6, 0]
fopt = 18
self.assertEqual(x, res['x'])
self.assertEqual(fopt, res['fopt'])
def test_1997_UG_exam(self):
'''Example problem from [3]_.'''
c = [1, 1]
A_ub = [
[50, 24],
[30, 33],
]
b_ub = [40 * 60, 35 * 60]
A_lb = [
[1, 0],
[0, 1],
]
b_lb = [45, 5]
res = simplex(
c=c,
A_ub=A_ub,
b_ub=b_ub,
A_lb=A_lb,
b_lb=b_lb,
)
x = [45, 6.25]
fopt = 1.25
self.assertEqual(x, res['x'])
self.assertEqual(fopt, res['fopt'] - 50)
def test_primal_dual_equality(self):
'''Example from stanford [11]_.'''
c = [3, 2.5]
A_ub = [
[4.44, 0],
[0, 6.67],
[4, 2.86],
[3, 6],
]
b_ub = [100, 100, 100, 100]
res = simplex(c=c, A_ub=A_ub, b_ub=b_ub)
print(res)
# Round do precision given in ref
xres = [round(x0, 1) for x0 in res['x']]
fres = round(res['fopt'], 1)
# Make sure primal is good
x = [20.4, 6.5]
fopt = 77.3
self.assertEqual(x, xres)
self.assertEqual(fopt, fres)
# Check dual while we're at it
ures = [round(u0, 3) for u0 in res['dual']]
u = [0, 0, .681, .092]
self.assertEqual(u, ures)
# Solve the dual directly
dres = simplex(
c=[-1 * b0 for b0 in b_ub],
A_lb=[list(i) for i in zip(*A_ub)],
b_lb=c,
)
# Make sure both solutions agree
self.assertEqual([round(u0, 9) for u0 in res['dual']],
[round(x0, 9) for x0 in dres['x']])
self.assertEqual([round(x0, 9) for x0 in res['x']],
[round(u0, 9) for u0 in dres['dual']])
def test_two_phase_example(self):
'''Two phase simplex example from [6]_.'''
c = [-1, -1, 1, 1]
A_eq = [
[1, 2, 1, 1],
[2, -1, -1, -3],
]
b_eq = [7, -1]
res = simplex(c, A_eq=A_eq, b_eq=b_eq)
x = [2, 0, 5, 0]
fopt = -3
self.assertEqual(x, res['x'])
self.assertEqual(fopt, -1 * res['fopt'])
def test_prob2(self):
'''Example prob from bottom of pg 25 in [1]_.'''
c = [3, 2, -4]
A = [
[1, 4, 0],
[2, 4, -2],
[1, 1, -2],
]
b = [5, 6, 2]
res = simplex(c, A, b)
x = [4, 0, 1]
fopt = 8
self.assertEqual(x, res['x'])
self.assertEqual(fopt, res['fopt'])
def test_wsu_example(self):
'''Example from WSU guide [5]_.'''
c = [3, 1]
A = [
[2, 1],
[2, 3],
]
b = [8, 12]
res = simplex(c, A, b)
x = [4, 0]
s = [0, 4]
fopt = 12
self.assertEqual(x, res['x'])
self.assertEqual(s, res['slack'])
self.assertEqual(fopt, res['fopt'])
def test_wikipedia_example(self):
'''Example from [4]_.'''
c = [2, 3, 4]
A = [
[3, 2, 1],
[2, 5, 3],
]
b = [10, 15]
res = simplex(c, A, b)
x = [0, 0, 5]
s = [5, 0]
fopt = -20
self.assertEqual(x, res['x'])
self.assertEqual(s, res['slack'])
self.assertEqual(fopt, -1 * res['fopt'])
def test_1995_UG_exam(self):
'''Example problem from [3]_.'''
c = [13, 5]
A_ub = [
[15, 7],
[25, 45],
[1, 0],
[0, 1],
]
b_ub = [20 * 60, 15 * 60, 37, 14]
res = simplex(c, A_ub=A_ub, b_ub=b_ub)
x = [36, 0]
fopt = 343
self.assertEqual(x, res['x'])
self.assertEqual(fopt, res['fopt'] - 125)
def test_prob1(self):
'''Example prob (2.1) from [1]_.'''
c = [5, 4, 3]
A_ub = [
[2, 3, 1],
[4, 1, 2],
[3, 4, 2],
]
b_ub = [5, 11, 8]
res = simplex(c, A_ub=A_ub, b_ub=b_ub)
x = [2, 0, 1]
s = [0, 1, 0]
z = 13
self.assertEqual(x, res['x'])
self.assertEqual(s, res['slack'])
self.assertEqual(z, res['fopt'])
def test_simple_example(self):
'''Simple example on pg 50 from [7]_.'''
c = [6, 14, 13]
A_ub = [
[1 / 2, 2, 1],
[1, 2, 4],
]
b_ub = [24, 60]
res = simplex(c, A_ub=A_ub, b_ub=b_ub)
# Round to match solution
xres = [round(x0, 6) for x0 in res['x']]
x = [36, 0, 6]
fopt = 294
self.assertEqual(x, xres)
self.assertEqual(fopt, res['fopt'])
def test_prob3(self):
'''Example prob from [2]_.'''
c = [4, 3]
A = [
[2, 3],
[-3, 2],
[0, 2],
[2, 1],
]
b = [6, 3, 5, 4]
res = simplex(c, A, b)
x = [3 / 2, 1]
s = [0, 11 / 2, 3, 0]
fopt = 9
self.assertEqual(x, res['x'])
self.assertEqual(s, res['slack'])
self.assertEqual(fopt, res['fopt'])
def test_1992_UG_exam(self):
'''Example problem from [3]_.'''
c = [3, 5]
A_ub = [
[12, 25],
[2 / 5, -1],
]
b_ub = [30 * 60, 0]
res = simplex(c, A_ub=A_ub, b_ub=b_ub)
# Need to get rounded to match given exam solutions
xres = [round(x0, 1) for x0 in res['x']]
fres = round(sum([c0 * x0 for c0, x0 in zip(c, xres)]), 1)
x = [81.8, 32.7]
fopt = 408.9
self.assertEqual(x, xres)
self.assertEqual(fopt, fres)
def test_1986_UG_exam(self):
'''Example problem from [3]_.'''
c = [30, 10]
A = [
[6, 3],
[3, -1],
[1, 1 / 4],
]
b = [40, 0, 4]
res = simplex(c, A, b)
dig = 6
xres = [round(x0, dig) for x0 in res['x']]
fres = round(res['fopt'], dig)
x = [round(4 / 3, dig), round(64 / 6, dig)]
fopt = round(146.666666666666666666666666, dig)
self.assertEqual(x, xres)
self.assertEqual(fopt, fres)
def test_symmetric_dual2(self):
'''Try another dual from pg 104 of [10]_.'''
c = [3, 1, -2]
A_ub = [
[1, 2, 1],
[2, -1, 3],
]
b_ub = [5, 4]
res = simplex(c, A_ub=A_ub, b_ub=b_ub)
# Make sure primal is correct
x = [13 / 5, 6 / 5, 0]
s = [0, 0]
fopt = 9
self.assertEqual(x, res['x'])
self.assertEqual(s, res['slack'])
self.assertEqual(fopt, res['fopt'])
# Now make sure dual is correct
u = [1, 1]
self.assertEqual(u, res['dual'])
def test_1987_UG_exam(self):
'''Example problem from [3]_.'''
c = [5, 6]
A_ub = [
[1, 1],
[5, 4],
]
b_ub = [10, 35]
A_lb = [
[1, -1],
]
b_lb = [3]
res = simplex(
c=c,
A_ub=A_ub,
b_ub=b_ub,
A_lb=A_lb,
b_lb=b_lb,
)
x = [47 / 9, 20 / 9]
fopt = 355 / 9
self.assertEqual(x, res['x'])
self.assertEqual(fopt, res['fopt'])
