def test_sum_exp_int(self):
prob = LpProblem('unit test')
x1 = prob.variable("x1",0)
f = x1 + 6
g = f + 3
self.assertEqual(g[x1.name], 1)
self.assertEqual(g.constant, 9)
def test_paint_case(self):
"""
Status: Optimal
LatexPaint = 4.0
EmanelPaint = 0.0
p1 = 0.0
n1 = 0.0
p2 = 0.0
n2 = 600.0
p3 = 0.0
n3 = 7.0
"""
prob = LpProblem("The Paint Company Problem")
x1 = prob.variable("LatexPaint",0)
x2 = prob.variable("EmanelPaint",0)
n1 = prob.variable("n1",0)
n2 = prob.variable("n2",0)
n3 = prob.variable("n3",0)
p1 = prob.variable("p1",0)
p2 = prob.variable("p2",0)
p3 = prob.variable("p3",0)
f1 = 10*x1 + 15*x2 + n1 - p1 == 40
f2 = 100*x1 + 100*x2 + n2 - p2 == 1000
f3 = x2 + n3 - p3 == 7
prob.constraints = f1
prob.constraints.append(f2)
prob.constraints.append(f3)
prob.objective = [p1, n2, n3]
prob.solve()
self.assertEqual(x1.result, 4)
self.assertEqual(x2.result,0)
def test_sum_int_exp(self):
prob = LpProblem('unit test')
x1 = prob.variable("x1",0)
g = x1 + 4
f = 2 + g
self.assertEqual(f[x1.name], 1)
self.assertEqual(f.constant, 6)
def test_mult_exp_int(self):
prob = LpProblem('unit test')
x1 = prob.variable("x1",0)
g = x1 + 2
f = g * 7
self.assertEqual(f[x1.name], 7)
self.assertEqual(f.constant, 14)
def test_sum_var_var(self):
prob = LpProblem('unit test')
x1 = prob.variable("x1",0)
x2 = prob.variable("x2",0)
f = x1 + x2
self.assertEqual(f[x1.name], 1)
self.assertEqual(f[x2.name], 1)
def test_ignizio2_case(self):
"""
pass
"""
prob = LpProblem()
x1 = prob.variable("x1", 0)
x2 = prob.variable("x2", 0)
p1 = prob.variable("p1", 0)
p2 = prob.variable("p2", 0)
p3 = prob.variable("p3", 0)
p4 = prob.variable("p4", 0)
n1 = prob.variable("n1", 0)
n2 = prob.variable("n2", 0)
n3 = prob.variable("n3", 0)
n4 = prob.variable("n4", 0)
prob.constraints = [
8*x1 + 12*x2 + n1 - p1 == 1000,
x1 + 2*x2 + n2 - p2 == 40,
x1 + n3 - p3 == 30,
x2 + n4 - p4 == 15
]
prob.objective = [(p3+p4), n1, p2, (1.5*n4 + n3)]
prob.solve()
self.assertEqual(x1.result, 30)
self.assertEqual(x2.result, 15)
def test_sum_exp_var(self):
prob = LpProblem('unit test')
x1 = prob.variable("x1",0)
x2 = prob.variable("x2",0)
f = x1 + 6
g = f + x2
self.assertEqual(g[x1.name], 1)
self.assertEqual(g[x2.name], 1)
self.assertEqual(g.constant, 6)
def test_sub_var_exp(self):
prob = LpProblem('unit test')
x1 = prob.variable("x1",0)
x2 = prob.variable("x2",0)
f = x1 + 6
g = x2 - f
self.assertEqual(g[x1.name], -1)
self.assertEqual(g[x2.name], 1)
self.assertEqual(g.constant, -6)
def test_sum_exp_exp(self):
prob = LpProblem('unit test')
x1 = prob.variable("x1",0)
x2 = prob.variable("x2",0)
g = x1 + 4
h = x2 + 3
f = g + h
self.assertEqual(f[x1.name], 1)
self.assertEqual(f[x2.name], 1)
self.assertEqual(f.constant, 7)
def test_ignizio_example_case(self):
"""
OPTIMAL SOLUTION FOUND
Status: Optimal
x1 = 4.0
x2 = 6.0
objective function: 18.0
"""
prob = LpProblem("Lp Programming Test Problem")
x1 = prob.variable("x1",0)
x2 = prob.variable("x2",0)
n1 = prob.variable("n1",0)
n2 = prob.variable("n2",0)
n3 = prob.variable("n3",0)
p1 = prob.variable("p1",0)
p2 = prob.variable("p2",0)
p3 = prob.variable("p3",0)
f1 = x1 + x2 + n1 - p1 == 10, "some name"
f2 = x1 + n2 - p2 == 4
f3 = 5*x1 + 3*x2 + n3 - p3 == 56
prob.constraints = [f1, f2, f3]
prob.objective = [2*p1 + 3*p2,n3]
prob.solve()
self.assertEqual(x1.result, 4.0)
self.assertEqual(x2.result, 6.0)
def test_class1_case(self):
"""
pass
"""
prob = LpProblem()
x1 = prob.variable("x1", 0, 6)
x2 = prob.variable("x2", 0)
p1 = prob.variable("p1", 0)
p2 = prob.variable("p2", 0)
n1 = prob.variable("n1", 0)
n2 = prob.variable("n2", 0)
prob.constraints = [
x1 + 2*x2 <= 10,
4*x1 + 8*x2 + n1 - p1 == 45,
8*x1 + 24*x2 + n2 - p2 == 100
]
prob.objective = 2*n1 + p2
prob.solve()
def test_pyglpk_StdExample_case(self):
"""
http://www.cs.cornell.edu/~tomf/pyglpk/ex_ref.html
RESULTS:
x0 = 33.3333; x1 = 66.6667; x2 = 0
"""
prob = LpProblem("Lp Programming Test Problem", 'max')
x0 = prob.variable("x0",0)
x1 = prob.variable("x1",0)
x2 = prob.variable("x2",0)
prob.constraints = [
x0 + x1 + x2 <= 100,
10*x0 + 4*x1 + 5*x2 <= 600,
2*x0 + 2*x1 + 6*x2 <= 300
]
prob.objective = [10*x0 + 6*x1 + 4*x2]
prob.solve()
self.assertEqual(round(x0.result, 3), 33.333)
self.assertEqual(round(x1.result, 3), 66.667)
def test_stdform_example_case(self):
"""
Status: Optimal
ChickenPercent = 33.3333
BeefPercent = 66.6667
Total Cost of Ingredients per can = 0.9666665
"""
prob = LpProblem()
x1 = prob.variable("x1", 0)
x2 = prob.variable("x2", 0)
prob.objective = 0.013*x1 + 0.008*x2
prob.constraints = [
x1 + x2 == 100,
0.10*x1 + 0.20*x2 >= 8,
0.080*x1 + 0.100*x2 >= 6,
0.001*x1 + 0.005*x2 <= 2,
0.002*x1 + 0.005*x2 <= 0.4
]
prob.solve()
self.assertEqual(round(x1.result, 3), 33.333)
self.assertEqual(round(x2.result, 3), 66.667)
def test_sum_int_var(self):
prob = LpProblem('unit test')
x1 = prob.variable("x1",0)
f = 2 + x1
self.assertEqual(f[x1.name], 1)
self.assertEqual(f.constant, 2)
def test_mult_var_int(self):
prob = LpProblem('unit test')
x1 = prob.variable("x1",0)
f = x1 * 2
self.assertEqual(f[x1.name], 2)
self.assertEqual(f.constant, 0)
def test_pyglpk_GoalExample_case(self):
"""
http://www.cs.cornell.edu/~tomf/pyglpk/ex_ref.html
RESULTS:
x0 = 33.3333; x1 = 66.6667; x2 = 0
"""
prob = LpProblem("Lp Programming Test Problem")
x0 = prob.variable("x0",0)
x1 = prob.variable("x1",0)
x2 = prob.variable("x2",0)
n1 = prob.variable("n1",0)
n2 = prob.variable("n2",0)
n3 = prob.variable("n3",0)
n4 = prob.variable("n4",0)
p1 = prob.variable("p1",0)
p2 = prob.variable("p2",0)
p3 = prob.variable("p3",0)
p4 = prob.variable("p4",0)
f1 = 10*x0 + 6*x1 + 4*x2 + n1 - p1 == 1000
f2 = x0 + x1 + x2 + n2 - p2 == 100
f3 = 10*x0 + 4*x1 + 5*x2 + n3 - p3 == 600
f4 = 2*x0 + 2*x1 + 6*x2 + n4 - p4 == 300
prob.constraints = [f1, f2, f3, f4]
prob.objective = [p2+p3+p4, n1]
prob.solve()
self.assertEqual(round(x0.result, 3), 33.333)
self.assertEqual(round(x1.result, 3), 66.667)
def test_class2_case(self):
"""
pass
"""
prob = LpProblem()
x1 = prob.variable("x1", 0, 6)
x2 = prob.variable("x2", 0)
p1 = prob.variable("p1", 0)
p2 = prob.variable("p2", 0)
p3 = prob.variable("p3", 0)
p4 = prob.variable("p4", 0)
n1 = prob.variable("n1", 0)
n2 = prob.variable("n2", 0)
n3 = prob.variable("n3", 0)
n4 = prob.variable("n4", 0)
prob.constraints = [
7*x1 + 3*x2 + n1 - p1 == 40,
10*x1 + 5*x2 + n2 - p2 == 60,
5*x1 + 4*x2 + n3 - p3 == 35,
100*x1 + 60*x2 <= 600
]
prob.objective = 200*n1 + 100*n2 + 50*n3
prob.solve()
def test_sum_var_int(self):
prob = LpProblem('unit test')
x1 = prob.variable("x1",0)
f = x1 + 6
self.assertEqual(f[x1.name], 1)
self.assertEqual(f.constant, 6)
def test_birdsong_case(self):
"""
pass
"""
prob = LpProblem()
x1 = prob.variable("x1", 0)
x2 = prob.variable("x2", 0)
x3 = prob.variable("x3", 0)
x4 = prob.variable("x4", 0)
p1 = prob.variable("p1", 0)
p2 = prob.variable("p2", 0)
p3 = prob.variable("p3", 0)
p4 = prob.variable("p4", 0)
p5 = prob.variable("p4", 0)
p6 = prob.variable("p6", 0)
p7 = prob.variable("p7", 0)
n1 = prob.variable("n1", 0)
n2 = prob.variable("n2", 0)
n3 = prob.variable("n3", 0)
n4 = prob.variable("n4", 0)
n5 = prob.variable("n5", 0)
n6 = prob.variable("n6", 0)
n7 = prob.variable("n7", 0)
f1 = x1 + x2 + x3 + x4 + n1 - p1 == 50000, "profit"
f2 = x1 + n2 - p2 == 20000, "assembly hours"
f3 = x2 + n3 - p3 == 5000, "demand deluxe"
f4 = x2 + n4 - p4 == 15000, "demand supreme"
f5 = x3 + n5 - p5 == 10000, "foobar"
f6 = x4 + n6 - p6 == 30000, "barfoo"
f7 = .06*x1 + .05*x2 +.08*x3 + .07*x4 + n7 - p7 == 4000, "dsds"
prob.constraints = [f1,f2,f3,f4,f5,f6,f7]
prob.objective = p1
prob.objective.append(n2 + 2*n3 + 2*p4)
prob.objective.append(n6)
prob.objective.append(p5 + n7)
prob.solve()
self.assertEqual(x1.result, 20000.0)
self.assertEqual(x2.result, 5000.0)
self.assertEqual(x3.result, 0.0)
self.assertEqual(x4.result, 25000.0)
p = x0 + x1 + x2
q = 10x0 + 4x1 + 5x2
r = 2x0 + 2x1 + 6x2
and bounds of variables:
-inf < p <= 100 0 <= x0 < inf
-inf < q <= 600 0 <= x1 < inf
-inf < r <= 300 0 <= x2 < inf
"""
from pytorovich import LpProblem
prob = LpProblem("Goal Exammple")
x0 = prob.variable("x0",0)
x1 = prob.variable("x1",0)
x2 = prob.variable("x2",0)
n1 = prob.variable("n1",0)
n2 = prob.variable("n2",0)
n3 = prob.variable("n3",0)
n4 = prob.variable("n4",0)
p1 = prob.variable("p1",0)
p2 = prob.variable("p2",0)
p3 = prob.variable("p3",0)
p4 = prob.variable("p4",0)
f1 = 10*x0 + 6*x1 + 4*x2 + n1 - p1 == 1000
f2 = x0 + x1 + x2 + n2 - p2 == 100
f3 = 10*x0 + 4*x1 + 5*x2 + n3 - p3 == 600
"""
------------------------
Knapsack Problem from
http://xkcd.com/287/
------------------------
"""
from pytorovich import LpProblem
prob = LpProblem("Linear Programming Test Problem")
items = ( ('MIXED FRUIT', 2.15),
('FRENCH FRIES', 2.75),
('SIDE SALAD', 3.35),
('HOT WINGS', 3.55),
('MOZZ STICKS', 4.20),
('SAMPLER PLATE', 5.80),
('BARBEQUE', 6.55) )
exactcost = 15.05
f = [prob.variable(item[0],0,None,int) *
item[1] for item in items]
prob.objective = [sum(f)]
prob.constraints = [sum(f) == exactcost]
prob.solve()
for key, val in prob.variables.iteritems():
q = 10x0 + 4x1 + 5x2
r = 2x0 + 2x1 + 6x2
and bounds of variables:
-inf < p <= 100 0 <= x0 < inf
-inf < q <= 600 0 <= x1 < inf
-inf < r <= 300 0 <= x2 < inf
"""
from pytorovich import LpProblem
prob = LpProblem("Standard Example", 'max')
x0 = prob.variable("x0")
x1 = prob.variable("x1")
x2 = prob.variable("x2")
prob.constraints = [
x0 + x1 + x2 <= 100,
10*x0 + 4*x1 + 5*x2 <= 600,
2*x0 + 2*x1 + 6*x2 <= 300
]
prob.objective = [10*x0 + 6*x1 + 4*x2]
prob.solve()
for key, val in prob.variables.iteritems():
