def run():
#TODO:
# fill missing test based on the example_01_solvable.py
# to make the test a bit more interesting:
# * make the model unfeasible in a way detectable by the 2-phase simplex
#
model = Model("example_05_unfeasible")
x1 = model.create_variable("x1")
x2 = model.create_variable("x2")
model.add_constraint(x1 >= 6)
model.add_constraint(x2 >= 6)
model.add_constraint(x1 + x2 <= 11)
model.minimize(x1 + x2)
try:
model.solve()
raise AssertionError(
"Your algorithm found a solution to an unfeasible problem. This shouldn't happen..."
)
except Exception as e:
logging.info(
"Congratulations! This problem is unfeasible and your algorithm has found that :) \n"
+ "Alghoritm raise an exception: " + e.__str__())
def run():
model = Model("example_02_solvable")
x1 = model.create_variable("x1")
x2 = model.create_variable("x2")
x3 = model.create_variable("x3")
model.add_constraint(x1 + 2 * x2 + x3 >= -100)
model.add_constraint(2 * x1 + x2 + 3 * x3 >= -200)
model.add_constraint(x1 + 2 * x2 + 4 * x3 <= 300)
model.minimize(9 * x1 + 9 * x2 + 7 * x3)
try:
solution = model.solve()
except:
raise AssertionError(
"This problem has a solution and your algorithm hasn't found it!")
logging.info(solution)
assert (solution.assignment == [
0.0, 0.0, 0.0, 100.0, 200.0, 300.0
]), "Your algorithm found an incorrect solution!"
logging.info("Congratulations! This solution seems to be alright!")
def run():
primal = Model("example_06_dual")
x0 = primal.create_variable("x0")
x1 = primal.create_variable("x1")
x2 = primal.create_variable("x2")
primal.add_constraint(4*x0 + 8*x1 - x2 <= 5)
primal.add_constraint(7*x0 - 2*x1 + 2*x2 >= 4)
primal.maximize(3*x0 + 2*x1 - 6*x2)
expected_dual = Model("example_06_dual (expected dual)")
y0 = expected_dual.create_variable("y0")
y1 = expected_dual.create_variable("y1")
expected_dual.add_constraint(4*y0 - 7*y1 >= 3)
expected_dual.add_constraint(8*y0 + 2*y1 >= 2)
expected_dual.add_constraint(-1*y0 - 2*y1 >= -6)
expected_dual.minimize(5 * y0 - 4 * y1)
dual = primal.dual()
assert dual.is_equivalent(expected_dual), "dual wasn't calculated as expected"
assert primal.is_equivalent(dual.dual()), "double dual should equal the initial model"
primal_solution = primal.solve()
dual_solution = dual.solve()
assert primal_solution.objective_value() == dual_solution.objective_value(), "dual and primal should have the same value at optimum"
logging.info("Congratulations! The dual creation seems to be implemented correctly :)")
def run():
model = Model("example_03_unbounded")
x1 = model.create_variable("x1")
x2 = model.create_variable("x2")
x3 = model.create_variable("x3")
model.add_constraint(x1 - 3*x2 + 2*x3 <= 10)
model.add_constraint(x1 + 5*x2 - 1*x3 >= -7)
model.minimize(5 * x1 + 8 * x2)
try:
model.solve()
raise AssertionError("Your algorithm found a solution to an unbounded problem. This shouldn't happen...")
except:
logging.info("Congratulations! This problem is unbounded and your algorithm has found that :)")
def run():
#TODO:
# fill missing test based on the example_01_solvable.py
# to make the test a bit more interesting:
# * minimize the objective (so the solver would have to normalize it)
# * make some "=>" constraints
# * the model still has to be solvable by the basix simplex withour artificial variables
#
# TIP: you may use other solvers (e.g. https://online-optimizer.appspot.com)
# to find the correct solution
model = Model("example_02_solvable")
x1 = model.create_variable("x1")
x2 = model.create_variable("x2")
x3 = model.create_variable("x3")
x4 = model.create_variable("x4")
model.add_constraint(-2 * x1 - 4 * x2 - 3 * x3 - 7 * x4 >= -800)
model.add_constraint(-4 * x1 - 5 * x2 - 3 * x3 - 2 * x4 >= -640)
model.add_constraint(-4 * x1 - 1 * x2 - 4 * x3 - 1 * x4 >= -600)
model.minimize(-80 * x1 - 60 * x2 - 30 * x3 - 50 * x4)
try:
solution = model.solve()
except:
raise AssertionError(
"This problem has a solution and your algorithm hasn't found it!")
logging.info(solution)
assert (solution.assignment == [
120.0, 0, 0, 80.0, 0.0, 0.0, 40
]), "Your algorithm found an incorrect solution!"
logging.info("Congratulations! This solution seems to be alright :)")
from saport.simplex.model import Model
model = Model("zadanie 2")
x1 = model.create_variable("x1")
x2 = model.create_variable("x2")
x3 = model.create_variable("x3")
x4 = model.create_variable("x4")
model.add_constraint(0.8 * x1 + 2.4 * x2 + 0.9 * x3 + 0.4 * x4 >= 1200)
model.add_constraint(0.6 * x1 + 0.6 * x2 + 0.3 * x3 + 0.3 * x4 >= 600)
model.minimize(9.6 * x1 + 14.4 * x2 + 10.8 * x3 + 7.2 * x4)
solution = model.solve()
print(solution)
def run():
primal = Model("Zad1")
# x1 -> SS - super
# x2 -> S - standardowy
# x3 -> O - oszczędny
x1 = primal.create_variable("x1")
x2 = primal.create_variable("x2")
x3 = primal.create_variable("x3")
primal.add_constraint(2 * x1 + 2 * x2 + 5 * x3 <= 40)
primal.add_constraint(x1 + 3 * x2 + 2 * x3 <= 30)
primal.add_constraint(3 * x1 + x2 + 3 * x3 <= 30)
primal.maximize(32 * x1 + 24 * x2 + 48 * x3)
expected_dual = Model("Zad1")
y1 = expected_dual.create_variable("y1")
y2 = expected_dual.create_variable("y2")
y3 = expected_dual.create_variable("y3")
expected_dual.add_constraint(2 * y1 + y2 + 3 * y3 >= 32)
expected_dual.add_constraint(2 * y1 + 3 * y2 + y3 >= 24)
expected_dual.add_constraint(5 * y1 + 2 * y2 + 3 * y3 >= 48)
expected_dual.minimize(40 * y1 + 30 * y2 + 30 * y3)
expected_bounds = [(19.6363636363, 44.57142857),
(17.77777777, 53.333333333), (37.0, 61.99999999999)]
dual = primal.dual()
assert dual.is_equivalent(
expected_dual), "dual wasn't calculated as expected"
assert primal.is_equivalent(
dual.dual()), "double dual should equal the initial model"
primal_solution = primal.solve()
dual_solution = dual.solve()
assert math.isclose(
primal_solution.objective_value(),
dual_solution.objective_value(),
abs_tol=0.000001
), "dual and primal should have the same value at optimum"
logging.info(
"Congratulations! The dual creation seems to be implemented correctly :)\n"
)
analyser = Analyser()
analysis_results = analyser.analyse(primal_solution)
analyser.interpret_results(primal_solution, analysis_results, logging.info)
objective_analysis_results = analysis_results[
ObjectiveSensitivityAnalyser.name()]
tolerance = 0.001
for (i, bounds_pair) in enumerate(objective_analysis_results):
assert math.isclose(
bounds_pair[0], expected_bounds[i][0], abs_tol=tolerance
), f"left bound of the coefficient range seems to be incorrect, expected {expected_bounds[i][0]}, got {bounds_pair[0]}"
assert math.isclose(
bounds_pair[1], expected_bounds[i][1], abs_tol=tolerance
), f"right bound of the coefficient range seems to be incorrect, expected {expected_bounds[i][1]}, got {bounds_pair[1]}"
logging.info(
"Congratulations! This cost coefficients analysis look alright :)")
print(dual)
print(analyser.interpret_results(primal_solution, analysis_results))
from saport.simplex.model import Model
model = Model("z3")
x = model.create_variable("x")
y = model.create_variable("y")
model.add_constraint(15 * x + 2 * y <= 60)
model.add_constraint(5 * x + 15 * y >= 50)
model.add_constraint(20 * x + 5 * y >= 40)
model.minimize(8 * x + 4 * y)
solution = model.solve()
print(solution)
x1 = model.create_variable("x1")
x2 = model.create_variable("x2")
x3 = model.create_variable("x3")
# 4. FYI: You can create expression and evaluate them
expr1 = 0.16 * x1 - 0.94 * x2 + 0.9 * x3
print(
f"Value of the expression for the specified assignment is {expr1.evaluate([1, 1, 2])}\n"
)
# 5. Then add constraints to the model
model.add_constraint(expr1 <= 1200)
model.add_constraint(0.2 * x2 + 0.3 * x2 + 0.3 * x3 + 0.1 * x1 <= 600)
# 6. Set the objective!
model.minimize(1.1 * x1 + 3.4 * x2 + 2.2 * x3)
# 7. You can print the model
print("Before solving:")
print(model)
# 8. And finally solve it!
solution = model.solve(Solver())
# 9. Model is being simplified before being solver
print("After solving:")
print(model)
# 10. Print solution (uncomment after finishing assignment)
# print("Solution: ")
# print(solution)
from saport.simplex.solver import Solver
from saport.simplex.model import Model
model = Model("Zadanie 4")
# LICZBA SPOSOBÓW OGRANICZONA DO 5 PONIEWAŻ INNE NIE MAJĄ SENSU I MOŻNA JE ODRZUCIC
x1 = model.create_variable("sps_1") #1x 105cm + 1x 75cm + 0x35cm => odpad: 20
x2 = model.create_variable("sps_2") #1x 105cm + 0x 75cm + 2x35cm => odpad: 25
x3 = model.create_variable("sps_3") #0x 105cm + 2x 75cm + 1x35cm => odpad: 15
x4 = model.create_variable("sps_4") #0x 105cm + 1x 75cm + 3x35cm => odpad: 20
x5 = model.create_variable("sps_5") #0x 105cm + 0x 75cm + 5x35cm => odpad: 25
expr1 = x1 + x2
expr2 = x1 + 2 * x3 + x4
expr3 = 2 * x2 + x3 + 3 * x4 + 5 * x5
model.add_constraint(expr1 == 150)
model.add_constraint(expr2 == 200)
model.add_constraint(expr3 == 150)
model.minimize(20 * x1 + 25 * x2 + 15 * x3 + 20 * x4 + 25 * x5)
print("Before solving:")
print(model)
solution = model.solve()
print("Solution: ")
print(solution)
from saport.simplex.model import Model
model = Model("z2")
a = model.create_variable("a")
b = model.create_variable("b")
c = model.create_variable("c")
d = model.create_variable("d")
model.add_constraint(0.8*a + 2.4*b + 0.9*c + 0.4*d >= 1200)
model.add_constraint(0.6*a + 0.6*b + 0.3*c + 0.3*d >= 600)
model.minimize(9.6*a + 14.4*b + 10.8*c + 7.2*d)
solution = model.solve()
print(solution)
from saport.simplex.model import Model
model = Model("z4")
x = [model.create_variable(f'x{i}') for i in range(14)]
model.add_constraint(x[2] + 2 * x[3] + x[5] + 2 * x[6] + 3 * x[7] + x[9] +
2 * x[10] + 3 * x[11] + 4 * x[12] + 5 * x[13] >= 150)
model.add_constraint(x[0] + x[1] + x[2] + x[3] >= 150)
model.add_constraint(
x[1] + x[4] + x[5] + x[6] + x[7] + 2 * x[8] + 2 * x[9] >= 200)
model.minimize(95 * x[0] + 20 * x[1] + 60 * x[2] + 25 * x[3] + 125 * x[4] +
90 * x[5] + 55 * x[6] + 20 * x[7] + 50 * x[8] + 15 * x[9] +
130 * x[10] + 95 * x[11] + 60 * x[12] + 25 * x[13])
solution = model.solve()
print(solution)
# 4. FYI: You can create expression and evaluate them
expr1 = 5 * x1 + 15 * x2
expr2 = 20 * x1 + 5 * x2
expr3 = 15 * x1 + 2 * x2
print(
f"Value of the expression for the specified assignment is {expr1.evaluate([1, 1, 2])}\n"
)
# 5. Then add constraints to the model
model.add_constraint(expr1 >= 50)
model.add_constraint(expr2 >= 40)
model.add_constraint(expr3 <= 60)
# 6. Set the objective!
model.minimize(8 * x1 + 4 * x2)
# 7. You can print the model
print("Before solving:")
print(model)
# 8. And finally solve it!
solution = model.solve()
# 9. Model is being simplified before being solver
# print("After solving:")
# print(model)
# 10. Print solution (uncomment after finishing assignment)
print("Solution: ")
print(solution)
# 3. Add variables
p1 = model.create_variable("p1")
p2 = model.create_variable("p2")
p3 = model.create_variable("p3")
p4 = model.create_variable("p4")
# 4. FYI: You can create expression and evaluate them
# expr1 = 0.16 * x1 - 0.94 * x2 + 0.9 * x3
# print(f"Value of the expression for the specified assignment is {expr1.evaluate([1, 1, 2])}\n")
# 5. Then add constraints to the model
model.add_constraint(0.8 * p1 + 2.4 * p2 + 0.9 * p3 + 0.4 * p4 >= 1200)
model.add_constraint(0.6 * p1 + 0.6 * p2 + 0.3 * p3 + 0.3 * p4 >= 600)
# 6. Set the objective!
model.minimize(9.6 * p1 + 14.4 * p2 + 10.8 * p3 + 7.2 * p4)
# 7. You can print the model
print("Before solving:")
print(model)
# 8. And finally solve it!
solution = model.solve(Solver())
# 9. Model is being simplified before being solver
# print("After solving:")
# print(model)
# 10. Print solution (uncomment after finishing assignment)
# print("Solution: ")
# print(solution)
from saport.simplex.solver import Solver
from saport.simplex.model import Model
from saport.simplex.expressions.expression import Expression
model = Model("zadanie 4")
x_i = [model.create_variable(f'x{i}') for i in range(14)]
# constraints
model.add_constraint(x_i[0] + x_i[1] + x_i[2] + x_i[3] >= 150)
model.add_constraint(x_i[1] + x_i[4] + x_i[5] + x_i[6] + x_i[7] + 2 * x_i[8] +
2 * x_i[9] >= 200)
model.add_constraint(
x_i[2] + 2 * x_i[3] + x_i[5] + 2 * x_i[6] + 3 * x_i[7] + 1 * x_i[9] +
2 * x_i[10] + 3 * x_i[11] + 4 * x_i[12] + 5 * x_i[13] >= 150)
model.minimize(sum(x_i, start=Expression()))
model.solve(Solver())
def run():
primal = Model("Zad2")
# x1 -> ławki
# x2 -> stoły
# x3 -> krzesła
x1 = primal.create_variable("x1")
x2 = primal.create_variable("x2")
x3 = primal.create_variable("x3")
primal.add_constraint(8 * x1 + 6 * x2 + x3 <= 960)
primal.add_constraint(8 * x1 + 4 * x2 + 3 * x3 <= 800)
primal.add_constraint(4 * x1 + 3 * x2 + x3 <= 320)
primal.maximize(60 * x1 + 30 * x2 + 20 * x3)
expected_dual = Model("Zad2")
y1 = expected_dual.create_variable("y1")
y2 = expected_dual.create_variable("y2")
y3 = expected_dual.create_variable("y3")
expected_dual.add_constraint(8 * y1 + 8 * y2 + 4 * y3 >= 60)
expected_dual.add_constraint(6 * y1 + 4 * y2 + 3 * y3 >= 30)
expected_dual.add_constraint(y1 + 3 * y2 + y3 >= 20)
expected_dual.minimize(960 * y1 + 800 * y2 + 320 * y3)
expected_bounds = [(56.0, 80.0), (float("-inf"), 35.0), (15.0, 22.5)]
dual = primal.dual()
assert dual.is_equivalent(
expected_dual), "dual wasn't calculated as expected"
assert primal.is_equivalent(
dual.dual()), "double dual should equal the initial model"
primal_solution = primal.solve()
dual_solution = dual.solve()
assert math.isclose(
primal_solution.objective_value(),
dual_solution.objective_value(),
abs_tol=0.000001
), "dual and primal should have the same value at optimum"
logging.info(
"Congratulations! The dual creation seems to be implemented correctly :)\n"
)
analyser = Analyser()
analysis_results = analyser.analyse(primal_solution)
analyser.interpret_results(primal_solution, analysis_results, logging.info)
objective_analysis_results = analysis_results[
ObjectiveSensitivityAnalyser.name()]
tolerance = 0.001
for (i, bounds_pair) in enumerate(objective_analysis_results):
assert math.isclose(
bounds_pair[0], expected_bounds[i][0], abs_tol=tolerance
), f"left bound of the coefficient range seems to be incorrect, expected {expected_bounds[i][0]}, got {bounds_pair[0]}"
assert math.isclose(
bounds_pair[1], expected_bounds[i][1], abs_tol=tolerance
), f"right bound of the coefficient range seems to be incorrect, expected {expected_bounds[i][1]}, got {bounds_pair[1]}"
logging.info(
"Congratulations! This cost coefficients analysis look alright :)")
print(dual)
print(analyser.interpret_results(primal_solution, analysis_results))
from saport.simplex.model import Model
model = Model("zadanie 4")
xs = [model.create_variable(f'x{i}') for i in range(14)]
model.add_constraint(xs[0] + xs[1] + xs[2] + xs[3] >= 150)
model.add_constraint(
xs[1] + xs[4] + xs[5] + xs[6] + xs[7] + 2 * xs[8] + 2 * xs[9] >= 200)
model.add_constraint(
xs[2] + 2 * xs[3] + xs[5] + 2 * xs[6] + 3 * xs[7] + 1 * xs[9] +
2 * xs[10] + 3 * xs[11] + 4 * xs[12] + 5 * xs[13] >= 150)
model.minimize(95 * xs[0] + 20 * xs[1] + 60 * xs[2] + 25 * xs[3] +
125 * xs[4] + 90 * xs[5] + 55 * xs[6] + 20 * xs[7] +
50 * xs[8] + 15 * xs[9] + 130 * xs[10] + 95 * xs[11] +
60 * xs[12] + 25 * xs[13])
solution = model.solve()
print(solution)