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#!/usr/bin/env python
"""
An optimization problem with mixed discrete input variables.
Simple PLNE :
maximize 15*x + 12*y + 4*z + 2*t
subject to -(8*x + 5*y + 3*z + 2*t - 10) >= 0
where x, y, z, t in {0,1}
Solution is [0, 1, 1, 1] with objectif value = 18
Without discrete constraint, we get :
x*= [0.625,1,0,0], f(x*)= [-21.375]
References
https://ocw.mit.edu/courses/sloan-school-of-management/15-053-optimization-methods-in-management-science-spring-2013/tutorials/MIT15_053S13_tut10.pdf
"""
import openturns as ot
import openturns.testing as ott
# Define the objective function
objectiveFun = ot.SymbolicFunction(["x", "y", "z", "t"], ["-(15*x + 12*y + 4*z + 2*t)"])
constraintFun = ot.SymbolicFunction(
["x", "y", "z", "t"], ["-(8*x + 5*y + 3*z + 2*t -10)"]
)
x = [0, 1, 1, 1]
print(f"f(x)={objectiveFun(x)}")
print(f"g(x)={constraintFun(x)}")
# Define problem
problem = ot.OptimizationProblem(objectiveFun)
problem.setInequalityConstraint(constraintFun)
bounds = ot.Interval([0.0] * 4, [1.0] * 4)
problem.setBounds(bounds)
problem.setMinimization(True)
problem.setVariablesType(
[
ot.OptimizationProblemImplementation.BINARY,
ot.OptimizationProblemImplementation.BINARY,
ot.OptimizationProblemImplementation.BINARY,
ot.OptimizationProblemImplementation.BINARY,
]
)
# Define OptimizationAlgorithm
x0 = [0.0] * 4
algo = ot.Bonmin(problem)
algo.setStartingPoint(x0)
algo.setMaximumCallsNumber(10000)
algo.setMaximumIterationNumber(1000)
for name in ot.Bonmin.GetAlgorithmNames():
print(f"-- {name} algorithm...")
algo.setAlgorithmName(name)
algo.run()
# Retrieve result
result = algo.getResult()
x_star = result.getOptimalPoint()
print("x*=", x_star)
y_star = result.getOptimalValue()
neval = result.getCallsNumber()
print(f"f(x*)={y_star} neval={neval}")
print(f"g(x*)={constraintFun(x_star)}")
ott.assert_almost_equal(x_star, [0, 1, 1, 1], 1, 5e-4)
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