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#!/usr/bin/env python
"""
An optimization problem with mixed discrete input variables "4d soo".
min f(x1,x2,disc_b,logic)
where
x1 in [-5,5], x2 in [-3,3], disc_b in {True,False}, logic in {True,False}
4D function with a mixed decision space (two numeric, one discrete,
and one logical parameter)
In the original problem, we have disc_b in {"a","b"}.
Reference
Ported from R to Python.
Package ‘smoof’, August 14, 2017
Single and Multi-Objective Optimization Test Functions
Jakob Bossek
"""
import openturns as ot
import openturns.testing as ott
def fourdsoo(x):
x1, x2, disc_b, logic = x
# minimum : f([-5,-3,1,1]) = -18
if round(disc_b) == 0.0:
result = x1**2 + x2**2 + 10 * round(logic)
else:
result = x1 + x2 - 10 * round(logic)
return [result]
# Create the objective function
objectiveFun = ot.PythonFunction(4, 1, fourdsoo)
x = [-5, -3, 1, 1]
print(f"f(x)={objectiveFun(x)}")
# Define bounds
bounds = ot.Interval([-5.0, -3.0, 0.0, 0.0], [5.0, 3.0, 1, 1])
# Define variable types
varTypes = [
ot.OptimizationProblemImplementation.CONTINUOUS,
ot.OptimizationProblemImplementation.CONTINUOUS,
ot.OptimizationProblemImplementation.BINARY,
ot.OptimizationProblemImplementation.INTEGER,
]
# Define problem
problem = ot.OptimizationProblem(objectiveFun)
problem.setVariablesType(varTypes)
problem.setBounds(bounds)
problem.setMinimization(True)
x0 = [0.0] * 4
algo = ot.Bonmin(problem)
algo.setStartingPoint(x0)
algo.setMaximumCallsNumber(10000)
algo.setMaximumIterationNumber(1000)
for name in ot.Bonmin.GetAlgorithmNames():
if name in ["B-OA", "B-QG", "B-Ecp"]:
continue
print(f"-- {name} algorithm...")
algo.setAlgorithmName(name)
algo.run()
result = algo.getResult()
x_star = result.getOptimalPoint()
print(f"x*={x_star}")
y_star = result.getOptimalValue()
neval = result.getCallsNumber()
print(f"f(x*)={y_star} neval={neval}")
ott.assert_almost_equal(x_star, [-5, -3, 1, 1], 5e-4)
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