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#!/usr/bin/env python
# An optimization problem with mixed discrete input variables.
#
# min f(x1,x2,x3)
# where
# x1 is discrete in {0,1,2,3,4}
# x2 and x3 are real in [0,1]
#
# Mixed parameter space with one discrete parameter \eqn{x_1 \in \{0, 1, 2, 3, 4\}}
# and two numerical parameters \eqn{x_1, x_2 \in [0, 1]}.
# The function is defined as follows:
# f(\mathbf{x}) = \\
# \sin(2\pi x_3 - \pi) + 7 \sin^2(2 \pi x_2 - \pi) \, if \, x_1 = 0 \\
# \sin(2\pi x_3 - \pi) + 7 \sin^2(2 \pi x_2 - \pi) + 12 \sin(2 \pi x_3 - \pi) \, if \, x_1 = 1 \\
# \sin(2\pi x_3 - \pi) + 7 \sin^2(2 \pi x_2 - \pi) + 0.5 \sin(2 \pi x_3 - \pi) \, if \, x_1 = 2 \\
# \sin(2\pi x_3 - \pi) + 7 \sin^2(2 \pi x_2 - \pi) + 8.0 \sin(2 \pi x_3 - \pi) \, if \, x_1 = 3 \\
# \sin(2\pi x_3 - \pi) + 7 \sin^2(2 \pi x_2 - \pi) + 3.5 \sin(2 \pi x_3 - \pi) \, if \, x_1 = 4.
#
# Reference
# Ported from R to Python, based on
# https://rdrr.io/cran/smoof/src/R/sof.swiler2014.R
import math
import openturns as ot
import openturns.testing as ott
def swiler2014(x):
x1, x2, x3 = x
# minimum = f([1, 0 , 0.25])=-13
a = math.sin(2 * math.pi * x3 - math.pi)
b = 7 * math.sin(2 * math.pi * x2 - math.pi) ** 2
facs = [0, 12.0, 0.5, 8.0, 3.5] # A set of numeric values
fac = facs[int(x1)] # Convert to int, then use the value in the list
result = a + b + fac * a
# print("x=",[x1,x2,x3],"f(x)=",result)
return [result]
# Create the objective function
objectiveFun = ot.PythonFunction(3, 1, swiler2014)
x = [1, 0, 0.25]
print("Evaluate f at x=", x)
print(f"f(x)={objectiveFun(x)}")
# Define OptimizationProblem
problem = ot.OptimizationProblem(objectiveFun)
bounds = ot.Interval([0.0] * 3, [1.0, 1.0, 4.0])
varTypes = [
ot.OptimizationProblemImplementation.INTEGER,
ot.OptimizationProblemImplementation.CONTINUOUS,
ot.OptimizationProblemImplementation.CONTINUOUS,
]
problem.setBounds(bounds)
problem.setVariablesType(varTypes)
problem.setMinimization(True)
# Define OptimizationAlgorithm
x0 = [0.0] * 3
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(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, [1.0, 0.0, 0.25], 1, 5e-4)
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