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#! /usr/bin/env python
import openturns as ot
import math as m
import openturns.testing
ot.Log.Show(ot.Log.NONE)
ot.TBB.Disable()
#
# branin
dim = 2
# model
formula = (
"((x2-(5.1/(4*pi_^2))*x1^2+5*x1/pi_-6)^2+10*(1-1/8*pi_)*cos(x1)+10-54.8104)/51.9496"
)
branin = ot.SymbolicFunction(["x1", "x2"], [formula])
transfo = ot.SymbolicFunction(["u1", "u2"], ["15*u1-5", "15*u2"])
model = ot.ComposedFunction(branin, transfo)
noiseModel = ot.SymbolicFunction(["x1", "x2"], ["0.96"]) # assume constant noise var
# problem
problem = ot.OptimizationProblem()
problem.setObjective(model)
bounds = ot.Interval([0.0] * dim, [1.0] * dim)
problem.setBounds(bounds)
# design
experiment = ot.Box([1, 1])
inputSample = experiment.generate()
outputSample = model(inputSample)
# first kriging model
covarianceModel = ot.SquaredExponential([0.3007, 0.2483], [0.981959])
basis = ot.ConstantBasisFactory(dim).build()
kriging = ot.KrigingAlgorithm(inputSample, outputSample, covarianceModel, basis)
noise = [x[0] for x in noiseModel(inputSample)]
kriging.setNoise(noise)
kriging.run()
# algo
algo = ot.EfficientGlobalOptimization(problem, kriging.getResult(), noiseModel)
algo.setMaximumCallsNumber(14)
algo.setAEITradeoff(0.66744898)
algo.run()
result = algo.getResult()
# print('1st pass result=', result)
print("iteration=", result.getIterationNumber())
assert (
result.getIterationNumber() > 3 and result.getIterationNumber() < 15
), "Too few/much iterations"
print(result.getInputSample())
print(result.getOutputSample())
# openturns.testing.assert_almost_equal(result.getOptimalPoint(), [0.5, 0.0], 1e-5, 1e-5)
# openturns.testing.assert_almost_equal(result.getOptimalValue(),
# [-0.802223], 1e-5, 1e-5)
# local refinement even though the model is noisy (we still want to check
# we're not too far from optimum)
problem.setObjective(model.getMarginal(0))
algo2 = ot.TNC(problem)
# we have to use getFinalPoints as our objective function is 2-d
algo2.setStartingPoint(result.getOptimalPoint())
algo2.run()
result = algo2.getResult()
# print(result)
# openturns.testing.assert_almost_equal(result.getOptimalPoint(), [0.542773, 0.151666], 1e-5, 1e-5)
# openturns.testing.assert_almost_equal(result.getOptimalPoint(),
# [0.123895, 0.818329], 1e-5, 1e-5)
openturns.testing.assert_almost_equal(
result.getOptimalPoint(), [0.961652, 0.165000], 1e-5, 1e-5
)
openturns.testing.assert_almost_equal(result.getOptimalValue(), [-0.979476], 1e-5, 1e-5)
#
# ackley 2-d
ot.RandomGenerator.SetSeed(0)
dim = 2
# model
def ackley(X):
a = 20.0
b = 0.2
c = 2.0 * m.pi
d = len(X)
f = (
-a * m.exp(-b * m.sqrt(sum(x**2 for x in X) / d))
- m.exp(sum(m.cos(c * x) for x in X) / d)
+ a
+ m.exp(1.0)
)
# print(X, f)
return [f]
model = ot.PythonFunction(dim, 1, ackley)
# problem
problem = ot.OptimizationProblem()
problem.setObjective(model)
bounds = ot.Interval([-15.0] * dim, [15.0] * dim)
problem.setBounds(bounds)
# design
center = [0.5] * dim
levels = [2.0, 4.0, 8.0, 14.0]
experiment = ot.Factorial(center, levels)
inputSample = experiment.generate()
outputSample = model(inputSample)
# first kriging model
covarianceModel = ot.SquaredExponential([2.50057] * dim, [0.1])
basis = ot.ConstantBasisFactory(dim).build()
kriging = ot.KrigingAlgorithm(inputSample, outputSample, covarianceModel, basis)
kriging.run()
# algo
algo = ot.EfficientGlobalOptimization(problem, kriging.getResult())
# solver = ot.NLopt('GN_ESCH')
# solver = ot.NLopt('GN_MLSL')
algo.setMaximumCallsNumber(15)
algo.setMaximumAbsoluteError(1e-10)
algo.setMaximumRelativeError(1e-10)
algo.setMaximumResidualError(1e-10)
algo.setMaximumConstraintError(1e-10)
algo.setMultiStartExperimentSize(
100
) # number of multistart candidates improvement optim
algo.setMultiStartNumber(20) # number of multistart points for improvement optim
algo.setParameterEstimationPeriod(1) # relearn kriging parameters every X iteration
algo.setCorrelationLengthFactor(1.0) # correlation length stopping criterion factor
algo.run()
result = algo.getResult()
# print('1st pass result=', result)
assert (
result.getIterationNumber() > 0 and result.getIterationNumber() < 16
), "Too few/much iterations"
print("iteration=", result.getIterationNumber())
print(result.getInputSample())
print(result.getOutputSample())
# local refinement
algo2 = ot.TNC(problem)
algo2.setStartingPoint(result.getOptimalPoint())
algo2.run()
result = algo2.getResult()
openturns.testing.assert_almost_equal(result.getOptimalPoint(), [0.0] * dim, 1e-7, 1e-5)
openturns.testing.assert_almost_equal(result.getOptimalValue(), [0.0], 1e-15, 2.4e-5)
# ei = algo.getExpectedImprovement()
# print(ei)
# Cobyla out of bound test
ot.RandomGenerator.SetSeed(0)
dim = 4
model = ot.SymbolicFunction(["x1", "x2", "x3", "x4"], ["x1*x1+x2^3*x1+x3+x4"])
model = ot.MemoizeFunction(model)
bounds = ot.Interval([-5.0] * dim, [5.0] * dim)
problem = ot.OptimizationProblem()
problem.setObjective(model)
problem.setBounds(bounds)
experiment = ot.Composite([0.0] * dim, [1.0, 2.0, 4.0])
inputSample = experiment.generate()
outputSample = model(inputSample)
covarianceModel = ot.SquaredExponential([2.0] * dim, [0.1])
basis = ot.ConstantBasisFactory(dim).build()
kriging = ot.KrigingAlgorithm(inputSample, outputSample, covarianceModel, basis)
kriging.run()
algo = ot.EfficientGlobalOptimization(problem, kriging.getResult())
algo.setMaximumCallsNumber(10)
algo.run()
result = algo.getResult()
# check maximization
problem.setMinimization(False)
algo = ot.EfficientGlobalOptimization(problem, kriging.getResult())
algo.setMaximumCallsNumber(10)
algo.run()
result = algo.getResult()
assert result.getOptimalValue()[0] >= 650.0
print("OK")
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