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Example 3ΒΆ

Problem statement:

\begin{aligned} & \underset{x}{\text{minimize}} & & \mathbb{E}_{\cD}(x^3 - x + \Theta) \\ & \text{subject to} & & \mathbb{P}_{\cD}(x + \Theta - 2 \leq 0) \geq 0.9 \\ & & & \Theta \thicksim \cE(2) \end{aligned}

Solution: \hat{x} = -1

import openturns as ot
import otrobopt

# ot.Log.Show(ot.Log.Info)

calJ = ot.SymbolicFunction(['x', 'theta'], ['x^3 - 3*x + theta'])
calG = ot.SymbolicFunction(['x', 'theta'], ['-(x + theta - 2)'])
J = ot.ParametricFunction(calJ, [1], [0.5])
g = ot.ParametricFunction(calG, [1], [0.5])

dim = J.getInputDimension()

solver = ot.Cobyla()
solver.setMaximumIterationNumber(1000)
solver.setStartingPoint([0.0] * dim)

thetaDist = ot.Exponential(2.0)
robustnessMeasure = otrobopt.MeanMeasure(J, thetaDist)
reliabilityMeasure = otrobopt.JointChanceMeasure(
    g, thetaDist, ot.Greater(), 0.9)
problem = otrobopt.RobustOptimizationProblem(
    robustnessMeasure, reliabilityMeasure)
problem.setMinimization(False)

algo = otrobopt.SequentialMonteCarloRobustAlgorithm(problem, solver)
algo.setMaximumIterationNumber(10)
algo.setMaximumAbsoluteError(1e-3)
algo.setInitialSamplingSize(10)
algo.run()
result = algo.getResult()
print('x*=', result.getOptimalPoint(), 'J(x*)=',
      result.getOptimalValue(), 'iteration=', result.getIterationNumber())

x*= [-1] J(x*)= [2.66295] iteration= 2

Total running time of the script: (0 minutes 0.002 seconds)