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Example 1ΒΆ

Problem statement:

\begin{aligned} & \underset{x}{\text{minimize}} & & \mathbb{E}_{\cD}((x_0-2)^2 + 2x_1^2 -4x_1 + \Theta) \\ & \text{subject to} & & \mathbb{P}_{\cD}(-x_0 + 4x_1 + \Theta -3 \leq 0) \geq 0.9 \\ & & & \Theta \thicksim \cU(1, 3) \end{aligned}

Solution: \hat{x} = [2.2, 0.6]

import openturns as ot
import otrobopt

# ot.Log.Show(ot.Log.Info)
calJ = ot.SymbolicFunction(
    ['x0', 'x1', 'theta'], ['(x0-2)^2 + 2*x1^2 - 4*x1 + theta'])
calG = ot.SymbolicFunction(
    ['x0', 'x1', 'theta'], ['-(-x0 + 4*x1 + theta - 3)'])
J = ot.ParametricFunction(calJ, [2], [2.0])
g = ot.ParametricFunction(calG, [2], [2.0])

dim = J.getInputDimension()

solver = ot.Cobyla()
solver.setCheckStatus(False)
solver.setMaximumIterationNumber(1000)

thetaDist = ot.Uniform(1.0, 3.0)
robustnessMeasure = otrobopt.MeanMeasure(J, thetaDist)
reliabilityMeasure = otrobopt.JointChanceMeasure(
    g, thetaDist, ot.Greater(), 0.9)
problem = otrobopt.RobustOptimizationProblem(
    robustnessMeasure, reliabilityMeasure)
bounds = ot.Interval([-10.0] * dim, [10.0] * dim)
problem.setBounds(bounds)

algo = otrobopt.SequentialMonteCarloRobustAlgorithm(problem, solver)
algo.setMaximumIterationNumber(10)
algo.setMaximumAbsoluteError(1e-3)
algo.setInitialSamplingSize(10)
algo.setInitialSearch(100)
algo.run()
result = algo.getResult()
print('x*=', result.getOptimalPoint(),
      'J(x*)=', result.getOptimalValue(),
      'iteration=', result.getIterationNumber())

x*= [2.1791,0.620063] J(x*)= [0.19849] iteration= 3

Total running time of the script: (0 minutes 0.312 seconds)