Example 2

Problem statement:

Solution:

import openturns as ot
import openturns.testing
import otrobopt

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

calJ = ot.SymbolicFunction(
    ['x0', 'x1', 'theta'], ['sqrt(x0) * sqrt(x1) * theta'])
g = ot.SymbolicFunction(['x0', 'x1'], ['-(2*x1 + 4*x0 -120)'])
J = ot.ParametricFunction(calJ, [2], [1.0])

dim = J.getInputDimension()

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

thetaDist = ot.Normal(1.0, 3.0)
robustnessMeasure = otrobopt.MeanMeasure(J, thetaDist)
problem = otrobopt.RobustOptimizationProblem(robustnessMeasure, g)
problem.setMinimization(False)
bounds = ot.Interval([5.0] * dim, [50.0] * 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()
# openturns.testing.assert_almost_equal(
# result.getOptimalPoint(), [46.2957, 46.634], 1e-3)
print('x*=', result.getOptimalPoint(),
      'J(x*)=', result.getOptimalValue(),
      'iteration=', result.getIterationNumber())

x*= [15.0002,30.0004] J(x*)= [40.7026] iteration= 2