Mix/max search using optimization

In this example we are going to evaluate the min and max values of the output variable of interest in a domain using an optimization algorithm.

import openturns as ot

ot.Log.Show(ot.Log.NONE)

Create the marginal distributions of the parameters

dist_E = ot.Beta(0.93, 2.27, 2.8e7, 4.8e7)
dist_F = ot.LogNormalMuSigma(30000, 9000, 15000).getDistribution()
dist_L = ot.Uniform(250, 260)
dist_I = ot.Beta(2.5, 1.5, 3.1e2, 4.5e2)
marginals = [dist_E, dist_F, dist_L, dist_I]
distribution = ot.ComposedDistribution(marginals)

Define bounds

lowerBound = [marginal.computeQuantile(0.1)[0] for marginal in marginals]
upperBound = [marginal.computeQuantile(0.9)[0] for marginal in marginals]
bounds = ot.Interval(lowerBound, upperBound)

Create the model

model = ot.SymbolicFunction(["E", "F", "L", "I"], ["F*L^3/(3*E*I)"])

Define the problems

minProblem = ot.OptimizationProblem(model)
minProblem.setBounds(bounds)

maxProblem = ot.OptimizationProblem(model)
maxProblem.setBounds(bounds)
maxProblem.setMinimization(False)

Create a solver

solver = ot.TNC()
solver.setStartingPoint(distribution.getMean())

Solve the problems

solver.setProblem(minProblem)
solver.run()
minResult = solver.getResult()
print("min: y=", minResult.getOptimalValue(), "with x=", minResult.getOptimalPoint())

solver.setProblem(maxProblem)
solver.run()
maxResult = solver.getResult()
print("max: y=", maxResult.getOptimalValue(), "with x=", maxResult.getOptimalPoint())

min: y= [6.37642] with x= [4.04419e+07,21319.7,251,435.785]
max: y= [23.4246] with x= [2.87477e+07,41178.7,259,354.141]