Control algorithm termination

In this examples we are going to expose ways to control the termination of optimization and simulation algorithms using callbacks.

import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
import math as m
import time
ot.Log.Show(ot.Log.NONE)

Define an event to compute a probability

myFunction = ot.SymbolicFunction(['E', 'F', 'L', 'I'], ['-F*L^3/(3.0*E*I)'])
dim = myFunction.getInputDimension()
mean = [50.0, 1.0, 10.0, 5.0]
sigma = [1.0] * dim
R = ot.IdentityMatrix(dim)
myDistribution = ot.Normal(mean, sigma, R)
vect = ot.RandomVector(myDistribution)
output = ot.CompositeRandomVector(myFunction, vect)
myEvent = ot.ThresholdEvent(output, ot.Less(), -3.0)

Stop a FORM algorithm using a calls number limit

A FORM algorithm termination can be controlled by the maximum number of iterations

of its underlying optimization solver, but not directly by a maximum number of evaluations.

Create the optimization algorithm

myCobyla = ot.Cobyla()
myCobyla.setMaximumEvaluationNumber(400)
myCobyla.setMaximumAbsoluteError(1.0e-10)
myCobyla.setMaximumRelativeError(1.0e-10)
myCobyla.setMaximumResidualError(1.0e-10)
myCobyla.setMaximumConstraintError(1.0e-10)

Define the stopping criterion

def stop():
    return myFunction.getCallsNumber() > 100


myCobyla.setStopCallback(stop)

Run FORM

myAlgo = ot.FORM(myCobyla, myEvent, mean)
myAlgo.run()
result = myAlgo.getResult()
print('event probability:', result.getEventProbability())
print('calls number:', myFunction.getCallsNumber())

Out:

event probability: 0.15642619199519509
calls number: 102

Stop a simulation algorithm using a time limit

Here we will create a callback to not exceed a specified simulation time.

Create simulation

experiment = ot.MonteCarloExperiment()
myAlgo = ot.ProbabilitySimulationAlgorithm(myEvent, experiment)
myAlgo.setMaximumOuterSampling(1000000)
myAlgo.setMaximumCoefficientOfVariation(-1.0)

Define the stopping criterion

timer = ot.TimerCallback(0.01)
myAlgo.setStopCallback(timer)

Run algorithm

myAlgo.run()
result = myAlgo.getResult()
print('event probability:', result.getProbabilityEstimate())
print('calls number:', myFunction.getCallsNumber())

Out:

event probability: 0.14398943196829608
calls number: 3887