Control algorithm termination

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

from __future__ import print_function
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: 0.1285801340645948
calls number: 1743