SequentialMonteCarloRobustAlgorithm¶

class otrobopt.SequentialMonteCarloRobustAlgorithm(*args)¶

Sequential Monte Carlo robust optimization algorithm.

Solves a robust optimization problem by alternating discretizing measures and solving deterministic problems.

Measures are discretized using an initial size that can be set with setInitialSamplingSize() and a size increment that is set with setSamplingSizeIncrement().

The optimization problems relies on a Multi-Start algorithm from an initial LHS experiment and an internal solver that can be set by setOptimizationAlgorithm(). The ResourceMap key SequentialMonteCarloRobustAlgorithm-ConvergenceFactor can be used to control the convergence criteria of the inner solver.

The algorithm stops when the number of iterations has been reached or the absolute error is small enough.

Parameters:

problemRobustOptimizationProblem: Robust optimization problem
solveropenturns.OptimizationAlgorithm: Optimization solver

Methods

`getCheckStatus`()	Accessor to check status flag.
`getClassName`()	Accessor to the object's name.
`getInitialSamplingSize`()	Initial sampling size accessor.
`getInitialSearch`()	Multi-start number accessor.
`getInitialStartingPoints`()	Multi-start optimization starting points accessor.
`getMaximumAbsoluteError`()	Accessor to maximum allowed absolute error.
`getMaximumCallsNumber`()	Accessor to maximum allowed number of calls.
`getMaximumConstraintError`()	Accessor to maximum allowed constraint error.
`getMaximumIterationNumber`()	Accessor to maximum allowed number of iterations.
`getMaximumRelativeError`()	Accessor to maximum allowed relative error.
`getMaximumResidualError`()	Accessor to maximum allowed residual error.
`getMaximumTimeDuration`()	Accessor to the maximum duration.
`getName`()	Accessor to the object's name.
`getOptimizationAlgorithm`()	Optimization solver accessor.
`getProblem`()	Accessor to optimization problem.
`getResult`()	Accessor to optimization result.
`getResultCollection`()	Optimization intermediate results accessor.
`getRobustProblem`()	Robust optimization problem accessor.
`getSamplingSizeIncrement`()	Sampling size increment accessor.
`getStartingPoint`()	Accessor to starting point.
`hasName`()	Test if the object is named.
`run`()	Launch the optimization.
`setCheckStatus`(checkStatus)	Accessor to check status flag.
`setInitialSamplingSize`(N0)	Initial sampling size accessor.
`setInitialSearch`(initialSearch)	Multi-start number accessor.
`setMaximumAbsoluteError`(maximumAbsoluteError)	Accessor to maximum allowed absolute error.
`setMaximumCallsNumber`(maximumCallsNumber)	Accessor to maximum allowed number of calls
`setMaximumConstraintError`(maximumConstraintError)	Accessor to maximum allowed constraint error.
`setMaximumIterationNumber`(maximumIterationNumber)	Accessor to maximum allowed number of iterations.
`setMaximumRelativeError`(maximumRelativeError)	Accessor to maximum allowed relative error.
`setMaximumResidualError`(maximumResidualError)	Accessor to maximum allowed residual error.
`setMaximumTimeDuration`(maximumTime)	Accessor to the maximum duration.
`setName`(name)	Accessor to the object's name.
`setOptimizationAlgorithm`(solver)	Optimization solver accessor.
`setProblem`(problem)	Accessor to optimization problem.
`setProgressCallback`(*args)	Set up a progress callback.
`setResult`(result)	Accessor to optimization result.
`setRobustProblem`(problem)	Robust optimization problem accessor.
`setSamplingSizeIncrement`(samplingSizeIncrement)	Sampling size increment accessor.
`setStartingPoint`(startingPoint)	Accessor to starting point.
`setStopCallback`(*args)	Set up a stop callback.

getMaximumEvaluationNumber
setMaximumEvaluationNumber

__init__(*args)¶

getCheckStatus()¶

Accessor to check status flag.

Returns:

checkStatusbool: Whether to check the termination status. If set to False, run() will not throw an exception if the algorithm does not fully converge and will allow one to still find a feasible candidate.

getClassName()¶

Accessor to the object’s name.

Returns:

class_namestr: The object class name (object.__class__.__name__).

getInitialSamplingSize()¶

Initial sampling size accessor.

Initial size of the discretization of $\theta$ .

Returns:

initialSamplingSizeint: Initial sampling size

getInitialSearch()¶

Multi-start number accessor.

Initial number of start points used.

Problem bounds must be specified when multi-start is used as start points are drawn uniformly into the bounding box.

Returns:

initialSearchint, 0 by default (no multi-start): Multi-start number

getInitialStartingPoints()¶

Multi-start optimization starting points accessor.

Optimization starting points during the initial search phase.

Returns:

startPointsopenturns.Sample: List of optimization starting points

getMaximumAbsoluteError()¶

Accessor to maximum allowed absolute error.

Returns:

maximumAbsoluteErrorfloat: Maximum allowed absolute error, where the absolute error is defined by $\epsilon^a_n=\|\vect{x}_{n+1}-\vect{x}_n\|_{\infty}$ where $\vect{x}_{n+1}$ and $\vect{x}_n$ are two consecutive approximations of the optimum.

getMaximumCallsNumber()¶

Accessor to maximum allowed number of calls.

Returns:

maximumEvaluationNumberint: Maximum allowed number of direct objective function calls through the () operator. Does not take into account eventual indirect calls through finite difference gradient calls.

getMaximumConstraintError()¶

Accessor to maximum allowed constraint error.

Returns:

maximumConstraintErrorfloat: Maximum allowed constraint error, where the constraint error is defined by $\gamma_n=\|g(\vect{x}_n)\|_{\infty}$ where $\vect{x}_n$ is the current approximation of the optimum and $g$ is the function that gathers all the equality and inequality constraints (violated values only)

getMaximumIterationNumber()¶

Accessor to maximum allowed number of iterations.

Returns:

maximumIterationNumberint: Maximum allowed number of iterations.

getMaximumRelativeError()¶

Accessor to maximum allowed relative error.

Returns:

maximumRelativeErrorfloat: Maximum allowed relative error, where the relative error is defined by $\epsilon^r_n=\epsilon^a_n/\|\vect{x}_{n+1}\|_{\infty}$ if $\|\vect{x}_{n+1}\|_{\infty}\neq 0$ , else $\epsilon^r_n=-1$ .

getMaximumResidualError()¶

Accessor to maximum allowed residual error.

Returns:

maximumResidualErrorfloat: Maximum allowed residual error, where the residual error is defined by $\epsilon^r_n=\frac{\|f(\vect{x}_{n+1})-f(\vect{x}_{n})\|}{\|f(\vect{x}_{n+1})\|}$ if $\|f(\vect{x}_{n+1})\|\neq 0$ , else $\epsilon^r_n=-1$ .

getMaximumTimeDuration()¶

Accessor to the maximum duration.

Returns:

maximumTimefloat: Maximum optimization duration in seconds.

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getOptimizationAlgorithm()¶

Optimization solver accessor.

Returns:

solveropenturns.OptimizationAlgorithm: Optimization solver

getProblem()¶

Accessor to optimization problem.

Returns:

problemOptimizationProblem: Optimization problem.

getResult()¶

Accessor to optimization result.

Returns:

resultOptimizationResult: Result class.

getResultCollection()¶

Optimization intermediate results accessor.

Optimization results at each step.

Returns:

resultCollsequence of openturns.OptimizationResult: List of optimization results

getRobustProblem()¶

Robust optimization problem accessor.

Returns:

problemRobustOptimizationProblem: Robust optimization problem

getSamplingSizeIncrement()¶

Sampling size increment accessor.

Sampling size increment of $\theta$ as a function of the total size at the previous iteration.

Returns:

samplingSizeIncrementopenturns.Function: Sampling size increment

getStartingPoint()¶

Accessor to starting point.

Returns:

startingPointPoint: Starting point.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

run()¶: Launch the optimization.

setCheckStatus(checkStatus)¶

Accessor to check status flag.

Parameters:

checkStatusbool: Whether to check the termination status. If set to False, run() will not throw an exception if the algorithm does not fully converge and will allow one to still find a feasible candidate.

setInitialSamplingSize(N0)¶

Initial sampling size accessor.

Initial size of the discretization of $\theta$ .

Parameters:

initialSamplingSizeint: Initial sampling size

setInitialSearch(initialSearch)¶

Multi-start number accessor.

Initial number of start points used.

Problem bounds must be specified when multi-start is used as start points are drawn uniformly into the bounding box using an LHS experiment.

Parameters:

initialSearchint, 0 by default (no multi-start): Multi-start number

setMaximumAbsoluteError(maximumAbsoluteError)¶

Accessor to maximum allowed absolute error.

Parameters:

maximumAbsoluteErrorfloat: Maximum allowed absolute error, where the absolute error is defined by $\epsilon^a_n=\|\vect{x}_{n+1}-\vect{x}_n\|_{\infty}$ where $\vect{x}_{n+1}$ and $\vect{x}_n$ are two consecutive approximations of the optimum.

setMaximumCallsNumber(maximumCallsNumber)¶

Accessor to maximum allowed number of calls

Parameters:

maximumEvaluationNumberint: Maximum allowed number of direct objective function calls through the () operator. Does not take into account eventual indirect calls through finite difference gradient calls.

setMaximumConstraintError(maximumConstraintError)¶

Accessor to maximum allowed constraint error.

Parameters:

maximumConstraintErrorfloat: Maximum allowed constraint error, where the constraint error is defined by $\gamma_n=\|g(\vect{x}_n)\|_{\infty}$ where $\vect{x}_n$ is the current approximation of the optimum and $g$ is the function that gathers all the equality and inequality constraints (violated values only)

setMaximumIterationNumber(maximumIterationNumber)¶

Accessor to maximum allowed number of iterations.

Parameters:

maximumIterationNumberint: Maximum allowed number of iterations.

setMaximumRelativeError(maximumRelativeError)¶

Accessor to maximum allowed relative error.

Parameters:

maximumRelativeErrorfloat: Maximum allowed relative error, where the relative error is defined by $\epsilon^r_n=\epsilon^a_n/\|\vect{x}_{n+1}\|_{\infty}$ if $\|\vect{x}_{n+1}\|_{\infty}\neq 0$ , else $\epsilon^r_n=-1$ .

setMaximumResidualError(maximumResidualError)¶

Accessor to maximum allowed residual error.

Parameters:

maximumResidualErrorfloat: Maximum allowed residual error, where the residual error is defined by $\epsilon^r_n=\frac{\|f(\vect{x}_{n+1})-f(\vect{x}_{n})\|}{\|f(\vect{x}_{n+1})\|}$ if $\|f(\vect{x}_{n+1})\|\neq 0$ , else $\epsilon^r_n=-1$ .

setMaximumTimeDuration(maximumTime)¶

Accessor to the maximum duration.

Parameters:

maximumTimefloat: Maximum optimization duration in seconds.

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setOptimizationAlgorithm(solver)¶

Optimization solver accessor.

Parameters:

solveropenturns.OptimizationAlgorithm: Optimization solver

setProblem(problem)¶

Accessor to optimization problem.

Parameters:

problemOptimizationProblem: Optimization problem.

setProgressCallback(*args)¶

Set up a progress callback.

Can be used to programmatically report the progress of an optimization.

Parameters:

callbackcallable: Takes a float as argument as percentage of progress.

Examples

>>> import sys
>>> import openturns as ot
>>> rosenbrock = ot.SymbolicFunction(['x1', 'x2'], ['(1-x1)^2+100*(x2-x1^2)^2'])
>>> problem = ot.OptimizationProblem(rosenbrock)
>>> solver = ot.OptimizationAlgorithm(problem)
>>> solver.setStartingPoint([0, 0])
>>> solver.setMaximumResidualError(1.e-3)
>>> solver.setMaximumCallsNumber(10000)
>>> def report_progress(progress):
...     sys.stderr.write('-- progress=' + str(progress) + '%\n')
>>> solver.setProgressCallback(report_progress)
>>> solver.run()

setResult(result)¶

Accessor to optimization result.

Parameters:

resultOptimizationResult: Result class.

setRobustProblem(problem)¶

Robust optimization problem accessor.

Parameters:

problemRobustOptimizationProblem: Robust optimization problem

setSamplingSizeIncrement(samplingSizeIncrement)¶

Sampling size increment accessor.

Sampling size increment of $\theta$ as a function of the total size at the previous iteration.

Parameters:

samplingSizeIncrementopenturns.Function: Sampling size increment

setStartingPoint(startingPoint)¶

Accessor to starting point.

Parameters:

startingPointPoint: Starting point.

setStopCallback(*args)¶

Set up a stop callback.

Can be used to programmatically stop an optimization.

Parameters:

callbackcallable: Returns an int deciding whether to stop or continue.

Examples

>>> import openturns as ot
>>> rosenbrock = ot.SymbolicFunction(['x1', 'x2'], ['(1-x1)^2+100*(x2-x1^2)^2'])
>>> problem = ot.OptimizationProblem(rosenbrock)
>>> solver = ot.OptimizationAlgorithm(problem)
>>> solver.setStartingPoint([0, 0])
>>> solver.setMaximumResidualError(1.e-3)
>>> solver.setMaximumCallsNumber(10000)
>>> def ask_stop():
...     return True
>>> solver.setStopCallback(ask_stop)
>>> solver.run()

SequentialMonteCarloRobustAlgorithm¶

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