MultiStart¶

class MultiStart(*args)¶

Multi-start optimization algorithm.

The algorithm runs an optimization solver for multiple starting points and returns the best result of each local search. The algorithm succeeds when at least one local search succeeds.

Parameters:

solverOptimizationAlgorithm: The internal solver
startingSample2-d sequence of float: Starting points set

Notes

The starting point of the internal solver is ignored. If you want to use it, add it to startingSample.

Stopping criteria used are the ones set in the internal solver.

A global number of evaluations can be set, in that case all starting points might not be used depending on the number of evaluations allocated to the internal solver.

Starting points provided through the startingSample parameter should be within the bounds of the OptimizationProblem, but this is not enforced.

Examples

First define the OptimizationAlgorithm to be run from multiple starting points.

>>> import openturns as ot
>>> dim = 2
>>> model = ot.SymbolicFunction(['x', 'y'], ['x^2+y^2*(1-x)^3'])
>>> bounds = ot.Interval([-2.0] * dim, [3.0] * dim)
>>> problem = ot.OptimizationProblem(model)
>>> problem.setBounds(bounds)
>>> solver = ot.TNC(problem)

Starting points must be manually specified.

>>> uniform = ot.JointDistribution([ot.Uniform(-2.0, 3.0)] * dim)
>>> ot.RandomGenerator.SetSeed(0)
>>> startingSample = uniform.getSample(5)
>>> print(startingSample)
    [ X0        X1        ]
0 : [  1.14938   2.84712  ]
1 : [  2.41403   2.6034   ]
2 : [ -1.32362   0.515201 ]
3 : [ -1.83749  -1.68397  ]
4 : [ -0.264715 -0.536216 ]
>>> algo = ot.MultiStart(solver, startingSample)
>>> algo.run()
>>> result = algo.getResult()
>>> print(result.getOptimalPoint())
[3,3]

Methods

`getCheckStatus`()	Accessor to check status flag.
`getClassName`()	Accessor to the object's name.
`getKeepResults`()	Flag to keep intermediate results 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`()	Internal solver accessor.
`getProblem`()	Accessor to optimization problem.
`getResult`()	Accessor to optimization result.
`getResultCollection`()	Intermediate optimization results accessor.
`getStartingPoint`()	Inherited but raises an Exception.
`getStartingSample`()	Accessor to the sample of starting points.
`hasName`()	Test if the object is named.
`run`()	Launch the optimization.
`setCheckStatus`(checkStatus)	Accessor to check status flag.
`setKeepResults`(keepResults)	Flag to keep intermediate results 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)	Internal solver accessor.
`setProblem`(problem)	Sets the optimization problem.
`setProgressCallback`(*args)	Set up a progress callback.
`setResult`(result)	Accessor to optimization result.
`setStartingPoint`(point)	Inherited but raises an Exception.
`setStartingSample`(startingSample)	Accessor to the sample of starting points.
`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__).

getKeepResults()¶

Flag to keep intermediate results accessor.

Returns:

keepResultsbool: If True all the intermediate results are stored, otherwise they are ignored. Default value is MultiStart-KeepResults in ResourceMap

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()¶

Internal solver accessor.

Returns:

solverOptimizationAlgorithm: The internal solver

getProblem()¶

Accessor to optimization problem.

Returns:

problemOptimizationProblem: Optimization problem.

getResult()¶

Accessor to optimization result.

Returns:

resultOptimizationResult: Result class.

getResultCollection()¶

Intermediate optimization results accessor.

Returns:

resultsOptimizationResultCollection: Intermediate optimization results

getStartingPoint()¶

Inherited but raises an Exception.

Notes

This method is inherited from OptimizationAlgorithm but makes no sense in a multi-start context.

getStartingSample()¶: Accessor to the sample of starting points.

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.

setKeepResults(keepResults)¶

Flag to keep intermediate results accessor.

Parameters:

keepResultsbool: If True all the intermediate results are stored, otherwise they are ignored. Default value is MultiStart-KeepResults in ResourceMap

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)¶

Internal solver accessor.

Parameters:

solverOptimizationAlgorithm: The internal solver

setProblem(problem)¶

Sets the 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.

setStartingPoint(point)¶

Inherited but raises an Exception.

Notes

This method is inherited from OptimizationAlgorithm but makes no sense in a multi-start context.

setStartingSample(startingSample)¶

Accessor to the sample of starting points.

Parameters:

startingSample2-d sequence of float: A new sample of starting points to overwrite the existing sample

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()