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

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

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

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

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.ComposedDistribution([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

`getClassName`()	Accessor to the object's name.
`getId`()	Accessor to the object's id.
`getKeepResults`()	Flag to keep intermediate results accessor.
`getMaximumAbsoluteError`()	Accessor to maximum allowed absolute error.
`getMaximumConstraintError`()	Accessor to maximum allowed constraint error.
`getMaximumEvaluationNumber`()	Accessor to maximum allowed number of evaluations.
`getMaximumIterationNumber`()	Accessor to maximum allowed number of iterations.
`getMaximumRelativeError`()	Accessor to maximum allowed relative error.
`getMaximumResidualError`()	Accessor to maximum allowed residual error.
`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.
`getShadowedId`()	Accessor to the object's shadowed id.
`getStartingPoint`()	Inherited but raises an Exception.
`getStartingSample`()	Accessor to the sample of starting points.
`getVerbose`()	Accessor to the verbosity flag.
`getVisibility`()	Accessor to the object's visibility state.
`hasName`()	Test if the object is named.
`hasVisibleName`()	Test if the object has a distinguishable name.
`run`()	Launch the optimization.
`setKeepResults`(keepResults)	Flag to keep intermediate results accessor.
`setMaximumAbsoluteError`(maximumAbsoluteError)	Accessor to maximum allowed absolute error.
`setMaximumConstraintError`(maximumConstraintError)	Accessor to maximum allowed constraint error.
`setMaximumEvaluationNumber`(...)	Accessor to maximum allowed number of evaluations.
`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.
`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.
`setShadowedId`(id)	Accessor to the object's shadowed id.
`setStartingPoint`(point)	Inherited but raises an Exception.
`setStartingSample`(startingSample)	Accessor to the sample of starting points.
`setStopCallback`(*args)	Set up a stop callback.
`setVerbose`(verbose)	Accessor to the verbosity flag.
`setVisibility`(visible)	Accessor to the object's visibility state.

__init__(*args)¶

getClassName()¶

Accessor to the object’s name.

Returns:

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

getId()¶

Accessor to the object’s id.

Returns:

idint: Internal unique identifier.

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.

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)

getMaximumEvaluationNumber()¶

Accessor to maximum allowed number of evaluations.

Returns:

Nint: Maximum allowed number of evaluations.

getMaximumIterationNumber()¶

Accessor to maximum allowed number of iterations.

Returns:

Nint: 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 $\epsilon^r_n=-1$ .

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

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns:

idint: Internal unique identifier.

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.

getVerbose()¶

Accessor to the verbosity flag.

Returns:

verbosebool: Verbosity flag state.

getVisibility()¶

Accessor to the object’s visibility state.

Returns:

visiblebool: Visibility flag.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

hasVisibleName()¶

Test if the object has a distinguishable name.

Returns:

hasVisibleNamebool: True if the name is not empty and not the default one.

run()¶: Launch the optimization.

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.

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)

setMaximumEvaluationNumber(maximumEvaluationNumber)¶

Accessor to maximum allowed number of evaluations.

Parameters:

Nint: Maximum allowed number of evaluations.

setMaximumIterationNumber(maximumIterationNumber)¶

Accessor to maximum allowed number of iterations.

Parameters:

Nint: 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:

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

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.setMaximumEvaluationNumber(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.

setShadowedId(id)¶

Accessor to the object’s shadowed id.

Parameters:

idint: Internal unique identifier.

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.setMaximumEvaluationNumber(10000)
>>> def ask_stop():
...     return True
>>> solver.setStopCallback(ask_stop)
>>> solver.run()