MultiStart¶
-
class
MultiStart
(*args)¶ Multi start optimization algorithm.
The algorithm runs an optimization solver for N starting points and returns the best result of each local search. The algorithm succeeds when at least one local search succeeds.
Available constructors:
MultiStart(solver, startingPoints)Parameters: - solver :
OptimizationAlgorithm
The internal solver
- startingPoints : 2-d sequence of float
Starting point candidates
Examples
>>> import openturns as ot >>> ot.RandomGenerator.SetSeed(0) >>> dim = 2 >>> model = ot.SymbolicFunction(['x', 'y'], ['x^2+y^2*(1-x)^3']) >>> bounds = ot.Interval([-3.0] * dim, [3.0] * dim) >>> problem = ot.OptimizationProblem(model) >>> problem.setBounds(bounds) >>> solver = ot.TNC(problem) >>> startingPoints = ot.Normal(dim).getSample(3) >>> algo = ot.MultiStart(solver, startingPoints) >>> algo.run() >>> result = algo.getResult()
Methods
computeLagrangeMultipliers
(x)Compute the Lagrange multipliers of a problem at a given point. getClassName
()Accessor to the object’s name. getId
()Accessor to the object’s id. 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
()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
()Accessor to starting point. getStartingPoints
()Starting points accessor. 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. 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)Solver accessor. setProblem
(problem)Accessor to 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
(startingPoint)Accessor to starting point. setStartingPoints
(sample)Starting points accessor. 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)¶ Initialize self. See help(type(self)) for accurate signature.
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computeLagrangeMultipliers
(x)¶ Compute the Lagrange multipliers of a problem at a given point.
Parameters: - x : sequence of float
Point at which the Lagrange multipliers are computed.
Returns: - lagrangeMultiplier : sequence of float
Lagrange multipliers of the problem at the given point.
Notes
The Lagrange multipliers
are associated with the following Lagrangian formulation of the optimization problem:
where
.
- The Lagrange multipliers are stored as
, where:
is of dimension 0 if there is no equality constraint, else of dimension the dimension of
ie the number of scalar equality constraints
and
are of dimension 0 if there is no bound constraint, else of dimension of
is of dimension 0 if there is no inequality constraint, else of dimension the dimension of
ie the number of scalar inequality constraints
The vector
is solution of the following linear system:
If there is no constraint of any kind,
is of dimension 0, as well as if no constraint is active.
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getClassName
()¶ Accessor to the object’s name.
Returns: - class_name : str
The object class name (object.__class__.__name__).
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getId
()¶ Accessor to the object’s id.
Returns: - id : int
Internal unique identifier.
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getMaximumAbsoluteError
()¶ Accessor to maximum allowed absolute error.
Returns: - maximumAbsoluteError : float
Maximum allowed absolute error.
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getMaximumConstraintError
()¶ Accessor to maximum allowed constraint error.
Returns: - maximumConstraintError : float
Maximum allowed constraint error.
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getMaximumEvaluationNumber
()¶ Accessor to maximum allowed number of evaluations.
Returns: - N : int
Maximum allowed number of evaluations.
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getMaximumIterationNumber
()¶ Accessor to maximum allowed number of iterations.
Returns: - N : int
Maximum allowed number of iterations.
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getMaximumRelativeError
()¶ Accessor to maximum allowed relative error.
Returns: - maximumRelativeError : float
Maximum allowed relative error.
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getMaximumResidualError
()¶ Accessor to maximum allowed residual error.
Returns: - maximumResidualError : float
Maximum allowed residual error.
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getName
()¶ Accessor to the object’s name.
Returns: - name : str
The name of the object.
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getOptimizationAlgorithm
()¶ Solver accessor.
Returns: - solver :
OptimizationAlgorithm
The internal solver
- solver :
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getProblem
()¶ Accessor to optimization problem.
Returns: - problem :
OptimizationProblem
Optimization problem.
- problem :
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getResult
()¶ Accessor to optimization result.
Returns: - result :
OptimizationResult
Result class.
- result :
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getResultCollection
()¶ Intermediate optimization results accessor.
Returns: - results :
OptimizationResultCollection
Intermediate optimization results
- results :
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getShadowedId
()¶ Accessor to the object’s shadowed id.
Returns: - id : int
Internal unique identifier.
-
getStartingPoints
()¶ Starting points accessor.
Returns: - startingPointNumber :
Sample
Starting points
- startingPointNumber :
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getVerbose
()¶ Accessor to the verbosity flag.
Returns: - verbose : bool
Verbosity flag state.
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getVisibility
()¶ Accessor to the object’s visibility state.
Returns: - visible : bool
Visibility flag.
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hasName
()¶ Test if the object is named.
Returns: - hasName : bool
True if the name is not empty.
-
hasVisibleName
()¶ Test if the object has a distinguishable name.
Returns: - hasVisibleName : bool
True if the name is not empty and not the default one.
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run
()¶ Launch the optimization.
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setMaximumAbsoluteError
(maximumAbsoluteError)¶ Accessor to maximum allowed absolute error.
Parameters: - maximumAbsoluteError : float
Maximum allowed absolute error.
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setMaximumConstraintError
(maximumConstraintError)¶ Accessor to maximum allowed constraint error.
Parameters: - maximumConstraintError : float
Maximum allowed constraint error.
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setMaximumEvaluationNumber
(maximumEvaluationNumber)¶ Accessor to maximum allowed number of evaluations.
Parameters: - N : int
Maximum allowed number of evaluations.
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setMaximumIterationNumber
(maximumIterationNumber)¶ Accessor to maximum allowed number of iterations.
Parameters: - N : int
Maximum allowed number of iterations.
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setMaximumRelativeError
(maximumRelativeError)¶ Accessor to maximum allowed relative error.
Parameters: - maximumRelativeError : float
Maximum allowed relative error.
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setMaximumResidualError
(maximumResidualError)¶ Accessor to maximum allowed residual error.
Parameters: - maximumResidualError : float
Maximum allowed residual error.
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setName
(name)¶ Accessor to the object’s name.
Parameters: - name : str
The name of the object.
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setOptimizationAlgorithm
(solver)¶ Solver accessor.
Parameters: - solver :
OptimizationAlgorithm
The internal solver
- solver :
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setProblem
(problem)¶ Accessor to optimization problem.
Parameters: - problem :
OptimizationProblem
Optimization problem.
- problem :
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setProgressCallback
(*args)¶ Set up a progress callback.
Parameters: - callback : callable
Takes a float as argument as percentage of progress.
Notes
May not be implemented by all solvers, refer to the solver documentation.
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setResult
(result)¶ Accessor to optimization result.
Parameters: - result :
OptimizationResult
Result class.
- result :
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setShadowedId
(id)¶ Accessor to the object’s shadowed id.
Parameters: - id : int
Internal unique identifier.
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setStartingPoint
(startingPoint)¶ Accessor to starting point.
Parameters: - startingPoint :
Point
Starting point.
- startingPoint :
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setStartingPoints
(sample)¶ Starting points accessor.
Parameters: - startingPointNumber :
Sample
Starting points
- startingPointNumber :
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setStopCallback
(*args)¶ Set up a stop callback.
Parameters: - callback : callable
Returns an int deciding whether to stop or continue.
Notes
May not be implemented by all solvers, refer to the solver documentation.
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setVerbose
(verbose)¶ Accessor to the verbosity flag.
Parameters: - verbose : bool
Verbosity flag state.
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setVisibility
(visible)¶ Accessor to the object’s visibility state.
Parameters: - visible : bool
Visibility flag.
- solver :