SimulatedAnnealingLHS

class SimulatedAnnealingLHS(*args)

LHS optimization using simulated annealing.

Performs the optimization of an LHS using simulated annealing algorithm.

Available constructors:

SimulatedAnnealingLHS(lhsDesign)

SimulatedAnnealingLHS(lhsDesign, profile)

SimulatedAnnealingLHS(lhsDesign, profile, spaceFilling)

SimulatedAnnealingLHS(initialDesign, distribution)

SimulatedAnnealingLHS(initialDesign, distribution, profile)

SimulatedAnnealingLHS(initialDesign, distribution, profile, spaceFilling)

Parameters:

lhsDesign : LHSExperiment

Factory that generate designs

initialDesign : 2d-array sequence

Initial design to be optimized

distribution : Distribution

Distribution of designs

profile : TemperatureProfile

Temperature profile used by the simulated annealing algorithm Default one is GeometricProfile

spaceFilling : SpaceFilling

Criterion to be optimized Default one is SpaceFillingMinDist

Notes

With the first constructor, the initial design is generated thanks to lhsDesign. With the second usage, we fix it. Starting from this design, a new design is obtained by permuting one random coordinate of two randomly chosen elements; by construction, this design is also an LHS design. If the new design is better than the previous one, it is kept. If it is worse, it may anyway be kept with some probability, which depends on how these designs compare, but also on a temperature profile T which decreases over time. This means that jumping away from local extrema becomes less probable over time.

Examples

>>> import openturns as ot
>>> dimension = 3
>>> size = 100
>>> # Build standard randomized LHS algorithm
>>> distribution = ot.ComposedDistribution([ot.Uniform(0.0, 1.0)]*dimension)
>>> lhs = ot.LHSExperiment(distribution, size)
>>> lhs.setAlwaysShuffle(True) # randomized
>>> # Defining space fillings
>>> spaceFilling = ot.SpaceFillingC2()
>>> # Geometric profile
>>> geomProfile = ot.GeometricProfile(10.0, 0.95, 2000)
>>> # Simulated Annealing LHS with geometric temperature profile, C2 optimization
>>> optimalLHSAlgorithm = ot.SimulatedAnnealingLHS(lhs, geomProfile, spaceFilling)

Methods

generate() Generate points according to the type of the experiment.
generateWithRestart(nRestart)
generateWithWeights() Generate points and their associated weight according to the type of the experiment.
getClassName() Accessor to the object’s name.
getDistribution() Accessor to the distribution.
getId() Accessor to the object’s id.
getLHS() Return the LHS design.
getName() Accessor to the object’s name.
getResult() Result accessor.
getShadowedId() Accessor to the object’s shadowed id.
getSize() Accessor to the size of the generated sample.
getSpaceFilling() Return the space-filling criterion to be optimized.
getVisibility() Accessor to the object’s visibility state.
hasName() Test if the object is named.
hasUniformWeights() Ask whether the experiment has uniform weights.
hasVisibleName() Test if the object has a distinguishable name.
setDistribution(distribution) Accessor to the distribution.
setName(name) Accessor to the object’s name.
setShadowedId(id) Accessor to the object’s shadowed id.
setSize(size) Accessor to the size of the generated sample.
setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)

x.__init__(…) initializes x; see help(type(x)) for signature

generate()

Generate points according to the type of the experiment.

Returns:

sample : Sample

Points (\Xi_i)_{i \in I} which constitute the design of experiments with card I = size. The sampling method is defined by the nature of the weighted experiment.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> myExperiment = ot.MonteCarloExperiment(ot.Normal(2), 5)
>>> sample = myExperiment.generate()
>>> print(sample)
    [ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
3 : [ -0.355007  1.43725  ]
4 : [  0.810668  0.793156 ]
generateWithWeights()

Generate points and their associated weight according to the type of the experiment.

Returns:

sample : Sample

The points which constitute the design of experiments. The sampling method is defined by the nature of the experiment.

weights : Point of size cardI

Weights (\omega_i)_{i \in I} associated with the points. By default, all the weights are equal to 1/cardI.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> myExperiment = ot.MonteCarloExperiment(ot.Normal(2), 5)
>>> sample, weights = myExperiment.generateWithWeights()
>>> print(sample)
    [ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
3 : [ -0.355007  1.43725  ]
4 : [  0.810668  0.793156 ]
>>> print(weights)
[0.2,0.2,0.2,0.2,0.2]
getClassName()

Accessor to the object’s name.

Returns:

class_name : str

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

getDistribution()

Accessor to the distribution.

Returns:

distribution : Distribution

Distribution used to generate the set of input data.

getId()

Accessor to the object’s id.

Returns:

id : int

Internal unique identifier.

getLHS()

Return the LHS design.

Returns:

value : LHSExperiment

Result the factory that builds initial design to be optimized

getName()

Accessor to the object’s name.

Returns:

name : str

The name of the object.

getResult()

Result accessor.

Returns:

value : LHSResult

Result of generation that contains the optimal design, some criteria and history

getShadowedId()

Accessor to the object’s shadowed id.

Returns:

id : int

Internal unique identifier.

getSize()

Accessor to the size of the generated sample.

Returns:

size : positive int

Number cardI of points constituting the design of experiments.

getSpaceFilling()

Return the space-filling criterion to be optimized.

Returns:

value : SpaceFilling

Criterion function to be optimized

getVisibility()

Accessor to the object’s visibility state.

Returns:

visible : bool

Visibility flag.

hasName()

Test if the object is named.

Returns:

hasName : bool

True if the name is not empty.

hasUniformWeights()

Ask whether the experiment has uniform weights.

Returns:

hasUniformWeights : bool

Whether the experiment has uniform weights.

hasVisibleName()

Test if the object has a distinguishable name.

Returns:

hasVisibleName : bool

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

setDistribution(distribution)

Accessor to the distribution.

Parameters:

distribution : Distribution

Distribution used to generate the set of input data.

setName(name)

Accessor to the object’s name.

Parameters:

name : str

The name of the object.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters:

id : int

Internal unique identifier.

setSize(size)

Accessor to the size of the generated sample.

Parameters:

size : positive int

Number cardI of points constituting the design of experiments.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters:

visible : bool

Visibility flag.