Parameters¶

class modcma.parameters.Parameters(*args, **kwargs)¶

Bases: modcma.utils.AnnotatedStruct

AnnotatedStruct object for holding the parameters for the ModularCMAES.

d¶

The dimensionality of the problem

Type: int

x0¶

Initial guess of the population center of mass.

Type: np.ndarray

target¶

The absolute target of the optimization problem

Type: float = -float(“inf”)

budget¶

The maximum number of iterations

Type: int = None

n_generations¶

The number of generations to run the optimizer. If this value is specified this will override the default break-conditions, and the optimizer will only stop after n_generations. Target-reached and budget will be ignored.

Type: int = None

lambda_¶

The number of offspring in the population

Type: int = None

mu¶

The number of parents in the population

Type: int = None

sigma0¶

The initial value of sigma (step size)

Type: float = .5

a_tpa¶

Parameter used in TPA

Type: float = .5

b_tpa¶

Parameter used in TPA

Type: float = 0.

cs¶

Learning rate for the cumulation of the step size control

Type: float = None

cc¶

Learning rate for the rank-one update

Type: float = None

cmu¶

Learning rate for the rank-mu update

Type: float = None

c1¶

Learning rate for the rank-one update

Type: float = None

seq_cutoff_factor¶

Used in sequential selection, the number of times mu individuals must be seen before a sequential break can be performed

Type: int = 1

ub¶

The upper bound, used for bound correction and threshold convergence

Type: np.array = None

lb¶

The lower bound, used for bound correction and threshold convergence

Type: np.array = None

init_threshold¶

The initial length theshold used in treshold convergence

Type: float = 0.2

decay_factor¶

The decay for the threshold used in threshold covergence

Type: float = 0.995

max_resamples¶

The maximum amount of resamples which can be done when ‘dismiss’-boundary correction is used

Type: int

active¶

Specifying whether to use active update.: [1] G. Jastrebski, D. V. Arnold, et al. Improving evolution strategies through active covariance matrix adaptation. In Evolutionary Computation (CEC), 2006 IEEE Congress on, pages 2814–2821. IEEE, 2006

Type: bool = False

elitist¶

Specifying whether to use an elitist approach

Type: bool = False

sequential¶

Specifying whether to use sequential selection: [3] D. Brockhoff, A. Auger, N. Hansen, D. V. Arnold, and T. Hohm. Mirrored Sampling and Sequential Selection for Evolution Strategies. In R. Schaefer, C. Cotta, J. Kołodziej, and G. Rudolph, editors, Parallel Problem Solving from Nature, PPSN XI: 11th International Conference, Kraków, Poland, September 11-15, 2010, Proceedings, Part I, pages 11–21, Berlin, Heidelberg, 2010. Springer Berlin Heidelberg.

Type: bool = False

threshold_convergence¶

Specifying whether to use threshold convergence: [4] A. Piad-Morffis, S. Estevez-Velarde, A. Bolufe-Rohler, J. Montgomery, and S. Chen. Evolution strategies with thresheld convergence. In Evolutionary Computation (CEC), 2015 IEEE Congress on, pages 2097– 2104, May 2015.

Type: bool = False

bound_correction¶

Specifying whether to use bound correction to enforce ub and lb

Type: str = (None, ‘saturate’, ‘unif_resample’, ‘COTN’, ‘toroidal’, ‘mirror’,)

orthogonal¶

Specifying whether to use orthogonal sampling: [5] H. Wang, M. Emmerich, and T. Bäck. Mirrored Orthogonal Sampling with Pairwise Selection in Evolution Strategies. In Proceedings of the 29th Annual ACM Symposium on Applied Computing, pages 154–156.

Type: bool = False

local_restart¶

Specifying which local restart strategy should be used

IPOP:: [11] Anne Auger and Nikolaus Hansen. A restart cma evolution strategy with increasing population size. volume 2, pages 1769–1776, 01 2005

Type: str = (None, ‘IPOP’, )

base_sampler¶

Denoting which base sampler to use, ‘sobol’, ‘halton’ can be selected to sample from a quasi random sequence.

[6] A. Auger, M. Jebalia, and O. Teytaud. Algorithms (x, sigma, eta): random mutations for evolution strategies. In Artificial Evolution: 7th International Conference, Revised Selected Papers, pages 296–307. Springer, 2006.

Type: str = (‘gaussian’, ‘sobol’, ‘halton’,)

mirrored¶

Specifying whether to use mirrored sampling: [2] D. Brockhoff, A. Auger, N. Hansen, D. V. CMAEST. Hohm. Mirrored Sampling and Sequential SelectioCMAESion Strategies. In R. Schaefer, C. Cotta, J. Kołodziej, aCMAESh, editors, Parallel Problem Solving from Nature, PPSN XI: 11tCMAESnal Conference, Kraków, Poland, September 11-15, 2010, PrCMAESart I, pages 11–21, Berlin, Heidelberg, 2010. SpringerCMAESelberg. ACM, 2014.

Type: str = (None, ‘mirrored’, mirrored pairwise’, )

weights_option¶

Denoting the recombination weigths to be used.: [7] Sander van Rijn, Hao Wang, Matthijs van Leeuwen, and Thomas Bäck. 2016. Evolving the Structure of Evolution Strategies. Computer 49, 5 (May 2016), 54–63.

Type: str = (‘default’, ‘1/mu’, ‘1/2^mu’, )

step_size_adaptation¶

Specifying which step size adaptation mechanism should be used. csa:

[8] Nikolaus Hansen. The CMA evolution strategy: A tutorial.CoRR, abs/1604.00772, 2016

tpa:: [9] Nikolaus Hansen. CMA-ES with two-point step-size adaptation.CoRR, abs/0805.0231,2008.
msr:: [10] Ouassim Ait Elhara, Anne Auger, and Nikolaus Hansen. A Median Success Rule for Non-Elitist Evolution Strategies: Study of Feasibility. In Blum et al. Christian, editor,Genetic and Evolutionary Computation Conference, pages 415–422, Amsterdam, Nether-lands, July 2013. ACM, ACM Press.

Type: str = (‘csa’, ‘tpa’, ‘msr’, )

population¶

The current population of individuals

Type: TypeVar(‘Population’) = None

old_population¶

The old population of individuals

Type: TypeVar(‘Population’) = None

termination_criteria¶

A dictionary of termination criteria

Type: dict = {}

ipop_factor¶

The factor to increase the population after each resart (IPOP)

Type: int = 2

tolx¶

Use to compute restart condition

Type: float = 10e-12

tolup_sigma¶

Use to compute restart condition

Type: float = 10e20

condition_cov¶

Use to compute restart condition

Type: float = 10e14

ps_factor¶

Determines the frequence of exploration/expliotation 1 is neutral, lower is more expliotative, higher is more explorative

Type: float = 1.

sample_sigma¶

Whether to sample sigma for each individual from a lognormal distribution.

Type: bool = Flase

sampler¶

A generator object producing new samples

Type: generator

used_budget¶

The number of function evaluations used

Type: int

fopt¶

The fitness of the current best individual

Type: float

t¶

The number of generations

Type: int

sigma_over_time¶

The value sigma has in each generation

Type: list

best_fopts¶

The value of fopt in each generation

Type: list

median_fitnesses¶

The median fitness value in each generation

Type: list

best_fitnesses¶

The best fitness value observed in each generation

Type: list

flat_fitnesses = deque: A deque containing boolean values denoting if a flat fitness value is observed in recent generations

restarts¶

A list containing the t values (generations) where a restart has taken place

Type: list

seq_cutoff¶

The number of individuals that must be seen before a sequential break can be performed

Type: int

diameter¶

The diameter of the search space

Type: float

max_iter¶

The maximum number of iterations that can occur between two restarts.

Type: float

nbin¶

Used to determine a window for equal function values

Type: int

n_stagnation¶

Used to determine a window for stagnation

Type: int

flat_fitness_index¶

Used to determine which ranked individual should be the same as the first indivual in order to determine flat fitness values.

Type: int

sigma¶

The step size

Type: float

m¶

The mean value of the individuals

Type: np.ndarray

dm¶

The difference in the new mean value of the individuals versus the old mean value.

Type: np.ndarray

pc¶

The evolution path

Type: np.ndarray

ps¶

The conjugate evolution path

Type: np.ndarray

C¶

The covariance matrix

Type: np.ndarray

B¶

The eigenvectors of the covariance matrix C

Type: np.ndarray

D¶

The eigenvalues of the covariance matrix C

Type: np.ndarray

inv_root_C¶

The result of C**-(1/2)

Type: np.ndarray

s¶

Used for TPA

Type: float

rank_tpa¶

Used for TPA

Type: float

weights¶

The recombination weights.

Type: np.ndarray

pweights¶

The positive recombination weights.

Type: np.ndarray

nweights¶

The negative recombination weights, used in active update

Type: np.ndarray

mueff¶

The variance effective selection mass

Type: float

damps¶

Used for adapting sigma with csa

Type: float

chiN¶

Value approaching E||N(0,I)||

Type: np.ndarray

ds¶

Used for msr

Type: float

threshold¶

The length threshold used in threshold convergence

Type: float

last_restart¶

The generation in where the last restart has occored

Type: int

max_resamples¶

The maximum amount of resamples which can be done when ‘dismiss’-boundary correction is used

Type: int

n_out_of_bounds¶

The number of individals that are sampled out of bounds

Type: int

Attributes Summary

`a_tpa`	Data descriptor checks for correct types.
`active`	Data descriptor checks for correct types.
`b_tpa`	Data descriptor checks for correct types.
`base_sampler`	Descriptor, checks of value is Any of a specified sequence of options.
`bound_correction`	Descriptor, checks of value is Any of a specified sequence of options.
`budget`	Data descriptor checks for correct types.
`c1`	Data descriptor checks for correct types.
`cc`	Data descriptor checks for correct types.
`cmu`	Data descriptor checks for correct types.
`compute_termination_criteria`	Data descriptor checks for correct types.
`condition_cov`	Data descriptor checks for correct types.
`cs`	Data descriptor checks for correct types.
`d`	Data descriptor checks for correct types.
`decay_factor`	Data descriptor checks for correct types.
`elitist`	Data descriptor checks for correct types.
`init_threshold`	Data descriptor checks for correct types.
`ipop_factor`	Data descriptor checks for correct types.
`lambda_`	Data descriptor checks for correct types.
`last_restart`	Return the last index of self.restarts.
`lb`	Data descriptor checks for correct types.
`local_restart`	Descriptor, checks of value is Any of a specified sequence of options.
`max_resamples`	Data descriptor checks for correct types.
`mirrored`	Descriptor, checks of value is Any of a specified sequence of options.
`mu`	Data descriptor checks for correct types.
`old_population`	Data descriptor checks for correct types.
`orthogonal`	Data descriptor checks for correct types.
`population`	Data descriptor checks for correct types.
`ps_factor`	Data descriptor checks for correct types.
`seq_cutoff_factor`	Data descriptor checks for correct types.
`sequential`	Data descriptor checks for correct types.
`step_size_adaptation`	Descriptor, checks of value is Any of a specified sequence of options.
`target`	Data descriptor checks for correct types.
`termination_criteria`	Data descriptor checks for correct types.
`threshold`	Calculate threshold for mutation, used in threshold convergence.
`threshold_convergence`	Data descriptor checks for correct types.
`tolup_sigma`	Data descriptor checks for correct types.
`tolx`	Data descriptor checks for correct types.
`ub`	Data descriptor checks for correct types.
`weights_option`	Descriptor, checks of value is Any of a specified sequence of options.

Methods Summary

`adapt`()	Method for adapting the internal state parameters.
`adapt_covariance_matrix`()	Method for adapting the covariance matrix.
`adapt_sigma`()	Method to adapt the step size sigma.
`calculate_termination_criteria`()	Method for computing restart criteria.
`from_config_array`(d, config_array)	Instantiate a Parameters object from a configuration array.
`get_sampler`()	Function to return a sampler generator based on the values of other parameters.
`init_adaptation_parameters`()	Initialization function for parameters for self-adaptive processes.
`init_dynamic_parameters`()	Initialization function of parameters that represent the dynamic state of the CMA-ES.
`init_fixed_parameters`()	Initialization function for parameters that are not restarted during a run.
`init_local_restart_parameters`()	Initialization function for parameters for local restart strategies, i.e. IPOP.
`init_selection_parameters`()	Initialization function for parameters that influence in selection.
`load`(filename)	Load stored parameter objects from pickle.
`perform_eigendecomposition`()	Method to perform eigendecomposition.
`perform_local_restart`()	Method performing local restart, if a restart strategy is specified.
`record_statistics`()	Method for recording metadata.
`save`([filename])	Save a parameters object to pickle.

Attributes Documentation

a_tpa: float¶: Data descriptor checks for correct types.

active: bool¶: Data descriptor checks for correct types.

b_tpa: float¶: Data descriptor checks for correct types.

base_sampler: gaussian, sobol, halton¶: Descriptor, checks of value is Any of a specified sequence of options.

bound_correction: None, saturate, unif_resample, COTN, toroidal, mirror¶: Descriptor, checks of value is Any of a specified sequence of options.

budget: int¶: Data descriptor checks for correct types.

c1: float¶: Data descriptor checks for correct types.

cc: float¶: Data descriptor checks for correct types.

cmu: float¶: Data descriptor checks for correct types.

compute_termination_criteria: bool¶: Data descriptor checks for correct types.

condition_cov: float¶: Data descriptor checks for correct types.

cs: float¶: Data descriptor checks for correct types.

d: int¶: Data descriptor checks for correct types.

decay_factor: float¶: Data descriptor checks for correct types.

elitist: bool¶: Data descriptor checks for correct types.

init_threshold: float¶: Data descriptor checks for correct types.

ipop_factor: int¶: Data descriptor checks for correct types.

lambda_: int¶: Data descriptor checks for correct types.

last_restart¶: Return the last index of self.restarts.

lb: numpy.ndarray¶: Data descriptor checks for correct types.

local_restart: None, IPOP, BIPOP¶: Descriptor, checks of value is Any of a specified sequence of options.

max_resamples: int¶: Data descriptor checks for correct types.

mirrored: None, mirrored, mirrored pairwise¶: Descriptor, checks of value is Any of a specified sequence of options.

mu: int¶: Data descriptor checks for correct types.

old_population: Population¶: Data descriptor checks for correct types.

orthogonal: bool¶: Data descriptor checks for correct types.

population: Population¶: Data descriptor checks for correct types.

ps_factor: float¶: Data descriptor checks for correct types.

seq_cutoff_factor: int¶: Data descriptor checks for correct types.

sequential: bool¶: Data descriptor checks for correct types.

step_size_adaptation: csa, tpa, msr, xnes, m-xnes, lp-xnes, psr¶: Descriptor, checks of value is Any of a specified sequence of options.

target: float¶: Data descriptor checks for correct types.

termination_criteria: dict¶: Data descriptor checks for correct types.

threshold¶: Calculate threshold for mutation, used in threshold convergence.

threshold_convergence: bool¶: Data descriptor checks for correct types.

tolup_sigma: float¶: Data descriptor checks for correct types.

tolx: float¶: Data descriptor checks for correct types.

ub: numpy.ndarray¶: Data descriptor checks for correct types.

weights_option: default, equal, 1/2^lambda¶: Descriptor, checks of value is Any of a specified sequence of options.

Methods Documentation

adapt() → None¶

Method for adapting the internal state parameters.

The conjugate evolution path ps is calculated, in addition to the difference in mean x values dm. Thereafter, sigma is adapated, followed by the adapatation of the covariance matrix. TODO: eigendecomp is not neccesary to be beformed every iteration, says CMAES tut.

adapt_covariance_matrix() → None¶

Method for adapting the covariance matrix.

If the option active is specified, active update of the covariance matrix is performed, using negative weights.

adapt_sigma() → None¶

Method to adapt the step size sigma.

There are three variants in implemented here, namely:: ~ Cummulative Stepsize Adaptation (csa) ~ Two-Point Stepsize Adaptation (tpa) ~ Median Success Rule (msr) ~ xNES step size adaptation (xnes) ~ median-xNES step size adaptation (m-xnes) ~ xNES with Log-normal Prior step size adaptation (lp-xnes) ~ Population Step Size rule from lm-cmaes (psr)

One of these methods can be selected by setting the step_size_adaptation parameter.

calculate_termination_criteria() → None¶

Method for computing restart criteria.

Only computes when a local restart strategy is specified, or when explicitly told to do so, i.e.: self.compute_termination_criteria = True

static from_config_array(d: int, config_array: list) → modcma.parameters.Parameters ¶

Instantiate a Parameters object from a configuration array.

Parameters

d (int) – The dimensionality of the problem
config_array (list) –

A list of length len(Parameters.__modules__),
containing ints from 0 to 2

Returns

Return type

A new Parameters instance

get_sampler() → Generator¶

Function to return a sampler generator based on the values of other parameters.

Returns: a sampler
Return type: generator

init_adaptation_parameters() → None¶

Initialization function for parameters for self-adaptive processes.

Examples are recombination weights and learning rates for the covariance matrix adapation.

init_dynamic_parameters() → None¶

Initialization function of parameters that represent the dynamic state of the CMA-ES.

Examples of such parameters are the Covariance matrix C and its eigenvectors and the learning rate sigma.

init_fixed_parameters() → None¶: Initialization function for parameters that are not restarted during a run.

init_local_restart_parameters() → None¶

Initialization function for parameters for local restart strategies, i.e. IPOP.

TODO: check if we can move this to separate object.

init_selection_parameters() → None¶: Initialization function for parameters that influence in selection.

static load(filename: str) → modcma.parameters.Parameters ¶

Load stored parameter objects from pickle.

Parameters: filename (str) – A file path
Returns
Return type: A Parameters object

perform_eigendecomposition() → None¶

Method to perform eigendecomposition.

If sigma or the coveriance matrix has degenerated, the dynamic parameters are reset.

perform_local_restart() → None¶: Method performing local restart, if a restart strategy is specified.

record_statistics() → None¶: Method for recording metadata.

save(filename: str = 'parameters.pkl') → None¶

Save a parameters object to pickle.

Parameters: filename (str) – The name of the file to save to.