Configuration Options

This document provides a comprehensive overview of the available configuration options for different algorithms in the pyHMS library.

CMA-ES Configuration (CMALevelConfig)

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is a powerful optimization algorithm for continuous domains.

Required Parameters

Parameter	Type	Description
problem	Problem	The optimization problem to solve
lsc	LocalStopCondition | UniversalStopCondition	Local stopping condition for this level
generations	int	Number of generations to run in each metaepoch

Optional Parameters

Parameter	Type	Default	Description
sigma0	float | None	None	Initial step size parameter. If None and set_stds=True, defaults to 1.0. Otherwise (if None and set_stds=False) calculated automatically from the parent deme’s population.
set_stds	bool	False	If True, uses standard deviations estimated from parent deme population for each dimension separately instead of a single sigma value. This adapts the search to the local landscape shape.
**kwargs			Additional parameters passed directly to the CMAEvolutionStrategy constructor from the cma package (https://pypi.org/project/cma/). See pycma documentation for all available parameters.

Implementation Notes

• The CMA-ES implementation is based on the cma (https://pypi.org/project/cma/) package’s CMAEvolutionStrategy class

• The following parameters are set automatically:

  • bounds: Set from the problem’s bounds

  • CMA_stds: When set_stds=True, calculated from parent deme population

  • Random seed support through the random_seed option in TreeConfig

• The implementation is located in pyhms/demes/cma_deme.py

Evolutionary Algorithm Configuration (EALevelConfig)

The Evolutionary Algorithm (EA) implementations in pyHMS provide flexible population-based optimization approaches.

Required Parameters

Parameter	Type	Description
pop_size	int	Population size for the evolutionary algorithm
problem	Problem	The optimization problem to solve
lsc	LocalStopCondition | UniversalStopCondition	Local stopping condition for this level
generations	int	Number of generations to run in each metaepoch

Optional Parameters

Parameter	Type	Default	Description
ea_class	Type[BaseSEA]	SEA	The class of evolutionary algorithm to use. Must inherit from BaseSEA.
sample_std_dev	float	1.0	Standard deviation used when sampling new individuals around a sprout seed. Controls diversity of the initial population when sprouting.
mutation_std	float		Standard deviation for Gaussian mutation. Controls exploration vs exploitation balance.
mutation_std_step	float		Optional parameter to adapt mutation_std over time. If provided, mutation_std will increase by this amount after each generation if child deme was not sprouted.
k_elites	int		Number of elite individuals to preserve in each generation.
p_mutation	float		Probability of mutation for each individual.
p_crossover	float		Probability of crossover (used in SEAWithCrossover).

Available EA Classes

pyHMS offers several variants of evolutionary algorithms:

Class	Description
SEA	Standard Evolutionary Algorithm with tournament selection and Gaussian mutation
SEAWithCrossover	EA with tournament selection, arithmetic crossover, and Gaussian mutation
SEAWithAdaptiveMutation	EA with adaptive mutation rate that changes over time

Implementation Notes

• The implementation is located in pyhms/demes/ea_deme.py, with specific algorithm variants in pyhms/demes/single_pop_eas/

• When used as a root deme, the initial population is sampled uniformly within the problem bounds

• When used as a child deme, the initial population is sampled using a normal distribution around the sprout seed

• The random seed can be set via the random_seed option in TreeConfig

Differential Evolution Configuration (DELevelConfig)

Differential Evolution (DE) is a population-based optimization algorithm that’s particularly effective for continuous optimization problems and robust against noise.

Required Parameters

Parameter	Type	Description
pop_size	int	Population size for the DE algorithm
problem	Problem	The optimization problem to solve
lsc	LocalStopCondition | UniversalStopCondition	Local stopping condition for this level
generations	int	Number of generations to run in each metaepoch

Optional Parameters

Parameter	Type	Default	Description
sample_std_dev	float	1.0	Standard deviation used when sampling new individuals around a sprout seed. Controls diversity of the initial population when sprouting.
dither	bool	False	If True, uses adaptive scaling factor (dithering) which can improve convergence and robustness.
scaling	float	0.8	Differential weight (F) in the range [0, 2]. Controls the amplification of differential vectors during mutation.
crossover	float	0.9	Crossover probability (CR) in the range [0, 1]. Controls the fraction of parameter values copied from the mutant.

Implementation Notes

• The implementation is located in pyhms/demes/de_deme.py with the core DE algorithm in pyhms/demes/single_pop_eas/de.py

• When used as a root deme, the initial population is sampled uniformly within the problem bounds

• When used as a child deme, the initial population is sampled using a normal distribution around the sprout seed

• The random seed can be set via the random_seed option in TreeConfig

Success-History Based Adaptive DE Configuration (SHADELevelConfig)

Success-History based Adaptive Differential Evolution (SHADE) is an advanced variant of DE that adaptively tunes its parameters based on successful search history.

Required Parameters

Parameter	Type	Description
pop_size	int	Population size for the SHADE algorithm
problem	Problem	The optimization problem to solve
lsc	LocalStopCondition | UniversalStopCondition	Local stopping condition for this level
generations	int	Number of generations to run in each metaepoch
memory_size	int	Size of the historical memory used to store successful parameter values

Optional Parameters

Parameter	Type	Default	Description
sample_std_dev	float	1.0	Standard deviation used when sampling new individuals around a sprout seed. Controls diversity of the initial population when sprouting.

Implementation Notes

• The implementation is located in pyhms/demes/shade_deme.py with the core SHADE algorithm in pyhms/demes/single_pop_eas/de.py

• SHADE maintains a historical memory of successful control parameters (CR and F values)

• When used as a root deme, the initial population is sampled uniformly within the problem bounds

• When used as a child deme, the initial population is sampled using a normal distribution around the sprout seed

• The random seed can be set via the random_seed option in TreeConfig