Method parameters

Method parameters are listed and explained here.

Overview of methods and their variants

Avaliable methods and their variants are summarized in the following table.

Method	Variant	Supports constraints	Remarks
Particle Swarm Optimization (PSO)	‘Vanilla’
	‘TVAC’		User must provide at least one of the following stopping criteria: optimizer.max_iterations, optimizer.max_evaluations, optimizer.max_elapsed_time.
	‘Chaotic’
Fireworks Algorithm (FWA)	‘Vanilla’
	‘Rank’
Squirrel Search Algorithm (SSA)	‘Vanilla’		Showing poor performance on unbound problems.
Differential Evolution (DE)	‘SHADE’
	‘LSHADE’		User must provide at least one of the following stopping criteria: optimizer.max_iterations, optimizer.max_evaluations, optimizer.max_elapsed_time.
Bat Algorithm (BA)	‘Vanilla’		Showing poor performance on unbound problems.
Electromagnetic Field Optimization (EFO)	‘Vanilla’		Significantly slower than other methods. Does not support parallel evaluation.
Manta Ray Foraging Optimization (MRFO)	‘Vanilla’		User must provide at least one of the following stopping criteria: optimizer.max_iterations, optimizer.max_evaluations, optimizer.max_elapsed_time.
Artificial Bee Colony (ABC)	‘Vanilla’		Showing poor performance on unbound problems.
	‘FullyEmployed’		Showing poor performance on unbound problems.
Grey Wolf Optimizer (GWO)	‘Vanilla’		User must provide at least one of the following stopping criteria: optimizer.max_iterations, optimizer.max_evaluations, optimizer.max_elapsed_time.
Heap-Based Optimizer (HBO)	‘Vanilla’		User must provide at least one of the following stopping criteria: optimizer.max_iterations, optimizer.max_evaluations, optimizer.max_elapsed_time.
	‘Dynamic’		User must provide at least one of the following stopping criteria: optimizer.max_iterations, optimizer.max_evaluations, optimizer.max_elapsed_time.
Controlled Random Search (CRS)	‘Vanilla’		Slower than other methods. Does not support parallel evaluation.
Nelder-Mead (NM)	‘Vanilla’
	‘GaoHan’
Multi-Scale Grid Descent (MSGD)	‘Vanilla’		Does not support unbound optimization.
Random Search (RS)	‘Vanilla’		Showing poor performance on unbound optimization.

Legend: Default variant, Constraints supported, Constraints not supported

Specific parameters for each of the available methods and their variants are listed and explained below.

Particle Swarm Optimization (PSO)

Variant	Parameter	Allowed values	Range	Default	Description
all	swarm_size	(int)	[1, -]	max (10, dimensions)	Number of PSO particles
	inertia	(float)	[0.5, 1.0]	0.72	Inertia weight
		‘LDIW’			Linearly decreasing inertia weight (from 1.0 to 0.4)
		‘HSIW’			Half sinusoidal inertia weight (from 0.5 to 0.75 and back)
		‘anakatabatic’			Adaptive inertia weight technique (Družeta and Ivić, 2020)
‘Vanilla’	cognitive_rate	(float)	[0.0, 2.0]	1.0	PSO parameter also known as c1
	social_rate	(float)	[0.0, 2.0]	1.0	PSO parameter also known as c2
	akb_model	‘Languid’, ‘TipsySpider’, ‘FlyingStork’, ‘MessyTie’		‘Languid’	Secondary parameter when using inertia=’anakatabatic’
‘TVAC’	akb_model	‘Languid’, ‘RightwardPeaks’, ‘OrigamiSnake’		‘Languid’	Secondary parameter when using inertia=’anakatabatic’
‘Chaotic’	max_cls_it	(int)	[0, -]	10	Maximum number of chaotic local search iterations
	chaotic_elite	(float)	[0.0, 1.0]	0.2	Elite part of the swarm, immune to reinitialization
	akb_model	‘Languid’		‘Languid’	Secondary parameter when using inertia=’anakatabatic’

Fireworks Algorithm (FWA)

Variant	Parameter	Allowed values	Range	Default	Description
all	n	(int)	[1, -]	dimensions	Number of fireworks
	m1	(int)	[1, -]	dimensions / 2	Number of explosion sparks
	m2	(int)	[1, -]	dimensions / 2	Number of mutation sparks

Squirrel Search Algorithm (SSA)

Variant	Parameter	Allowed values	Range	Default	Description
‘Vanilla’	pop_size	(int)	[1, -]	max (20, 2 * dimensions)	Number of SSA squirrels
	ata	(float)	[0.0, 1.0]	0.5	Acorn tree attraction
	p_pred	(float)	[-, -]	0.1	Predator presence probability
	c_glide	(float)	[-, -]	1.9	Gliding constant
	gd_lim	(list of 2 floats)		[0.5, 1.11]	Gliding distance limits (min, max)

Differential Evolution (DE)

Variant	Parameter	Allowed values	Range	Default	Description
all	pop_init	(int)	[1, -]	max(30, 5 * dimensions)	Initial population size
	f_archive	(float)	[0.0, -]	2.6	External archive size factor
	hist_size	(int)	[1, -]	6	Size of historical memory
	p_mutation	(float)	[0.0, 1.0]	0.11	Mutation probability

Bat Algorithm (BA)

Variant	Parameter	Allowed values	Range	Default	Description
‘Vanilla’	pop_size	(int)	[1, -]	max (15, dimensions)	Number of BA bats
	loudness	(float)	[-, -]	1.0	Loudness
	pulse_rate	(float)	[-, -]	0.001	Pulse rate
	alpha	(float)	[-, -]	0.9	Alpha
	gamma	(float)	[-, -]	0.1	Gamma
	freq_range	(list of 2 floats)		[0.0, 1.0]	Frequency range (min, max)

Electromagnetic Field Optimization (EFO)

Variant	Parameter	Allowed values	Range	Default	Description
‘Vanilla’	pop_size	(int)	[1, -]	max (50, dimensions)	EFO population size
	R_rate	(float)	[0.1, 0.4]	0.25	Probability of changing one EM of generated particle with a random EM
	Ps_rate	(float)	[0.1, 0.4]	0.25	Probability of selecting EMs of generated particle from the positive field
	P_field	(float)	[0.05, 0.1]	0.075	Portion of population which belongs to positive field
	N_field	(float)	[0.4, 0.5]	0.45	Portion of population which belongs to negative field

Manta Ray Foraging Optimization (MRFO)

Variant	Parameter	Allowed values	Range	Default	Description
‘Vanilla’	pop_size	(int)	[1, -]	max (10, dimensions)	Number of MRFO mantas
	f_som	(float)	[-, -]	2.0	Somersault factor

Artificial Bee Colony (ABC)

Variant	Parameter	Allowed values	Range	Default	Description
all	pop_size	(int)	[2, -]	max (10, 2 * dimensions)	Total number of bees
	trial_limit	(int)	[1, -]	pop_size * dimensions / 2	Number of times a bee may try to find a better solution before it is reinitialized

Grey Wolf Optimizer (GWO)

Variant	Parameter	Allowed values	Range	Default	Description
‘Vanilla’	pop_size	(int)	[5, -]	max (10, dimensions)	Number of GWO wolves

Heap-Based Optimizer (HBO)

Variant	Parameter	Allowed values	Range	Default	Description
all	team_size	(int)	[2, -]	max (dimensions ^ 0.5, 3)	Number of workers under one boss
	levels	(int)	[2, -]	3	Number of levels in the corporate structure

Controlled Random Search (CRS)

Variant	Parameter	Allowed values	Range	Default	Description
‘Vanilla’	pop_scale	(float)	[1, -]	10	Population scale. Population size iz computed as pop_scale * (dimensions + 1)

Nelder-Mead (NM)

Variant	Parameter	Allowed values	Range	Default	Description
all	init_step	(float)	[0.0, 1.0]	0.4	Relative size of initial polytope
‘Vanilla’	alpha	(float)	[0.0, -]	1.0	Reflection factor
	gamma	(float)	[0.0, -]	2.0	Expansion factor
	rho	(float)	[0.0, -]	0.5	Contraction factor
	sigma	(float)	[0.0, -]	0.5	Reduction factor

Multi-Scale Grid Descent (MSGD)

Variant	Parameter	Allowed values	Range	Default	Description
‘Vanilla’	divisions	(ndarray or int)	[1, -]	10	Number of grid divisions in each dimension
	base	(int)	[1, -]	4	Base of the exponential grid refining (how many times is grid refined in each scale increment)
	max_scale	(int)	[1, -]	15	Maximum scale (maximum number of grid refinements)

Random Search (RS)

Variant	Parameter	Allowed values	Range	Default	Description
‘Vanilla’	batch_size	(int)	[1, -]	dimensions	Number of evaluations per iteration