Working on the Structural Components of Evolutionary Approaches

Alexandros Tzanetos

1 a

and Jakub K

udela

2 b

onk

oping AI Lab (JAIL), J

onk

oping University, Gjuterigatan 5, 553 18 J

onk

oping, Sweden

Institute of Automation and Computer Science, Faculty of Mechanical Engineering,

Brno University of Technology, Czech Republic

Keywords:

Evolutionary Computation, Swarm Intelligence, Nature-Inspired Intelligence, Mechanisms, Operators,

Modular Algorithms.

Abstract:

Several researchers have turned their attention to the structural components of Evolutionary Computation-

and Swarm Intelligence-oriented approaches. This direction offers various opportunities, such as developing

automatic design and conﬁguration frameworks and integrating operators and mechanisms addressing known

limitations. This work lists recent operators and discusses promising mechanisms found in existing nature-

inspired approaches. It also discusses how these algorithmic components can be integrated into modular

frameworks and how they can be assessed and benchmarked. The work aims to emphasize the importance of

the research direction about nature-inspired mechanisms and operators in the Evolutionary Computation ﬁeld.

1 INTRODUCTION

Evolutionary Computation (EC) and Swarm Intelli-

gence (SI) offer a variety of approaches to deal with

high-complexity real-world problems. Yet, not all al-

gorithms from these ﬁelds constitute a novel search

strategy. Most of them replicate the ideas introduced

in the established ones, i.e., Particle Swarm Optimiza-

tion (PSO), Ant Colony Optimization (ACO), and Ge-

netic Algorithm (GA) (Tzanetos, 2023).

Moreover, several recently introduced algorithms

contain a center-bias operator, making them unsuit-

able for optimization tasks (Kudela, 2022). Also, sev-

eral other structural biases have been detected in such

algorithms (Vermetten et al., 2022).

However, some algorithms contain promising

mechanisms that can be used to overcome known lim-

itations observed in stochastic nature-inspired algo-

rithms (Thymianis and Tzanetos, 2022). More such

mechanisms can potentially be found in the various

nature-inspired algorithms and beneﬁt other methods.

The current work aims to provide some examples, dis-

cuss their beneﬁts, and pinpoint the promising path

ahead.

Furthermore, novel operators have been proposed

to enhance the algorithms’ performance. Our work

brieﬂy overviews such operators and discusses poten-

https://orcid.org/0000-0002-1319-513X

https://orcid.org/0000-0002-4372-2105

tial future directions.

Motivated by the recent works pinpointing the

positive effect of improved operators and integrated

mechanisms to nature-inspired approaches (NIAs),

this position paper presents an initial step towards

putting more emphasis on the research direction about

nature-inspired mechanisms and operators in the EC

ﬁeld. Moreover, it concludes with a non-exhaustive

list of future directions that we believe align with the

topic’s agenda.

The following section provides background on the

heuristic nature of EC techniques. Section 3 lists re-

cent operators and discusses promising mechanisms

found in existing NIAs. Following the example of

(Campelo and Aranha, 2021), we avoid citing the

metaphor-based algorithms in which the mechanisms

were found. Section 4 discusses the opportunity to put

operators and mechanisms into a modular framework

context and assess and benchmark those operators and

mechanisms. Finally, in section 5, we mention some

potential directions in which research can focus.

2 BACKGROUND

The Merriam-Webster dictionary deﬁnes the word

“heuristic” as: “involving or serving as an aid to

learning, discovery, or problem-solving by experi-

mental and especially trial-and-error methods”, with

Tzanetos, A. and K˚udela, J.

Working on the Structural Components of Evolutionary Approaches.

DOI: 10.5220/0013083400003837

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 16th International Joint Conference on Computational Intelligence (IJCCI 2024), pages 375-382

ISBN: 978-989-758-721-4; ISSN: 2184-3236

375

its etymology being from the German “heuristisch”,

New Latin “heuristicus”, and Greek “heuriskein”

(εὑρίσκειν), meaning “to discover” (or “to happen

upon by chance”).

Many of the EC techniques were conceived by this

trial-and-error approach, with the useful mechanisms

and operators for their applicability “discovered by

chance”. For instance, the original description of Dif-

ferential Evolution (DE) (Storn and Price, 1997) is

given without any theoretical justiﬁcation and analy-

sis, treating it as a “pure heuristic”. Theoretical works

on the convergence properties of the different opera-

tors in DE, such as the crossover ones in (Zaharie,

2009), came well after it became widely used. Also,

the fact that DE has theoretically supported conver-

gence problems for certain multimodal functions (Hu

et al., 2016) does not bar it from being a successful

and widely used method.

One of the oldest and still widely used stochastic

heuristics is the Simulated Annealing (SA) algorithm

(Kirkpatrick et al., 1983). Interestingly, for SA, the

theoretically justiﬁed temperature control schemes

(Hajek, 1988) do not work well in practice (Kochen-

derfer and Wheeler, 2019), and other “heuristically

found” schemes are used instead.

In 1965, the Nelder-Mead (NM) simplex method,

one of the oldest deterministic optimization heuris-

tics, was introduced (Nelder and Mead, 1965). Al-

though the mechanisms of the NM method are not

very complex, it took more than 30 years from its in-

ception before the ﬁrst notable theoretical work about

its convergence properties was published (Lagarias

et al., 1998). In the paper, the authors prove that

the method converges for strictly convex functions

in 1D but not 2D (by counterexample). The paper

ends with the following statement: “Our general con-

clusion about the Nelder-Mead algorithm is that the

main mystery to be solved is not whether it ultimately

converges to a minimizer—for general (nonconvex)

functions, it does not—but rather why it tends to work

so well in practice by producing a rapid initial de-

crease in function values.” Further research led to

convergence proofs for 2D, but only for restricted

versions on strictly convex functions (Lagarias et al.,

2012), with the technique of the proof based on treat-

ing the method as a discrete dynamical system. And

new results (such as convergence proofs for dimen-

sions greater than 8) are expected to need techniques

that are not yet developed (Gal

antai, 2022).

What these results show is that, in many cases, the

theoretical justiﬁcations for EC methods (and heuris-

tics in general) might not lead to useful variants of

such methods (such as in the SA case) or may not be

derivable by currently available techniques (such as in

the NM case). It is not hard to imagine a simple mech-

anism, with inner workings akin to the 3n + 1 prob-

lem, that will elude theoretical analysis (Guy, 2004).

Nevertheless, there has been undeniable progress

in the theoretical works, mainly focusing on dis-

crete settings with “simpler” EC methods for which

tools such as drift analyses can be used (Doerr and

Neumann, 2021). For the continuous setting and

the “more involved” techniques, experimental meth-

ods for runtime analysis are available (Huang et al.,

2019).

3 NATURE-INSPIRED

MECHANISMS AND

OPERATORS

The difference between a mechanism and an operator

may not be obvious. Both terms appear in the litera-

ture, usually to describe algorithmic components.

A suitable deﬁnition for the word mechanism,

given by (Ross et al., 2022), states that it is “a process

or system that is used to produce a particular result”.

No standard deﬁnition exists for the word opera-

tor within the sciences concept. In mathematics, an

operator refers to a mapping or function that acts on

elements of a space to produce elements of another

space. In computer programming, operators are con-

structs deﬁned within programming languages that

behave like functions. A common ground in the above

deﬁnitions is the concept of a function. However,

we cannot claim that an operator is a function. The

Merriam-Webster dictionary deﬁnition seems more

suitable: “a single step performed by a computer in

the execution of a program”.

A more open-ended deﬁnition for Evolutionary

Operators is “a total parameter-alteration operation

on the parameterization of generalized coordinates of

a system along its dynamic path” given by (

Oz, 2005),

where the theoretical aspects of variational and ex-

tremum principle derived from various sciences are

studied.

To distinguish the two concepts within the EC

ﬁeld, we can say that a mechanism is a process ap-

plied to the whole population of candidate solutions.

In contrast, an operator is a single-step operation ap-

plied to some or selected candidate solutions.

3.1 Traditional Operators

The original idea of operators comes from the evo-

lutionary operations included in the Darwinian-like

evolutionary process in the ﬁrst evolutionary ap-

ECTA 2024 - 16th International Conference on Evolutionary Computation Theory and Applications

376

proaches (De Jong, 2012). These operations corre-

spond to (a) asexual reproduction, i.e., the mutation

operator, (b) sexual reproduction, i.e., the crossover

operator, and (c) natural selection, i.e., the selection

operator.

The mutation and crossover operators, also called

reproductive operators, create a mix of local and

global search. The selection operator aims to balance

exploration and exploitation effectively.

The above evolutionary operators are very simple

operations. Indeed, they involve combining elements

of more than one parent solution, altering some of

the current solution’s elements, and selecting which

candidate solutions will be passed to the next genera-

tion. The rationale behind these operators is to tackle

pseudo-Boolean optimization problems:

f : {0,1}

→ R (1)

which consisted of d binary decision variables. The

binary value solution space makes the above evolu-

tionary operators proper for searching different com-

binations of a given solution.

3.2 Recently Presented Operators

Several researchers have developed operators that

overcome the limitations of the original ones. Such

limitations are infeasible solutions created by the

reproduction operators, low-quality solutions trans-

ferred to the new population due to a poor selection

process, and premature convergence due to low diver-

sity in the population. Below, we present an example

for each evolutionary operator, i.e., crossover, muta-

tion, selection, and one example of a population man-

agement operator.

(Sharma et al., 2021) introduced the idea of en-

sembled crossover for evolutionary algorithms, con-

sidering that different crossovers are suitable for dif-

ferent optimization problems. As a result, the authors

mentioned that the ensembled crossover is more ro-

bust on various optimization problems with different

characteristics such as variable dependency or multi-

modality. The difference from the original crossover

operator is that the crossover probability is drawn

from various distributions, e.g., uniform, epsilon, ex-

ponential, etc. Each distribution has the same prob-

ability of being selected at the beginning. The algo-

rithm updates the probabilities based on the propor-

tion of survivors to the created offspring members.

The Neighbor-Hop mutation is a mutation oper-

ator where a gene is replaced randomly by one of

its neighbor nodes in a graph (Chawla and Cheney,

2023). The authors applied their Neighbor-Hop mu-

tation-based GA to the Inﬂuence Maximization Prob-

lem, i.e., ﬁnding the set of k most inﬂuential nodes in

a social network. The solution representation of the

GA for that problem is a sequence of k nodes from the

given graph. The introduced mutation operator is suit-

able for the application since it explores different seed

node permutations without causing any infeasible so-

lutions. That would not be the case if the problem was

the Travelling Salesman Problem. The Neighbor-Hop

mutation is an example of an operator introduced for

a speciﬁc problem type.

The ﬁtness-distance balance is a recent selection

operator introduced by (Kahraman et al., 2020) that

enables the proper determination of candidates with

the highest potential to improve the search process.

First, the distance between the candidate and the best

solution is calculated and stored in a distance vector.

Then, the distance vector and the ﬁtness vector are

normalized. The ﬁtness vector contains the ﬁtness

values of the candidate solutions in the same order

as the distance vector. The Fitness-Distance Balance

(FDB) score is calculated as:

FDB

= w · norm

+ (1 − w) · norm

(2)

where norm

is the normalized distance value of the

i-th candidate solution and norm

is the correspond-

ing candidate solution’s normalized ﬁtness value. The

weight coefﬁcient w ∈ (0,1) determines the impact of

ﬁtness and distance values.

An alternative way to calculate the FDB score is:

FDB

= norm

· norm

(3)

Another category of operators consists of the ones

considering population diversity. They monitor the

population diversity and perform changes, e.g., in the

algorithm’s selection operator (Strze

zek et al., 2015),

or in the population size.

(Morales-Castaneda et al., 2022) introduced a new

set of evolutionary operators that falls within the sec-

ond case. These operators permit the management

of the population size to avoid search stagnation and

allow more efﬁcient exploitation. To prevent search

stagnation, the Stagnation Correction Operator in-

troduces new candidate solutions using a dimension-

wise diversity measurement metric (Hussain et al.,

2019). To improve the exploitation efﬁciency, the

Exploitation Efﬁciency Operator compares the cur-

rent diversity with the maximum diversity previously

found, and based on a predeﬁned diversity percent-

age, the population is reduced. In their work, the au-

thors use 10% as the diversity percentage that indi-

cates the algorithm is entering its exploitation phase,

and they reduce the population by 1/5. For a diversity

percentage equal to 2%, indicating that the exploita-

tion phase is deep in progress, the population is more

signiﬁcantly reduced by 3/5.

Working on the Structural Components of Evolutionary Approaches

377

Diversity-based operators have shown promising

results (Cheng et al., 2021; Wang et al., 2023). Work

on such operators can be extended by considering

other diversity measures, such as the attraction basins-

based measure introduced by (Jerebic et al., 2021).

3.3 Promising Mechanisms

3.3.1 Cyclic Universe Theory

The cyclic universe theory (Steinhardt and Turok,

2002) inspired the Big Bang - Big Crunch (BB-BC)

algorithm. According to this theory, the universe un-

dergoes endless cycles of expansion and cooling, each

beginning with a “Big Bang” and ending in a “Big

Crunch”. The Big Bang phase is the expansion phase,

whereas, in the Big Crunch phase, the gravitational at-

traction of matter causes the universe to collapse back

in. The two phases described above comprise the BB-

BC algorithm.

During the Big Bang phase, the candidate solu-

tions are randomly placed in the solution space using

the following formula:

new

= x

× rand

(4)

where l

is the upper limit for the d-th dimension,

rand is a random number uniformly distributed and k

is the current iteration of the algorithm. This equation

considers the ”center of mass”

−→

= [x

,..., x

where ND is the number of the problem’s dimensions.

In the Big Crunch phase, the candidate solutions

converge to a single point, i.e., the center of mass,

calculated as:

∑

i=1

∑

i=1

(5)

where x

denotes the position of the i-th candidate so-

lution in the d-th dimension, f

denotes the value of

the i-th candidate solution in the ﬁtness function and

N is the population size.

The BB-BC algorithm iterates between these two

phases. The population of the previous generation is

used to calculate the center of mass using eq. 5 and

then, new candidate solutions are generated around

this center of mass using eq. 4.

This cyclic universe process is the equivalent of

killing the population in each generation and gener-

ating a new one. The advantage of this concept is

that the center of mass contains information from all

candidate solutions. In EC, and especially in evolu-

tionary algorithms, the new population is randomly

created. On the other hand, the continuous iteration

between ”killing the population” and ”creating a new

one” has the drawback of not letting any candidate

solutions evolve.

3.3.2 Mine Explosion Dynamics

The Mine Blast Algorithm (MBA) contains a mech-

anism inspired by the mine explosion dynamics.

Speciﬁcally, considering that

−→

X = {X

,..., X

}

represents the location of a mine and that N

shrap-

nel pieces are produced by the mine bomb explosion

causing another mine to explode at location X

e(n+1)

calculated as:

e(n+1)

= d

n+1

× cos θ (6)

where θ is the angle of the shrapnel pieces, which is

a constant value and is calculated using θ = 360/N

and d

n+1

is the distance of the thrown shrapnel pieces,

calculated as:

n+1

= d

· |randn|

(7)

where randn is a normally distributed random num-

ber, and n is a number deﬁned as n ∈ 1,2,...,N

The above formulation describes the algorithm’s

exploration phase. Additionally, another operator is

set for the algorithm’s exploitation phase. In that case,

the shrapnel’s position is calculated as:

n+1

= X

e(n+1)

+ exp(−

n+1

) · X

(8)

where d

n+1

and m

n+1

denote the distance and the di-

rection (slope) of the thrown shrapnel pieces in each

iteration, respectively. Also, X

e(n+1)

denotes the lo-

cation of exploding mine bomb collided by shrapnel,

given by:

e(n+1)

= d

· rand · cos θ (9)

where rand is a uniformly distributed random number

and θ is the angle of the shrapnel pieces which is a

constant value and is calculated using θ = 360/N

where N

denotes the number of shrapnel pieces.

The distance d

n+1

of the thrown shrapnel pieces is

calculated as:

n+1

− X

)

+ (F

n+1

− F

)

(10)

where F denotes the quality of each particle.

The direction m

n+1

of the thrown shrapnel pieces

is given by:

n+1

− F

n+1

− X

(11)

3.3.3 Negatively Charged Stepped Leader

The Lightning Search Algorithm (LSA)’s central con-

cept is inspired by the negatively charged stepped

leader moving from a cloud to the earth (Dul’zon

et al., 1999), i.e., the phenomenon of separations of

the luminous channel (i.e., projectile) that propagates

ECTA 2024 - 16th International Conference on Evolutionary Computation Theory and Applications

378

through ionized paths, creating this tree structure of

lightning.

Three projectile types are considered in LSA, i.e.,

transition, space, and lead. The transition projectiles

are used to create the ﬁrst-step leader population N,

the space projectiles are considered to reach the best

leader position, and the lead projectiles represent the

best position among the N step leaders.

Transition projectiles create a random population

of N ﬁrst-step leader uniformly distributed. They are

also used to create new projectiles when necessary.

The space projectile p

is calculated as:

i,new

= p

± exprand(µ

) (12)

where exprand(µ

) denotes an exponentially dis-

tributed random number. The operator ± in eq. 12

denotes that exprand(µ

) should be subtracted if p

negative, but it should be added if p

is positive. This

operation is used to avoid any change of direction in

the solution space since exprand(µ

) returns only pos-

itive values.

This step separates the projectile into stepped

leaders. If p

i,new

provides a good solution, the cor-

responding stepped leader will be further separated.

Otherwise, it will remain unchanged. If p

i,new

extends

all stepped leaders beyond the recent most extended

leader, it becomes the lead projectile.

Finally, the lead projectile p

is calculated as:

i,new

= p

± normrand(µ

,σ

) (13)

where normrand(µ

,σ

) denotes a normally dis-

tributed random number. This step is performed for

exploitation. As for the space projectile, if p

i,new

pro-

vides a better solution, it will be extended until no

better solution is found.

3.3.4 Spiral Dynamics

The Spiral Dynamic Algorithm (SDA) introduced a

concept inspired by spiral phenomena observed in na-

ture, such as galaxies, hurricanes, and tornadoes. The

concept is a spiral model that provides dynamic step

size for each candidate solution when searching the

solution space. The step size is larger at the begin-

ning to enable exploration and gets smaller during the

algorithm to focus on exploitation. The step size is

deﬁned based on a spiral radius r and the spiral rota-

tion angle θ, which are open parameters.

A similar concept was introduced in Hurricane-

based Optimization Algorithm (HOA) where solu-

tions are divided into j = d − 1 groups based on the

problem’s dimensions d. The candidate solution per-

forms a rotation in each dimension deﬁned by the

group k = i mod (d − 1) it belongs to. In this model,

more parameters are used but based on the same con-

cept, i.e., radial and angular coordinates.

The spiral movement concept also inspired the

Circular Water Wave (CWW) algorithm. The step

size is calculated using a simpler equation compared

to SDA and HOA. The spiral model used in this algo-

rithm considers a radius r

, a random value w that is

used as a coefﬁcient, and the wave number c

, where

1 ≤ j ≤ m, and m denotes the maximum number of

wave circles, i.e., iterations of the algorithm.

Even though different models are introduced in

the three algorithms mentioned above, the mechanism

is the same. That is, a radius and a rotation angle de-

ﬁne the step sizes, which are performed towards an

“eye”, i.e., a central point.

3.4 Discussion

As pointed out by (Tzanetos, 2023), only the cyclic

universe mechanism seems consistent with the phe-

nomenon inspired from. Also, the spiral dynamics

mechanism utilizes the mathematical background of

spiral dynamics. The rest of the mechanisms men-

tioned above are simpliﬁcations of a phenomenon.

Nevertheless, the mechanisms mentioned in the

current work can be useful components for modi-

ﬁed or improved versions of established approaches.

(Thymianis and Tzanetos, 2022) showed that the inte-

gration of the cyclic universe mechanism and the mine

explosion mechanism improve the exploration ability

of fast converging approaches, such as PSO.

We believe that a similar value can be found in

the rest of the above mechanisms. The Negatively

Charged Stepped Leader seems a promising explo-

ration strategy (Tzanetos, 2023), too. Moreover, it

could be combined with a population management

operator that eliminates non-promising solutions be-

fore further separation into stepped leaders occurs.

The spiral dynamics mechanism seems a promising

exploitation strategy, i.e., a local search component to

intensify the search around local optima.

Furthermore, other promising mechanisms can be

found in the literature. A crucial question is how we

can identify such mechanisms. This is not a trivial

task since using metaphor-based language does not

enable researchers to fully comprehend a method’s

mathematical background (Aranha et al., 2022).

While mechanisms constitute different stepwise

processes, most of the existing operators are vari-

ations of the evolutionary operators, i.e., crossover,

mutation, selection, or population management tech-

niques. Research on new operators is more estab-

lished than that on mechanisms. Apart from the nu-

merous papers found in the literature, relevant work-

Working on the Structural Components of Evolutionary Approaches

379

shops exist.

For example, dedicated workshops enable re-

searchers to investigate the selection aspect in EC.

The most recent such workshops are the Workshop on

Selection

and the Workshop on Search and Selection

in Continuous Domains

4 MODULAR FRAMEWORKS

Identifying the individual mechanisms and operators

of EC methods enables the creation and investigation

of modular frameworks, which facilitate the (either

manual or automatic) design of high-performance

implementations of EC methods (Camacho-Villal

et al., 2023). Among the ﬁrst modular frameworks

was ParadisEO (Cahon et al., 2004), which contains

four main modules/objects for the composition of EC

methods: estimation of distribution objects (for esti-

mation of distribution methods), evolving objects (for

population-based methods), moving objects (for local

search methods), and multiobjective evolving objects

(for multiobjective methods).

Recently, there has been an increased interest in

creating modular frameworks around established EC

methods, with a focus on the inclusion of the most

widely used/representative mechanisms and operators

for that method. The most notable ones are the modu-

lar frameworks for ACO (L

opez-Ib

nez et al., 2018),

PSO (Camacho-Villal

on et al., 2021), Covariance ma-

trix adaptation evolution strategy (CMAES) (de No-

bel et al., 2021), and DE (Vermetten et al., 2023).

There is a current debate about the different mer-

its of manual and automatic design of EC methods

using modular frameworks (Camacho-Villal

on et al.,

2023). The manual approaches rely heavily on an

“expert designer” who understands not only the in-

ner workings of the algorithms but also the problem

to which they are applied. On the other hand, the au-

tomatic design of EC methods usually utilizes con-

ﬁguration tools such as SMAC (Hutter et al., 2011)

or irace (L

opez-Ib

nez et al., 2016). However, these

tools still require some input from the user, such as

selecting a set of relevant operators and mechanisms.

For white-box problems, where the mathematical de-

scription of the problem to be solved is known, the

possibility of using a pre-processing tool that scans

the problem description and returns a reasonable set

of possible operators for the automatic selection tool

(hence requiring even less expertise from the user) is

https://www.yorku.ca/sychen/research/workshops/

CEC2021 Selection Workshop.html

https://www.yorku.ca/sychen/research/workshops/

CEC2024 Search and Selection Workshop.html

still a not very well explored area. Recent results of

using the various automatic conﬁguration tools in dis-

crete (Aziz-Alaoui et al., 2021; Ye et al., 2022) are

very promising.

Another relatively under-explored line of research

lies in assessing “usefulness” and benchmarking the

individual modules and their combinations. In (Niko-

likj et al., 2024), this assessment was performed with

the utilization of the functional ANOVA (f-ANOVA)

framework (Hutter et al., 2014). Although the exper-

iments were relatively large-scale in terms of com-

pared variants (324 CMAES and 576 DE variants),

they were only small-scale in terms of dimensions

(only dimensions 5 and 30 were investigated) and

computational budgets (100 ×ND - 1500 × ND func-

tion calls). Another approach utilizing the Search Tra-

jectory Networks, population diversity, and anytime

hypervolume values for the assessment of the impact

of the modules in the multiobjective setting was de-

scribed in (Lavinas et al., 2024). To assess budget-

dependent mechanisms/operators (such as linear pop-

ulation reduction schemes), the standard anytime per-

formance measures should be used cautiously (Tu

sar

et al., 2017).

5 CONCLUSIONS AND FUTURE

DIRECTIONS

This position paper presents an initial step towards

putting more emphasis on the research direction about

nature-inspired mechanisms and operators in the EC

ﬁeld. We believe this direction offers various oppor-

tunities, such as extending the automatic design and

conﬁguration frameworks by including proper mech-

anisms and operators, integrating existing operators

and mechanisms into established algorithms to ad-

dress their limitations, developing new proper oper-

ators, identifying other promising mechanisms, and

investigating performance measures to assess the ef-

fect of these algorithmic components.

Recent works pinpointed the positive effect of im-

proved operators and integrated mechanisms to NIAs.

Along those lines, we listed four recently developed

operators and four promising mechanisms found in

existing NIAs. We discussed the beneﬁts of those se-

lected operators and mechanisms. We also discussed

how these algorithmic components can be integrated

into modular frameworks and how they can be as-

sessed and benchmarked.

As mentioned above, we see this work as a starting

point in the research agenda on nature-inspired mech-

anisms and operators. Therefore, we list a few future

directions below that we believe align with the topic’s

ECTA 2024 - 16th International Conference on Evolutionary Computation Theory and Applications

380

agenda. We do not claim that these directions are ex-

haustive. We invite interested researchers to extend

this agenda.

Following the recent progress in the theoretical

background of evolutionary approaches, the mathe-

matical and theoretical analysis of mechanisms and

operators included in EC and SI algorithms could pro-

vide more insight into these algorithmic components

and their effects.

Identifying and implementing other mechanisms

being part of existing EC and SI algorithms will ex-

tend the options of algorithmic components. Iden-

tifying several mechanisms with various characteris-

tics enables selecting the most suitable to address an

algorithm’s known limitation. Also, EC researchers

could focus on developing improved operators that

overcome the defects of the existing ones.

Furthermore, a smooth integration between differ-

ent automatic operator selection tools with the exist-

ing modular frameworks could help identify the use-

fulness of both the individual mechanisms and opera-

tors and their interplay. The methodologies for prop-

erly assessing and benchmarking these components

are currently being developed and tested, leaving am-

ple room for extensions and improvements.

Last but not least, applying the modiﬁed algo-

rithms to real-world problems is equally important to

the theoretical work. After all, the ultimate goal of

developing an algorithm is to solve a problem. Thus,

investigating the modiﬁed algorithms’ performance

on real-world problems will reveal which components

may be more suitable for speciﬁc problem types.

ACKNOWLEDGEMENTS

The research work of J. K

udela was supported by a

grant (No. FSI-S-23-8394) from the IGA Brno Uni-

versity of Technology and by the project (no. 24-

12474S) funded by the Czech Science Foundation.

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