Niching Global Optimisation: Systematic Literature Review

Abstract

Niching in global optimisation refers to a set of techniques designed to identify multiple optimal solutions within a nonlinear, multimodal landscape. These algorithms enhance the exploratory capabilities of conventional metaheuristics by maintaining diversity and supporting coexisting subpopulations across a search space, thereby allowing a more deterministic approach to the true global optimum. Niching algorithms can be categorised into three primary subfamilies: sequential or temporal niching, parallel or spatial niching, and hybrid models which integrate various niching subparadigms. This research paper aims to explore the effectiveness and limitations of different niching algorithms by providing a systematic literature review of the theoretical frameworks within these subfamilies. Eleven major niching native subparadigms have been identified: fitness sharing, crowding, clearing, speciation, restricted tournament selection, clustering, multiobjectivisation, embedded hybrid methods, ensemble hybrid methods, and other hybrid approaches. This study offers a detailed examination of each paradigm’s theoretical foundation, including template algorithmic layouts, and delineates the unique elements of each approach. Research contributions from the inception of niching to 2024 have been aggregated from the SCOPUS database and systematically classified. Data aggregation included journal articles, conference papers, review papers, and research reports published in English only following the PRISMA framework. Application papers with novel theoretical ideas were also taken into account. In all, 203 research works were retained under the inclusion and exclusion criteria. This study concludes with overarching high-level recommendations for future research in modern niching optimisation, emphasising the development of space and time-scalable methods to enhance the adaptability and efficiency of optimisation algorithms in diverse, increasingly multivariable multimodal problems.

1. Introduction

Niching optimisation is a set of optimisation schemes which aims to enhance general-purpose metaheuristics and help them identify multiple local optima simultaneously [1,2,3]. Niching was introduced to maintain diversity within metaheuristic algorithms, which are often unimodal and tend to converge to a single promising region. These algorithms can be broadly classified into three families: sequential or temporal niching, parallel or spatial niching, and hybrid niching methods. These algorithms have been used to boost the exploration capacity in major metaheuristics, from genetic algorithms [4], particle swarm optimisation [5], differential evolution [6], and ant colony optimisation [7] to more modern optimisation methods, such as the bat algorithm [8], chimp optimisation [9], whale optimisation [10], and harmony search optimisation [11].

Parallel niching methods divide the population into independent subpopulations, each searching for different solutions simultaneously [12]. Sequential niching methods identify multiple optimum points one at a time [4]. Hybrid niching methods combine more than one niching paradigm to locate multiple optima. Niching techniques can be considered near-deterministic stochastic optimisation methods which can efficiently approximate the performance of rigorous global optimisation methods, which often suffer from extremely slow convergence speeds and intractability in complex problems [13,14,15]. Our research survey identified 10–11 niching subparadigms, namely sequential niching [4], fitness sharing [16,17], crowding [18], restricted tournament selection, clearing [19], speciation [5,20], clustering [12], multiobjectivisation [21], embedded hybrid methods [22], ensemble hybrid methods [2], and other hybrids [23] which are discussed in this study, including major trends, challenges, and potential future research directions.

1.1. Research Questions

The central question from which this study is motivated was as follows: What are the leading theoretical paradigms in niching metaheuristics for continuous global optimisation, and what are the current limitations? This led to the following more elaborate questions:

• RQ1 What are the existing theoretical frameworks in continuous niching metaheuristics?
• RQ2 How do they differ in popularity and contributions?
• RQ3 What are the leading challenges in the domain?
• RQ4 What future research avenues should be considered?

1.2. Search Process

In this systematic review, the SCOPUS database was used to summarise the theoretical trends in niching metaheuristics from inception to the current date.

The following keywords were used in this study:

• ("parallel" AND "niching")
• ("sequential" AND "niching")
• ("niching" AND "global" AND "optimisation")
• ("niching" AND "metaheuristics")

1.3. Inclusion and Exclusion Criteria

All search searches spanned from database inception until 2024 and included journal articles, conference papers, review papers, and research reports published in English only and following the PRISMA framework (Figure 1) [24]. The search mainly focused on reporting current theoretical frameworks for niching global optimisation, including their limitations and potential future works. Application papers with novel theoretical ideas were also retained. Only niching methods relevant to continuous and multimodal optimisation were kept, thus excluding combinatorial and binary optimisation. Papers were excluded by title, abstract reading, full-text reading, and accessibility.

The organisation of this paper is as follows. Section 1 introduces the systematic literature review and presents the data collection methods following the PRISMA framework. Section 2 discusses each distinct niching paradigm from the conventional taxonomy, including a presentation of the current research works in each subfamily. Section 3 summarises the features of each niching paradigm, provides an overview of the current trends, and offers performance insights into the different subfamilies based on comprehensive computational experiments found in the literature. Section 4 highlights the top-level challenges in the niching methods, and Section 5 provides a conclusion to this study.

2. Niching Paradigms

Niching paradigms can be broadly classified into three major families: sequential niching or temporal niching, parallel niching or spatial niching, and hybrid methods. The following section discusses the theoretical frameworks in each paradigm and subfamily, which are summarised in Figure 2.

2.1. Sequential Niching Paradigms

Sequential niching (or temporal niching) essentially consists of restarting the search optimisation scheme while banishing access to previously discovered basins of convergence using a hypersphere of a fixed radius. This technique was proposed in [4] three decades ago. The objective function is modified by the inclusion of a derating function using a recursive formula:   

$$\prod _{n+1}\left(x\right)=\prod _n\left(x\right)G(x,s_n)$$

(1)

where ${\prod }_{n+1}\left(x\right)$ is the modified objective function to be used for searching the $n+1^{th}$ minimum, ${\prod }_n\left(x\right)$ is the objective function used to for searching for the $n^{th}$ minimum, $G(x,s_n)$ is the derating function, and $s_n$ is the $n^{th}$ found minimum. We also have

$$G(x,s_n)=\left\{\begin{array}{c}exp\left(logm{\displaystyle \frac{r-d(x,s_n)}{r}}\right)\mathrm{if}d(x,s_n)<r\hfill \\ 1\mathrm{otherwise}\hfill \end{array}\right.$$

(2)

where m is the derating value, r is the niche radius, and $d(x,s_n)$ the distance between the current point x and the previously found minimum $s_n$. The authors of [25] proposed computing this radius as follows:   

$$r={\displaystyle \frac{\sqrt{d}}{2\sqrt[d]{p}}}$$

(3)

where d is the dimension of the problem and p, is the number of optima the problem is expected to have. This formula is applied to a normalised problem landscape $x\in [-1,1]$. Similar derating functions have been proposed in the literature, aiming to modify search agents by modifying the objective functions [26]. Most of these techniques fight the risk of flattening the objective function of discovering multiple optima or the risk of creating new local optima around the transformed basin of convergence. Algorithm 1 provides a pseudo-code of the sequential niching paradigm.

Algorithm 1: Typical sequential niching framework.

Advances in Sequential Niching

Although more attention in the research field has been directed towards parallel niching, some research has been conducted in the sequential niching paradigm. The authors of [27] proposed an improvement to the sequential niching in [4] by introducing a stretching function which deforms the search space to discover only optima points equal to or larger than previously discovered optima. The technique was effective in multi-global optima, but the effect of stretching could lead to losing other optima, including global optima, and introducing false local optima. The authors of [1] proposed a radius-free adaptive technique to locate basins of convergence using the hill-valley concavity test [28]. This technique yielded superior results, finding all global optima in the benchmarking testfunctions. However, because the hill concavity test requires function evaluations, the technique is computationally expensive in application problems where a single function evaluation is resource-intensive, such as in optimal control [29]. The authors of [30,31] proposed a memetic sequential niching algorithm which uses gradient-based hill climbing local search for exploration, a Gaussian derating function with clearing, and a genetic algorithm. The basin of convergence was still dependent on a fixed radius.

Table 1. A collection of sequential niching algorithms.

Authors	Year	Algorithm	Theoretical Ground	Type
[4]	1993	SN-GA	Multi-restart genetic algorithms with derating function.	Sequential
[27]	2001	SN-PSO	Landscape transformation via stretching to discover larger optima than previous ones.	Sequential
[1]	2006	SN-PSO	Radius-free sequential niching using hill concavity repulsion test.	Sequential
[30,31]	2008	SNMA	Sequential niching memetic algorithm combining genetic algorithms and local search for continuous multimodal function optimisation. It uses a Gaussian derating function and clearing to occupy different niches in the function to be optimised.	Sequential

gives an aggregation of the surveyed methods.

2.2. Parallel Niching Paradigms

Parallel niching (or spatial niching) essentially consists of searching for multiple optimum solutions simultaneously. In this approach, each search individual independently looks for a promising basin of convergence. Much attention has been given to parallel niching over sequential niching due to its ability to search for multiple optima at the same time. Several subparadigms exist in parallel niching: fitness sharing, crowding, clearing, speciation, restricted tournament selection, clustering, and multiobjectivisation.

2.2.1. Fitness Sharing

Fitness sharing is an approach which aims to penalise individuals in a crowd-populated region while rewarding individuals which are scattered in the search space in a bid to encourage search agents to discover new areas [32,33]. The original fitness function of each individual is thus penalised or modified based upon the density of its location region, forcing the particle to move away from the dense region and thus increasing exploration:

$$f_i^{\prime }={\displaystyle \frac{f_i}{m_i}}$$

(4)

where $m_i$ is the niche decimal count which measures the number of individuals with whom the fitness is shared such that

$$m_i=\sum _{j=i}^{N}sh\left(d_{ij}\right)$$

(5)

where N is the population size and $d_{ij}$ the distance between individuals i and j. The sharing function $sh(.)$ assigns a count $[0,1]$ based on the proximity of two agents:

$$sh\left(x\right)=\left\{\begin{array}{c}1-{\left({\displaystyle \frac{x}{\sigma }}\right)}^{\alpha },\mathrm{if}x<\sigma \hfill \\ 0,\mathrm{otherwise}\hfill \end{array}\right.$$

(6)

with a typical value of $\alpha =1$. Thus, the closer an agent is to another, the closer $sh(.)$ is to one, the larger $m_i$ is, and the greater the penalty $f_i^{\prime }$ for vacating the region from the least dominant to most dominant agent. Algorithm 2 provides a pseudo-code of the fitness-sharing paradigm.

Algorithm 2: Typical fitness sharing procedure.

Other more modern fitness-based niching methodologies [6,17] use a fitness-to-distance ratio ranking score which guides search agents in collaborating with their nearest fittest mates. In swarm intelligence, the fitness Euclidean distance estimator ranks neighbourhoods by computing a fitness distance to reward the closest and fittest neighbour around each search agent:

$$FE{R}_{(j,i)}=\alpha {\displaystyle \frac{f\left(\overrightarrow{p_j}\right)-f\left(\overrightarrow{p_i}\right)}{\left|\right|\overrightarrow{p_j}-\overrightarrow{p_i}\left|\right|}}$$

(7)

where $\alpha ={\displaystyle \frac{\left|\right|s\left|\right|}{f\left(\overrightarrow{p_g}\right)-f\left(\overrightarrow{p_w}\right)}}$, $\left|\right|s\left|\right|$, the estimated size of the search space is $\sqrt{{\sum }_{i=1}^D{(x_i^u-x_i^l)}^2}$, and $x^u$ and $x^l$ are the bounds of the search space. Using the fitness Euclidean distance score, search particles are directed to head towards the closest particle which is around the most promising basin in the local neighbourhood. Such an adaptation exists for evolutionary algorithms [6].

Table 2. Summary of niching algorithms: fitness sharing.

Authors	Year	Algorithm	Theoretical Ground	Type
[17]	2007	FER-PSO	Parameter free multi-peak particle swarm optimisation using the fitness-to-Euclidean ratio to identify local gBest	Fitness sharing
[16]	2011	NGA	Uses fitness sharing niching genetic algorithm to detect dominant resonant modes of rolling bearing faults, enhancing fault diagnosis by identifying multiple optimal solutions in vibration signals.	Fitness sharing
[34]	2012	MF-PSO	Memetic fitness-to-Euclidean distance particle swarm optimisation employs fitness sharing and Euclidean distance measures to maintain diverse particle swarms, enhancing multimodal optimisation by preventing premature convergence and facilitating the discovery of multiple global and local optima.	Fitness sharing
[11]	2012	NC-HS	Niching harmony search method employs fitness sharing and deterministic crowding to locate multiple optima, improving the original hs method’s capability in handling multimodal optimisation problems.	Fitness sharing
[6]	2014	FER-DE	Parameter free multi-peak differential evolution using the fitness-to-Euclidean ratio to select differential vectors.	Fitness sharing
[8]	2019	DNRBA	Extends the bat algorithm with a dynamic niche radius, adjusting the niche size based on the fitness landscape to prevent convergence on the same optima and maintain multiple peaks.	Fitness sharing
[35]	2019	SNRBF	Sharing niching technique trains RBF neural network to achieve global optimal nodes, combined with an improved NSGA-II using immune operators.	Fitness sharing
[36]	2019	N-PSO	Particle swarm optimisation for multimodal buckling maximisation in composite laminates, incorporating niching to maintain diversity and avoid premature convergence.	Fitness sharing
[37]	2020	FDLSEDE	Fitness- and distance-based local search with adaptive differential evolution employs fitness sharing and distance metrics to enhance local search and maintain multiple solutions in multimodal optimisation.	Fitness sharing
[9]	2022	NC-CHIMP	Robust niching in chimp optimisation algorithm identifies multiple peaks by penalising overcrowded areas and rewarding diverse solutions.	Fitness sharing
[38]	2022	NCO	Niching chimp optimisation algorithm incorporates constraint handling to optimise multiple objectives in engineering problems.	Fitness sharing
[39]	2023	EABC-DPS	Elitist artificial bee colony algorithm with dynamic population size adapts to the search environment, using fitness sharing to maintain diversity and find multiple optima.	Fitness sharing
[40]	2023	FMDE	Fitness-based niching division with adaptive mutation in differential evolution balances exploration and exploitation to prevent premature convergence and maintain diversity in global optimisation.	Fitness sharing

gives an exhaustive overview of the surveyed methods.

2.2.2. Crowding

While fitness sharing indirectly influences the formation of niches, crowding operates directly on the population by inserting new individuals which replace similar ones. The goal of crowding is to prevent overcrowded regions by discouraging dominance by a basin of convergence or chromosomal template. One state-of-the-art crowding approach is deterministic crowding (DC) [41], which restricts parent-offspring competition within local neighbourhoods to maintain local area exploitation over convergence to a dominant region. An offspring can replace a parent only when it is typically fitter and near the parent, thus encouraging local exploration and exploitation. The authors of [42] proposed a crowding technique which can be used as a parallel niching algorithm for multimodal genetic optimisation. The authors of [43] adapted crowding to differential evolution (CDE). The authors of [44] proposed a hybrid PSO with a recombination replacement crowding strategy (HN-PSO_P&A) which uses the local best PSO together with a crowding replacement strategy to encourage exploration of a search space towards searching for multiple peaks.

Table 3. Summary of niching algorithms: crowding.

Authors	Year	Algorithm	Theoretical Ground	Type
[18]	2003	DDC-GA	Improved crowding genetic algorithm using an additional dispersion feature to encourage dispersion of search agents and discovery of newer optima.	Crowding
[43]	2004	CDE	Crowding adapted to differential evolutio.n	Crowding
[45]	2008	GPCGA	Genetic algorithms incorporate crowding to replace individuals with similar ones, maintaining diversity by preventing premature convergence.	Crowding
[46]	2010	DMC-CROWDING	Distance measure comparison to improve crowding examines the performance of Mahalanobis and Euclidean distances in crowding techniques, finding that the Mahalanobis distance enhances the identification of multiple global optima.	Crowding
[47]	2012	AIWC	Artificial weed colonies use neighbourhood crowding schemes to maintain diversity in multimodal optimisation.	Crowding
[47]	2012	AWC-NC	Artificial weed colonies with a neighbourhood crowding scheme use crowding mechanisms to maintain diversity and prevent premature convergence in multimodal optimisation.	Crowding
[11]	2012	N-HS	Niching harmony search method integrates deterministic crowding with harmony search to maintain diversity and locate multiple optima in multimodal optimisation problems.	Crowding
[48]	2013	AMC	Adaptive mutation in crowding niching incorporates crowding mechanisms with adaptive mutation to balance exploration and exploitation, improving hierarchical multi-label gene function prediction by maintaining population diversity and enhancing convergence rates.	Crowding
[49]	2013	SNBDE	Spatially neighbors best search differential evolution uses crowding techniques to restrict competition among neighbouring solutions, maintaining multiple optima and enhancing global search capabilities by balancing exploration and exploitation.	Crowding
[48]	2013	AMC	Adaptive mutation in crowding niching incorporates crowding mechanisms with adaptive mutation to balance exploration and exploitation, improving hierarchical multi-label gene function prediction by maintaining population diversity and enhancing convergence rates.	Crowding
[49]	2013	SNBDE	Spatially neighbors best search differential evolution uses crowding techniques to restrict competition among neighbouring solutions, maintaining multiple optima and enhancing global search capabilities by balancing exploration and exploitation.	Crowding
[50]	2018	PC	Probabilistic crowding maintains population diversity by replacing individuals based on probabilistic selection rather than deterministic replacement.	Crowding
[51]	2019	MCSA	Modified crow search algorithm uses niching techniques to enhance diversity and prevent premature convergence.	Crowding
[52]	2020	TG-CGM	Genetic algorithm of tournament crowding based on Gaussian mutation uses tournament selection and Gaussian mutation to maintain diversity and avoid premature convergence in multimodal optimisation.	Crowding
[53]	2021	NDE	Niching differential evolution incorporates niching methods into differential evolution to maintain population diversity and balance global and local searching.	Crowding
[54]	2021	ANR-FA	Adaptive niche radius fireworks algorithm dynamically adjusts niche radius to maintain multiple solutions and improve convergence in multimodal optimisation.	Crowding
[55]	2022	NPE-CHIMP	Niching penalised chimp optimisation algorithm combines niching techniques with penalised objective functions to maintain diversity and avoid premature convergence in solving complex environmental economic dispatch problems.	Crowding

gives an exhaustive overview of the surveyed methods. Algorithm 3 provides a pseudo-code of deterministic crowding, a template commonly used in the crowding niching paradigm.

Algorithm 3: Deterministic crowding.

2.2.3. Restricted Tournament Selection (RTS)

Restricted tournament selection [56] is a niching paradigm initially developed for evolutionary algorithms. In RTS, a candidate parent is selected randomly from the population, and the choice of the second mating parent is restricted to a smaller subset in the neighbourhood of the first selected parent. This process ensures that local diversity is preserved and that search agents explore their location region rather than converge to one major attractive basin. Algorithm 4 provides a pseudo-code of the restricted tournament selection niching paradigm.

Aside from the original publication and related works [56,57], our database has no records of RTS used as a single paradigm in metaheuristics, but there is a record of use in ensemble hybridisation [2], mentioned in Section 2.3.

Algorithm 4: Typical RTS procedure.

2.2.4. Clearing

Clearing [19] is a niching technique which inherently prevents overcrowded regions. It consists of removing from the population search individuals which are too similar to maintain diversity and the discovery of multiple promising solutions. Upon formation of a population, sorting based on the fitness value is performed to identify the most dominant individuals in the search space. A clearing radius $c_r$ is defined to penalise individuals near the dominant individuals, thus pulling them away from each dominant basin of convergence and ensuring that they explore other regions in the next generation. Algorithm 5 provides a pseudo-code of the clearing niching paradigm.

Algorithm 5: Typical clearing procedure.

The authors of [58] proposed a differential evolution algorithm with topological clearing which uses topological heuristics [59] to determine the dominant population agents and clearing to penalise vectors which are suboptimal. The authors of [60] proposed a differential evolution algorithm with self-adaptive parameter estimation which uses clearing for niche formation.

Table 4. Summary of niching algorithms: clearing.

Authors	Year	Algorithm	Theoretical Ground	Type
[61]	2010	CBC	Context-based clearing procedure within genetic algorithms uses heterogeneity in subpopulations to dynamically adjust clearing radius, enhancing efficiency in finding multiple optima.	Clearing
[62]	2013	DANADE	Dynamic archive niching differential evolution maintains multiple niches using an archive-based niching mechanism and differential evolution, enhancing the exploration and exploitation capabilities.	Clearing
[63]	2013	VMO-NC	Variable mesh optimisation with niche clearing strategy dynamically adjusts the search space and employs clearing techniques to maintain multiple solutions in multimodal optimisation.	Clearing
[60]	2014	(M)TLDE	Differential evolution with self-adaptive parameter with niching based on clearing.	Clearing
[64]	2017	CMA-ES	Covariance matrix self-adaptation evolution strategy with repelling subpopulations to maintain diversity and prevent premature convergence.	Clearing
[65]	2017	DT-CLEARING	Enhanced clearing-based niching method using Delaunay triangulation, which divides the search space into simplices to improve the identification and maintenance of multiple niches.	Clearing
[66]	2017	NGA	Niching genetic algorithm enhances SiC crystal growth by maintaining high population diversity and preventing premature convergence through the use of clearing procedures, ensuring effective exploration of the search space and addressing both single-objective and multi-objective optimisation problems.	Clearing

gives an exhaustive overview of the surveyed methods.

2.2.5. Speciation

Speciation is an approach of forming multiple subpopulations which coexist with minimal to no social interaction. This technique aims to separate the population into species or subpopulations based on similarity. It proceeds by identifying species seeds (typical dominant individuals) around which other nearest individuals orbit, thus forming niches. Algorithm 6 provides a pseudo-code of the speciation niching paradigm.

Algorithm 6: Typical speciation procedure.

The authors of [5] proposed NichePSO, one of the earliest speciation niching methods. Initially, all particles are independent following a cognitive search topology. When a particle’s cognitive experiences stall, it forms a niche and can absorb neighbouring particles around it using a statistically estimated adaptive radius. Each formed niche followed a variant of the gBest topology to exploit its region. Formed niches have the potential to merge by configuration and when merging criteria are met. The authors of [67] proposed a type of speciation-based dynamic niching PSO similar to NichePSO [5], where particles are identified as species leaders (i.e., self masters) if they have the highest fitness in their neighbourhoods, forming a local gBest topology with their subordinate particles. Any two close subswarms are merged, and independent particles navigate using a cognitive model. The authors of [20] proposed a speciation-based PSO algorithm (SPSO) which identifies at each iteration a radius-based local neighbourhood for each particle to form independent niches or species which only interact locally and adaptively converge into multi-swarms. Each species uses its local gBest as its social experience component. This technique adapts the original PSO algorithm [68] to multimodal optimisation. The authors of [69] proposed a co-evolutionary multi-agent system with sexual selection to create multiple species in an evolutionary algorithm. Two types of evolutionary agents coexist—males and females—and they can reproduce only if they are located around the same optima. The hill-valley function concavity test [28] is used to determine whether two individuals share the same peak or not. Intermediate mutation and recombination with self-adaption are used for each gender type, allowing them to explore the solution space. The authors of [70] proposed a speciation-based genetic algorithm (ASCGA) which forms an independent subpopulation based on a speciation criterion comprising three criteria: the fittest individual in the region, a threshold radius of belongingness, and a threshold of the lowest fitness value of entry. The authors of [71] proposed a type of speciation-based niche PSO (NSPSO) similar to NichePSO [5]. A number of elite particles m are identified at the beginning of the search and allocated with m/n support particles for exploitation. The remaining particles follow a cognitive model to explore the search space. Solutions for the niches which converge are stored, and the niches’ particles are reused to discover other niches or support elsewhere. The process is repeated after a given number of user-defined iterations.

The authors of [72] proposed a method with speciation-based differential (EPSDE) which uses a member m to form niches around the fittest individuals rather than a radius size, which is typical of speciation. The algorithm includes an additional arithmetic recombination crossover operator. The authors of [73] proposed a type of speciation-based PSO which selects elites (niche heads) by using fitness values, moves particles based on a close neighbour topology, and updates particles aside from elites using differential evolution. The authors of [74] proposed a double-layer speciation differential evolution (DLCSDE) which initially forms an independent subpopulation based on an elitist formation. The fittest species form a niche around themselves with the nearest M individuals and evolve as independent DEs. In the second layer, the niche heads form a novel subpopulation running on a global DE to attempt to find missing local optima.

Table 5. Summary of niching algorithms: speciation.

Authors	Year	Algorithm	Theoretical Ground	Type
[75]	1999	NGA	Applies niching genetic algorithm to identify and optimise multiple seismological event locations within a complex search space.	Speciation
[76]	1999	ES-EP	Niching in an ES/EP context applies speciation techniques within evolutionary strategies and evolutionary programming frameworks to enhance the exploration and maintenance of multiple solutions, improving performance in complex multimodal landscapes.	Speciation
[77]	2000	DNGA	Distributed niching genetic algorithm divides the population into subgroups to evolve independently on multiple processors, enhancing the search for multiple optima.	Speciation
[78]	2001	EGA/LS	Enhances genetic algorithm with environmental niches and local search, facilitating parallel evolution of subpopulations to optimise flexible ligand docking.	Speciation
[79]	2001	RC-GA	Real-coded genetic algorithm uses a niching penalty approach to optimise the kinematic design of a Stewart platform, improving accuracy and compactness for applications in large radio telescopes.	Speciation
[80]	2001	NGALS	New genetic algorithm based on niche technique and local search method integrates niching strategies with local search to maintain multiple solutions and improve convergence.	Speciation
[81]	2001	EPNTE	Evolutionary programming with niching technique enhances model parameter extraction by maintaining multiple solutions and improving convergence.	Speciation
[82]	2002	NGA-GEO	Genetic algorithm with niching based on geocentric orbits in 3D elliptic restricted three-body problem, applying genetic diversity to explore multiple solutions.	Speciation
[5]	2002	NICHEPSO	Cognitive model search, merging operators, and local PSO exploitation.	Speciation
[83]	2003	MR-NP	Mating restriction and niching pressure uses mating restrictions to maintain diversity and avoid premature convergence in agent-based evolutionary computation.	Speciation
[20]	2004	SPSO	Cyclic speciation using a radius-determined gBest neighbourhood.	Speciation
[84]	2005	SEDA	Utilises substructural niching within the estimation of distribution algorithms to maintain diversity by creating subpopulations based on structural similarities.	Speciation
[85]	2005	PBS	Utilises structure niching and directed optimisation within a population-based search to find global minima in Lennard–Jones cluster optimisation.	Speciation
[86]	2006	VB-PSO	Vector-based PSO adapts niching for dynamic environments, utilising previous results to track and optimise multiple optima after environmental changes.	Speciation
[69]	2006	COEMAS	Co-evolutionary species with proximity-dependent reproduction using hill-valley concavity test.	Speciation
[87]	2006	NGDA	Niching genetic algorithm uses multi-criteria mechatronic design quotient for evaluating design alternatives.	Speciation
[88]	2006	HMWPSO	Hammerstein and Wiener models are identified using a multimodal particle swarm optimiser, which employs niching strategies to maintain diverse particle positions and locate multiple optimal solutions.	Speciation
[67]	2008	DNPSO	Speciation-based PSO using seed selection by elitism within local neighbours, with merging operators of close subswarms.	Speciation
[31]	2008	RMS	Real-coded niching memetic algorithm improves multimodal function optimisation by combining genetic algorithms with local search strategies, enhancing both global exploration and local exploitation to maintain diverse solutions.	Speciation
[71]	2009	NSPSO	Speciation-based PSO similar to NichePSO [5], where m elite particles are selected as niche heads and allocated a number m/n of support particles for exploitation. The remaining particles exploit the search space using a cognitive model. Solutions for converged niches are stored, and substandard niches are reallocated.	Speciation
[89]	2009	APPSO	Agent-based parallel particle swarm optimisation accelerates optimisation by distributing and managing a particle swarm across interconnected computers, using strategic niching and load balancing to maintain diversity and improve performance in distributed environments.	Speciation
[90]	2010	LPSO	Local best particle swarm optimisation with various position update rules and niching techniques to enhance multimodal search capabilities, maintaining diverse solutions throughout the search process.	Speciation
[91]	2010	ANRC	Adaptive niche radii and shapes with CMA-ES adjust niche parameters dynamically during evolution, improving the algorithm’s ability to find and maintain multiple optima.	Speciation
[92]	2010	MSDE	Modified species-based differential evolution with self-adaptive radius adjusts the niching radius dynamically to maintain population diversity and improve optimisation performance.	Speciation
[93]	2011	NSF-LSO	Niching swarm filtering combined with local optimisation integrates niching PSO with local optimisation to track full-body motion in real time, maintaining multiple solutions and enhancing accuracy.	Speciation
[94]	2011	SCGA	Species conserving genetic algorithm maintains population diversity in multimodal optimisation by preserving species throughout the optimisation process, preventing premature convergence and enhancing solution quality.	Speciation
[95]	2011	ANDE	Adaptive niche differential evolution algorithm dynamically adjusts the niching radius based on the problem’s characteristics, maintaining population diversity and enhancing solution quality.	Speciation
[96]	2012	LIPS	Niching PSO using locally informed topology whereby particles are influenced by the gBest of their m nearest neighbours.	Speciation
[97]	2012	NGS-BG	Niching genetic scheme with bond graphs optimises topology and parameters of mechatronic systems, using niching to ensure diverse and optimal solutions.	Speciation
[98]	2012	GBSSEA	Gradient-based, spatially structured evolutionary algorithm employs local fitness landscapes to promote parapatric speciation and optimise multiple solutions concurrently.	Speciation
[99]	2012	SOG-PGA	Self-organised parallel genetic algorithm dynamically adjusts search parameters to maintain diversity and ensure convergence in multimodal optimisation problems.	Speciation
[100]	2012	R-PSO	Restarting particle swarm optimisation introduces periodic restarts to avoid premature convergence in deceptive problems.	Speciation
[101]	2012	PPSO	Peer-to-peer particle swarm optimiser distributes PSO across multiple nodes, incorporating strategic niching and fault tolerance to maintain population diversity and ensure robust optimisation in distributed environments.	Speciation
[102]	2012	NC-PSO	Niching-based evolutionary PSO combines niching strategies with evolutionary PSO to address numerical optimisation problems by maintaining diversity and preventing premature convergence.	Speciation
[103]	2012	NIDE-IN	Niching differential evolution with index-based neighbourhoods combines differential evolution with an index-based neighbourhood strategy to maintain diverse solutions and improve performance in multimodal optimisation.	Speciation
[104]	2013	NCPSO	Niching-based cooperative particle swarm optimisation enhances neural network learning by maintaining diverse particle positions, leveraging cooperative and competitive interactions among particles to prevent premature convergence and improve solution quality.	Speciation
[105]	2014	LIS-DE	Local information sharing differential evolution induces niching behaviour by sharing information locally among individuals to find multiple optima.	Speciation
[106]	2014	LCM-PGA	Local competition model in island model PGA uses local information to achieve global diversification, maintaining multiple optima by allocating subpopulations to distinct search areas.	Speciation
[107]	2014	TN-CMA	Topological niching covariance matrix adaptation employs topological niching techniques to maintain diversity in the population, enhancing convergence by adapting covariance matrices.	Speciation
[108]	2014	PMP-DE	Pseudo multi-population differential evolution simulates multiple populations within a single run to maintain diversity and improve convergence.	Speciation
[109]	2014	QIEA-LL	Quantum-inspired evolutionary algorithm with linkage learning integrates quantum computing principles with linkage learning to enhance performance in multimodal optimisation, maintaining diverse solutions and improving convergence through the use of quantum-inspired operators and adaptive linkage models.	Speciation
[110]	2014	NCGA	Niching cumulative genetic algorithm uses evaluated probability to maintain diverse solutions in multimodal optimisation, leveraging cumulative selection pressure and niching mechanisms.	Speciation
[72]	2015	EPSDE	Speciation-based differential evolution with m neighbourhood members and arithmetic recombination crossover.	Speciation
[111]	2015	FFA	Firefly algorithm uses attractiveness and distance-based movement to optimise electromagnetic device shapes, incorporating niching to find multiple optima.	Speciation
[112]	2015	NPSO	Niching particle swarm optimisation with real-time object detection based on niching techniques.	Speciation
[113]	2015	IDE-CTHV	Improved differential evolution algorithm combines chaotic theory and a novel hill-valley method to enhance performance in large-scale multimodal optimisation problems.	Speciation
[114]	2016	NCPSO	Combines particle swarm optimisation with chaotic mutation and niche strategies to enhance global search and local refinement in multimodal optimisation.	Speciation
[115]	2016	MEDA	Estimation of distribution algorithms incorporating niching to maintain population diversity and explore multiple peaks in the fitness landscape.	Speciation
[116]	2016	BSS-DNPSO	Blind source separation algorithm using dynamic niching particle swarm optimisation incorporates dynamic niching mechanisms within PSO to maintain multiple solutions, addressing multimodal optimisation by adaptively changing the niche radius.	Speciation
[117]	2017	INEA	Improved niching evolutionary algorithm integrates enhanced niching strategies to optimise the design of composite laminated tubes, maintaining multiple solutions and improving convergence.	Speciation
[118]	2017	ISM-FSSA	Improved search mechanisms for the fish school search algorithm enhance the algorithm’s ability to explore and exploit multimodal search spaces by incorporating adaptive strategies and dynamic niching methods, maintaining solution diversity and preventing premature convergence.	Speciation
[119]	2017	PUSHGA	Genetic algorithm with a push operator enhances performance by maintaining population diversity, where the push operator helps escape local optima and explores new regions of the search space.	Speciation
[120]	2018	BB-NDE	Bare-bones niching differential evolution adapts parameters dynamically to locate multiple optima in complex search landscapes.	Speciation
[121]	2018	IDOS	Identifying multiple optima in aerodynamic design spaces involves a niching method which maintains diverse populations and employs clustering techniques to locate multiple solutions, improving the robustness and effectiveness of aerodynamic design optimisation.	Speciation
[122]	2019	LBPADE	Speciation-based adaptive differential evolution using image analysis-inspired local binary pattern.	Speciation
[123]	2019	FWA-ES	Fireworks algorithm enhanced with a distance-based exclusive strategy to prevent overlap and maintain multiple optima during the search process.	Speciation
[124]	2019	NPSO-OTSU	Niching particle swarm optimisation combined with Otsu’s method for accurate image segmentation in somatic cell analysis of milk.	Speciation
[125]	2019	CMA-OL	Covariance matrix adaptation with opposition learning enhances multimodal optimisation by improving exploration and convergence through adaptive covariance updates and opposition-based sampling.	Speciation
[73]	2020	CNMM-PSO	Speciation-based PSO which preselects elite-based fitness values, navigates particles based on closest neighbourhood and updates non-elites using differential evolution.	Speciation
[126]	2020	WSA-NEP	Whale swarm algorithm with niche identification and escape mechanism prevents convergence to local optima by dynamically adjusting niche boundaries.	Speciation
[10]	2020	WOA-NS	Enhances whale optimisation algorithm with niching and local search techniques to identify multiple optima in complex search spaces.	Speciation
[127]	2020	MOFOA	Integrates forest optimisation algorithm with niching strategies to enhance exploration and avoid premature convergence in multimodal functions.	Speciation
[74]	2021	SDLCSDE	Double layer speciation DE which forms on a first layer of independent niches based on elite particles and m nearest neighbours followed by later formation of global subpopulation from niche heads to discover eventually missed optima.	Speciation
[128]	2021	NGWO	Grey wolf optimiser integrates niching mechanisms to enhance the exploration and exploitation balance, locating multiple optima in multimodal problems.	Speciation
[129]	2021	SGPSA	Simple gravitational particle swarm algorithm employs gravitational attraction within a particle swarm to maintain multiple solutions in multimodal optimisation.	Speciation
[130]	2021	AOBSO	Attention-oriented brainstorm optimisation integrates attention mechanisms with brainstorm optimisation and improve performance in multimodal optimisation, enhancing both local and global search capabilities and maintaining diverse solutions to avoid premature convergence.	Speciation
[131]	2021	AMP	Adaptive multilevel prediction method for dynamic multimodal optimisation integrates prediction strategies with adaptive niching techniques to handle dynamic changes in multimodal optimisation problems, maintaining diverse solutions and improving convergence speed.	Speciation
[54]	2021	ANRFWA	Adaptive niche radius fireworks algorithm introduces the concept of dominating space of local optima, dynamically adjusting the niche radius to maintain solution diversity and prevent premature convergence in multimodal optimisation problems.	Speciation
[132]	2022	CNEA	Compact niching evolutionary algorithm leverages niching strategies within a compact genetic algorithm framework to maintain multiple solutions and improve the accuracy of matching knowledge graphs.	Speciation
[133]	2022	PRS-MO	Partition-based random search method divides the search space into partitions and employs random search within partitions to maintain multiple solutions and enhance exploration.	Speciation
[134]	2022	DOS	Direct search methods are used in niching strategies to locate multiple global optima without requiring niching parameters.	Speciation
[135]	2022	C-PSO	Community-based differential evolution for multimodal optimisation problems uses network community detection to maintain population diversity and locate multiple optima effectively.	Speciation
[136]	2023	HA-NDE	History archive-assisted niching differential evolution uses variable neighbourhood search to improve exploration and maintain multiple optima.	Speciation
[137]	2023	H-HV	History information-based hill-valley technique uses historical data to guide the search process, maintaining multiple solutions and improving convergence in multimodal optimisation.	Speciation
[138]	2023	MCDE	Multi-niche cooperation differential evolution enhances DE by utilising multi-niche cooperation strategies to maintain population diversity and improve performance in multimodal optimisation.	Speciation

gives an exhaustive overview of the surveyed methods.

2.2.6. Clustering

Clustering-based parallel niching techniques generate multiple subpopulations by grouping which uses clustering analysis and distance features. Typically, clustering differs from speciation in that clustering chooses the centroid of every niche based on proximity, while speciation selects centroids using an elitist mechanism whereby the most prominent individuals form seeds around which other individuals orbit. Algorithm 7 provides a pseudo-code of the clustering niching paradigm.

Algorithm 7: Typical clustering-based niching.

It is worth noting that some clustering-based niching methods make use of a single clustering pass [12] while others use regular cyclic passes [139] from niche formation to solution fine-tuning. The authors of [140] proposed a niching genetic algorithm (DCBN-GA) which uses density-based clustering to form subpopulations which can locally interbreed. Density-based clustering was used due to its ability to form non-spherical clusters. The algorithm obtained a better average peak ratio than fitness sharing and crowding-based genetic algorithms (≈${10}^4$), but they converged after many generations. The authors of [141] proposed a niching particle swarm optimiser which creates niches using the density clustering algorithms, thus generating coexisting swarms. The authors of [139] proposed an improved k-means clustering-based PSO optimiser which uses the cognitive model during the search phase and makes use of k-means clustering rather than merging operators to form niches. This approach combats the risk that NichePSO runs in merging all niches into one niche as the search continues. The authors of [142] proposed a clustering-based gravitational search algorithm (KGSA) which uses k-means clustering to form niches within which each uses the gravitational search algorithm (GSA), a Newtonian physics-based new generation metaheuristic [143] utilised to conduct local searches for the local optimum in each niche.

The authors of [12] proposed a Euclidean hierarchical clustering multiswarm PSO which uses the Euclidean distance lBest topology to form independent niches followed by k-apriori free hierarchical clustering to estimate the number of niches. The authors of [144] proposed a niching centre-distinguishing differential evolution (NCD-DE) multi-population method which forms niches by formulating an optimisation problem that determines the optimal niche centres. This optimisation problem is solved by an internal genetic algorithm solver which runs at each iteration. The authors of [127] used forest optimisation (FO), a new generation metaheuristic inspired by the life cycle of trees in forests [145], and adapted the algorithm to multimodal optimisation using a basic clustering sequential algorithmic scheme (BSAS), forming FO subpopulations based on a predefined radius threshold.

The authors of [146] proposed a multiple peak detection approach which assigns adaptively the most promising neighbourhood to each search individual using reinforcement learning (i.e., Q-learning). Upon initialisation of the search individuals, the Q-learning algorithm assesses the best subpopulation group which improves the agent’s fitness. This subpopulation group will be used to dictate the search direction of the agent in the next iteration. The proposed strategy was applied to particle swarm optimisation and the sparrow search algorithm [147] and equilibrium optimiser [148]. The authors of [149] proposed a clustering-based differential evolution which uses self-organising maps [150] for niche formation and dynamic resource allocation techniques to enrich niches. The authors of [122] proposed an adaptive differential evolution speciation-based algorithm (LBPADE) which uses a local binary pattern, a technique for texture analysis in image processing for the formation of niches. The authors of [151] proposed a clustering-based differential evolution (OPPDE) which uses the OPTICS density-based clustering approach [152], a parameter-insensitive method for the formation of niches and stagnation investigation strategy for saving computational resources by halting the exploitation of niches already discovered (i.e., niches with simple peaks) and using an additional Gaussian distribution-based local search strategy to improve exploitation of niche solutions. The authors of [40] proposed a clustering-based differential evolution (CMDE) algorithm which uses k-means clustering with a decreasing number of clusters to favour exploration at the beginning of the search and exploitation towards the end. Also, an adaptation mutation strategy is proposed to promote exploration in low-potential niches and exploitation in high-potential niches.

Table 6. Summary of niching algorithms: clustering.

Authors	Year	Algorithm	Theoretical Ground	Type
[153]	2001	C-UEGO	Combines clustering with niching in a global optimiser to improve the reliability and performance of evolutionary algorithms.	Clustering
[154]	2003	CEPC	Combined evolutionary programming and cluster analysis algorithm integrates evolutionary programming with cluster analysis to maintain multiple solutions in global optimisation.	Clustering
[140]	2005	DCBN-GA	Multi-subpopulation genetic algorithm using density clustering.	Clustering
[141]	2006	MSDC-PSO	Multi-swarm PSO using density clustering for niche formation.	Clustering
[155]	2007	NBPSO	Clustering with a weighted sum validity function using a niching PSO algorithm, which integrates niching PSO with cluster validity functions to automatically determine the number of clusters and partition the data set.	Clustering
[139]	2008	KPSO	Cognitive model search, optimal k-means clustering, and local PSO exploration.	Clustering
[156]	2011	NCBPGL	Basin identification on fixed-property generated landscapes evaluates clustering methods like nearest-better clustering and detect-multimodal to manage multimodal optimisation landscapes.	Clustering
[157]	2013	VMOP	Variable mesh size optimisation dynamically adjusts the granularity of the search space to identify multiple optima, ensuring a balance between exploration and exploitation.	Clustering
[158]	2014	ASMPSO	Accurate sub-swarm particle swarm optimisation dynamically partitions the swarm into sub-swarms using fitness and distance criteria, enhancing exploration and exploitation in service composition.	Clustering
[107]	2014	TN-CMA	Topological niching uses covariance matrix adaptation to explore multimodal landscapes effectively.	Clustering
[107]	2014	TN-CMA	Topological niching uses covariance matrix adaptation to explore multimodal landscapes effectively.	Clustering
[159]	2015	CMB-EA	Clustering-based model-building evolutionary algorithm integrates clustering techniques with model building EA to maintain multiple solutions and improve convergence in optimisation problems with binary and real-valued variables.	Clustering
[160]	2017	CNMMA	Combines cooperative co-evolution and niching-based multi-modal optimisation with adaptive clustering to handle large-scale optimisation problems.	Clustering
[161,162]	2018	HILLVALLEA	Two-stage multi-population evolutionary algorithm using radius-free hill-valley clustering and exploitation via core search algorithms.	Clustering
[142]	2018	KGSA	Niching GSA using k-means clustering for subpopulation formation and GSA for niche exploitation.	Clustering
[163]	2018	GATOR	Evolutionary niching in gator applies clustering-based niching techniques to predict molecular crystal structures, enhancing the discovery of diverse solutions.	Clustering
[164]	2018	MEDA-CCS	Multimodal estimation of distribution algorithm based on cooperative clustering strategy combines clustering and estimation of distribution methods to maintain diversity and improve convergence, leveraging cooperative interactions between subpopulations to enhance performance in multimodal optimisation.	Clustering
[165]	2018	NGEP-CM	Niche gene expression programming based on a clustering model maintains solution diversity by clustering similar individuals and evolving subpopulations independently.	Clustering
[12]	2020	EDHC-PSO	Euclidean lBest search, hierarchical clustering, and local PSO exploitation.	Clustering
[127]	2020	MMFOA	Forest optimisation adapted to multimodal optimisation using a basic sequential algorithmic scheme with a radius neighbourhood.	Clustering
[166]	2020	EDDDE	Adaptive estimation distribution-distributed differential evolution for multimodal optimisation problems combines estimation of distribution algorithms with differential evolution, maintaining diverse subpopulations through adaptive strategies to enhance solution quality and convergence.	Clustering
[144]	2021	NCD-DE	Multi-population differential evolution with (sub)optimal niche centre formation using an internal genetic algorithm.	Clustering
[149]	2022	SOMDE-DS	Clustering-based differential evolution using self-organising maps and adaptive resource allocation.	Clustering
[167]	2022	K-MEANS PSO	Integration of k-means clustering with PSO for variable subset selection, enhancing exploration by grouping particles based on proximity.	Clustering
[40]	2023	CMDE	Clustering-based differential evolution using k-means clustering with a k value with a temporal decrease and adaptative mutation strategy which favours exploration at the beginning of the search and exploitation towards the end. The mutation strategy favours exploitation in high-potential niches and exploration in low-potential ones.	Clustering
[151]	2023	OPPDE	A resource aware density clustering-based differential evolution with detection of peak convergence and with a Gaussian distribution-based local exploitation.	Clustering
[168]	2023	NASRM	Adaptive space reconstruction method uses niching to partition the search space, allowing efficient exploration of multiple aerodynamic designs in airfoil optimisation.	Clustering
[169]	2023	MSTNDE	Minimum spanning tree niching-based differential evolution uses knowledge-driven updates to efficiently explore multimodal landscapes.	Clustering
[170]	2023	RDDE-IT	Reachability distance-based differential evolution with individual transfer employs RDP niching to divide the population, ISM strategy for mutation, and AIM strategy to manage trapped individuals.	Clustering
[146]	2024	RLNS-MMOP	Local neighbourhood formation using reinforcement learning (RL)-based clustering.	Clustering

gives an exhaustive overview of the surveyed methods.

2.2.7. Multiobjectivisation

Multiobjectivisation is the process of transforming the single-objective optimisation problem into a multi-objectivisation approach to accommodate concurrent searches. Typically, the multi-objective goal will consist of identifying fitter individuals in a population while maintaining sufficient diversity. A multi-objective optimisation problem is devised with conflicting single-objective problems:

$$\begin{array}{cc}\hfill \underset{x}{\mathrm{Min}/\mathrm{Max}}& F\left(x\right)=(f_1\left(x\right),f_2\left(x\right),\dots f_m\left(x\right))\hfill \\ \hfill \mathrm{s}.\mathrm{t} x& =(x_1,x_2,\dots x_D)\hfill \end{array}$$

(8)

An example of multiobjectivisation would be a bi-objective optimisation problem, such as that in [171], which aims to find search agents with the maximal fitness and which are furthest apart from other agents:

$$\begin{array}{c}\hfill \underset{x_i}{max}{F}_1=f\left(x_i\right)\end{array}$$

(9)

$$\begin{array}{c}\hfill \underset{x_i}{max}{F}_2=\sum _{i=1}^{j=N}{\displaystyle \frac{1}{N}}\left|\right|x_i-x_j\left|\right|\end{array}$$

(10)

Non-dominated sorting can be used to find the solution points $x_i^{*}$ which are equally competing in terms of performance. Using non-dominated sorting and hypervolume measure-based sorting, the authors of [171], using bi-objective differential evolution (MOBIDE), achieved improved peak detection ratios when testing against crowding DE, speciation DE, speciation DE, and FERPSO, with improved peak success rates.

Table 7. Summary of niching algorithms: multiobjectivisation (MO).

Authors	Year	Algorithm	Theoretical Ground	Type
[21]	2010	BOEA	Converts single-objective multimodal optimisation into bi-objective optimisation to identify all optimal solutions as part of a weak Pareto-optimal set.	MO
[171]	2012	MOBIDE	Bi-objective differential evolution using non-domination sorting and hypervolume sorting.	MO
[7]	2016	AMCA	Adaptive multimodal continuous ant colony optimisation enhances pheromone updating and selection strategies to locate multiple global optima efficiently.	MO
[172]	2018	TRIDE	Tri-objective differential evolution approach balances three objectives for effective multimodal optimisation. It leverages niching strategies to maintain diverse solutions across multiple peaks.	MO
[173]	2023	NMPSO	Integrates sensor ontologies with niching multi-objective particle swarm optimisation to enhance search efficiency and solution diversity in complex environments.	MO
[174]	2023	NSGA-III	Eliminates non-dominated sorting in NSGA-III, using penalty boundary intersection niching to emphasise the best non-dominated solutions, enhancing performance for many-objective problems.	MO

gives an exhaustive overview of the surveyed methods. Algorithm 8 provides a pseudo-code of the multiobjectivisation niching paradigm.

Algorithm 8: Typical multiobjectivisation procedure.

2.3. Hybrid Niching Paradigms

Sequential and parallel niching perceptively have two distinct niching paradigms. While sequential niching is temporal (niching in time), parallel niching is spatial (niching concurrently in the search space). Hybrid families can emerge from these niching techniques which utilise the strengths of both and diminish their weaknesses. We can distinguish three types of algorithms within the hybrid section: embedded methods, ensemble methods, and other hybrid methods. An embedded method is a hybrid method which combines two or more native niching paradigms or ad hoc niching approaches, typically in sequence one after another, to form a newer method which combines the strength of each approach. An ensemble method tends to concurrently use each native niching paradigm, often in competition or collaboration during the optimisation process, and other hybrid methods are any other novel niching method which is neither an embedded nor ensemble method.

Table 8. Taxonomy of Hybrid methods.

Category	Definition	Temporal or Spatial
Embedded	Combines two or more niching paradigms or ad hoc techniques in sequence to leverage different strengths.	Temporal (sequential switching)
Ensemble	Use multiple niching paradigms concurrently, allowing competition or collaboration.	Spatial (multiple paradigms runs in parallel in the same or different populations)
Other Hybrid	Combine or integrate elements of both parallel and sequential paradigms in a unique way.	Both temporal and spatial, depending on the strategy or dynamic switching between methods

highlights elements of difference between the three sub-families.

The authors of [175] proposed an embedded clustering-based differential evolution (CbDE-wCA) which incorporates crowding to encourage exploration of unexplored areas and clearing to eliminate redundant solutions. Fuzzy-c mea766512cvnzns was used for niche formation, and the algorithm was proposed for optimisation in a dynamic environment where the locations of peaks change over time. The authors of [176] adapted chaos optimisation to niching using a constrictable multi-search scopes paradigm, where chaos elements are allowed to navigate. This technique is integrated with crowding, which permits the insertion of coexisting and competing chaos elements, and clearing, which discards chaos elements which are approaching the same peak based on a clearing radius. The authors of [177,178,179] proposed an embedded semi-concurrent sequential niching algorithm which discovers multiple optima sequentially and exploits them concurrently using parallel computing, thus saving computation search time. The proposed algorithm is beneficial for efficient sequential niching in practical optimisation, but it is still faced with the limitation of efficient radius estimation. The authors of [138] proposed a clustering-based niching algorithm with efficient resource usage (MNC-EA). Initially, search individuals are clustered into subpopulations and exploited independently, whereby niches which represent the same modality have some search individuals reallocated elsewhere, and underpopulated niches are assisted with search agents from other niches to accelerate convergence. When all niches converge to their peaks, the parallel search algorithms are restarted. The proposed algorithm is oriented towards efficiently using resources to discover as many niches as possible. The restarting nature of these novel algorithms will qualify them as parallel and sequential niching paradigms.

The authors of [180] proposed an ensemble multi-strategy multimodal genetic algorithm which combines clearing, sharing, clustering, restricted tournament selection, and crowding to exploit the search space with a co-evolving subpopulation. Initially, from the main population, an equal number of search agents is allocated to each niching scheme. The niching scheme which obtains better performance is assigned more resources (i.e., search individuals), while substandard niching schemes are maintained with a sub-minimum progressively. The authors of [181] proposed an adaptive ensemble niching differential evolution which selects a different niching scheme at each generation based on a quality measure which assesses fitness improvement and diversity. Three niching algorithms were used—deterministic crowding [42] (DC), restricted tournament selection [56] (RTS), and clearing [182] (Clr)—along with the original differential evolution. Initially, all niching schemes are given a chance to run on the population and ranked based on fitness improvement and diversity. They are then selected probabilistically based on quality score to dictate searching in the four coexisting populations. The proposed ensemble method was, however, parameter-intensive, using several configuration parameters.

The authors of [22] proposed neighbourhood-based differential evolution (N.DE), which limits the mutation process of vectors within an m-member neighbourhood of similar vectors to form niches. This approach was combined with crowding, sharing, and speciation-based differential evolution. The authors of [183] proposed a multilevel sampling strategy-based memetic differential evolution (MMDE) algorithm which combines speciation and clustering by forming niches from elite individuals using clustering and restricting crossover for individuals with poor fitness at the beginning of the search, favouring exploration, with a growing probability for fitter individuals at the end of the search favouring exploitation. The authors of [184] proposed a clustering-based genetic algorithm which uses density-based clustering to form niches and dynamic sharing to modify the raw fitness of population individuals within each niche using the niche population count.

Table 9. Summary of niching algorithms: hybrid methods (embedded).

Authors	Year	Algorithm	Theoretical Ground	Type
[185]	1994	SSE	Stochastic schemata exploiter utilises schemata processing to exploit local search capabilities while maintaining global search through stochastic sampling.	Embedded
[186]	2008	IK-DCA	Immune quantum evolutionary algorithm based on chaotic searching technique integrates immune principles, quantum computing, and chaotic searching to enhance global optimisation by maintaining solution diversity and improving convergence.	Embedded
[187]	2009	MA-GAO	Memetic algorithm for optimising high-inclination multiple gravity-assisted orbits combines evolutionary strategies with local search heuristics to maintain multiple solutions.	Embedded
[188]	2010	UGOMAC	Unbiased geometry optimisation of morse atomic clusters combines geometry optimisation with unbiased search strategies to improve performance in multimodal optimisation.	Embedded
[22]	2012	N(.)DE	Differential evolution local mutation using m-neighbour vectors (i.e., crowding or sharing and speciation).	Embedded
[189]	2013	HN-CA	Hybrid niche cultural algorithm integrates cultural evolutionary processes with niching strategies, enhancing global optimisation by combining cultural knowledge sharing and individual learning to explore and exploit multiple optima simultaneously.	Embedded
[189]	2013	HN-CA	Hybrid niche cultural algorithm integrates cultural evolutionary processes with niching strategies, enhancing global optimisation by combining cultural knowledge sharing and individual learning to explore and exploit multiple optima simultaneously.	Embedded
[190]	2013	S-DPSO	Self-adaptive differential particle swarm using a ring topology integrates self-adaptation and differential evolution within a ring topology to enhance diversity and convergence.	Embedded
[191]	2013	SELFCCDE	Adaptive parameter differential evolution with radius-based speciation and crowding.	Embedded
[192]	2014	PNPCDE	Differential evolution with crowding and parent-centric neighbourhood speciation mutation operator.	Embedded
[175]	2014	CBDE-WCA	Differential evolution with niche formation using fuzzy c-means, exploration enhancement using crowding, and redundancy reduction via clearing.	Embedded
[193]	2015	VMO-NICHING	Variable mesh optimisation framework uses a generic niching strategy to dynamically adjust the search space, maintaining multiple solutions and improving convergence in multimodal optimisation.	Embedded
[194]	2015	MS-GA	Multi-strategy genetic algorithm incorporates multiple niching strategies, such as crowding, fitness sharing, and speciation, to maintain diversity and enhance performance in multimodal optimisation, balancing exploration and exploitation to effectively address complex optimisation problems.	Embedded
[176]	2018	NCOA	Niching chaos optimisation using constrictable multi-search scopes with crowding and clearing.	Embedded
[195]	2019	CDE	Constrained niching using differential evolution maintains multiple feasible solutions in constrained optimisation problems by combining niching strategies with constraint-handling techniques.	Embedded
[196]	2019	MAMES	Matrix adaptation evolution strategy with multi-objective optimisation incorporates matrix adaptation and multi-objective optimisation to maintain diversity and enhance convergence in multimodal optimisation.	Embedded
[183]	2019	MMDE	Speciation- and clustering-based differential evolution, which form niches around elite individuals and favour crossover for less-fit individuals at the beginning of the search and selecting fitter individuals at the end of the search.	Embedded
[197]	2021	TO-PSM	Tornado optimisation with pattern search method integrates global and local search strategies, using pattern search to refine solutions and enhance convergence, effectively addressing multimodal optimisation challenges by maintaining solution diversity and avoiding local optima.	Embedded
[198]	2021	NCE-MSO	Niching cross-entropy method integrates niching strategies with the cross-entropy method to maintain solution diversity, improving the optimisation of multimodal satellite layout designs by preserving multiple solutions.	Embedded
[199]	2021	MA-MO	Memetic animal migration optimiser combines animal migration optimisation with memetic strategies, enhancing multimodal optimisation by leveraging local search heuristics to maintain multiple optima.	Embedded
[197]	2021	TO-PSM	Tornado optimisation with pattern search method integrates global and local search strategies, using pattern search to refine solutions and enhance convergence, effectively addressing multimodal optimisation challenges by maintaining solution diversity and avoiding local optima.	Embedded
[200]	2022	AMDEN	Adaptive memetic differential evolution incorporates multi-niche sampling and neighbourhood crossover strategies to balance exploration and exploitation in global optimisation.	Embedded
[199]	2022	MA-MO	Memetic animal migration optimiser combines animal migration optimisation with memetic strategies, enhancing multimodal optimisation by leveraging local search heuristics to maintain multiple optima.	Embedded
[201]	2022	CGS-DEA	Collaborative granular sieving algorithm uses a deterministic multi-evolutionary approach to maintain multiple solutions, enhancing the performance in multimodal optimisation problems.	Embedded
[202]	2022	ANCOA	Adaptive niching chaos optimisation algorithm integrates chaos theory with adaptive niching to improve the precision and robustness of mobile robot localisation in complex environments.	Embedded
[203]	2022	NC-LSGSA	Niching comprehensive learning gravitational search algorithm integrates comprehensive learning strategies with gravitational search to maintain diversity and avoid local optima in multimodal optimisation.	Embedded
[204]	2022	MSD	Study on six memetic strategies for multimodal optimisation by differential evolution evaluates different memetic strategies to maintain population diversity, combining differential evolution with various niching techniques to improve performance in multimodal optimisation problems.	Embedded
[177,178,179]	2022	SN-DE	Semi-concurrent multi-restart with simple derating function (i.e., sequential-parallel).	Embedded
[205]	2023	NE-PSO	Niching-enhanced particle swarm optimisation incorporates niching behaviour and covariance matrix adaptation to maintain diversity and improve convergence in multimodal optimisation.	Embedded
[206]	2023	OADE	Outlier-aware differential evolution integrates outlier detection with differential evolution to enhance performance in multimodal optimisation.	Embedded
[207]	2023	OBPC	Out-of-the-box parameter control for evolutionary and swarm-based algorithms uses distributed reinforcement learning to dynamically adjust parameters.	Embedded
[208]	2023	WC-GSA	Integrated heuristic optimiser combines water cycle algorithm with gravitational search algorithm, leveraging multi-objective optimisation techniques to enhance solution diversity and convergence.	Embedded
[209]	2023	PAENH	Promising area exploration based on hybrid niching employs several niching methods, including speciation, crowding, and clearing, to maintain population diversity and explore multiple areas in the search space.	Embedded
[138]	2023	MNC-NEA	Efficiency-oriented clustering-based collaborative niches with resource allocation and multiple restarts (i.e., parallel-sequential).	Embedded

,

Table 10. Summary of niching algorithms: hybrid methods (ensemble).

Authors	Year	Algorithm	Theoretical Ground	Type
[210]	2002	SMNE	Symbiotic memetic neuro-evolution integrates implicit fitness sharing and particle swarm optimisation to maintain genetic diversity and enhance local search in neuro-controller development for nonlinear processes.	Ensemble
[184]	2006	DBSCAN	GA with density-based clustering to form subpopulations and fitness sharing within niches.	Ensemble
[2]	2010	ENA	Competing clearing and restricted tournament selection with information interchange.	Ensemble
[211]	2014	APSAGA	Advanced particle swarm-assisted genetic algorithm integrates particle swarm optimisation and genetic algorithm to handle constraints and maintain diversity in solution populations.	Ensemble
[159]	2015	KB-DNCA	Knowledge-based differential covariance matrix adaptation cooperative algorithm combines knowledge-based heuristics with differential covariance matrix adaptation to maintain multiple solutions and improve convergence in optimisation problems with binary and real-valued variables.	Ensemble
[180]	2016	SELFMMOGA	Multistrategy and coevolutionary genetic algorithm using clearing, sharing, clustering, restricted tournament selection, and crowding with competitive resource allocation.	Ensemble
[212]	2021	ECDENM	Ensemble crowding differential evolution with neighbourhood mutation combines ensemble strategies with crowding mechanisms to maintain diversity and avoid premature convergence in multimodal optimisation.	Ensemble
[213]	2021	CEN-DE	Co-evolutionary niching differential evolution dynamically evolves niching methods and integrates them into DE to preserve population diversity and enhance global optimisation.	Ensemble
[214]	2022	DHN-DE	Dynamic hybrid niching differential evolution combines various niching strategies dynamically throughout the optimisation process to maintain diversity and convergence, effectively addressing multimodal optimisation by adapting to different search spaces.	Ensemble
[214]	2022	DHN-DE	Dynamically hybrid niching differential evolution combines various niching strategies dynamically throughout the optimisation process to maintain diversity and convergence, effectively addressing multimodal optimisation by adapting to different search spaces.	Ensemble
[181]	2022	ANSDE	Parallel population with adaptive probabilistic selection (DC, RTS, and CLR) of niching schemes using a fitness improvement and diversity quality measure.	Ensemble

and

Table 11. Summary of niching algorithms: other hybrid methods.

Authors	Year	Algorithm	Theoretical Ground	Type
[215]	2002	GGA	Gradient-guided niching enhances local search capabilities by guiding solutions towards gradient directions.	Hybrid
[216]	2008	PNIGA	Parallel genetic algorithm with niching technique enhances nuclear reactor core design optimisation by maintaining diversity and improving computational performance.	Hybrid
[217]	2014	VCGA	Variant-constrained genetic algorithm solves conditional nonlinear optimal perturbations using niching strategies to handle multiple constraints and maintain diversity.	Hybrid
[218]	2015	CDQ	Composite differential evolution uses queuing selection to maintain multiple solutions.	Hybrid
[23]	2019	QIGA	Quantum-inspired genetic algorithm integrates quantum computing principles with genetic algorithms for enhancing multimodal optimisation. It leverages quantum parallelism and superposition to explore multiple optima effectively.	Hybrid

give an exhaustive overview of the surveyed methods.

Table 12. Frequency count of contribution per niching paradigm.

Type	Frequency
Speciation	75
Embedded	34
Clustering	30
Crowding	17
Fitness sharing	13
Ensemble	11
Clearing	7
Multiobjectivisation	6
Hybrid	5
Sequential	4
RTS	1
Total	203

provides a summary count of theoretical framework contributions in each niching paradigm and

Table 13. Theoretical overview of niching paradigms.

Category	Niche Formation	Parameter	Representative Works
Sequential	Multiple restarts of unimodal metaheuristic searching scheme with region banning.	Niche radius or hill-valley concavity test	[1,179]
Speciation	Aggregation around domination particles using m-neighbourhood or distance measures.	Neighbourhood radius or m members	[5]
Crowding	Replacement of search individuals with similar ones to maintain local exploration. An offspring can replace a parent only when it is typically fitter and near the parent, thus maintaining diversity.	Parameterless (i.e., deterministic crowding)	[41]
Clustering	Niche formation by clustering analysis using nearness proximity estimation.	Based on k-cluster estimation methods	[10,139]
Clearing	Identify dominant search individuals and penalise all neighbouring individuals within a clearing radius to ensure they explore elsewhere.	Clearing radius and optional niche capacity (i.e., $n_c=1$)	[19]
Fitness Sharing	Downgrade fitness of overcrowded individuals or encourage attraction towards fitter, closer neighbourhoods.	Niche radius and scaling factor or parameterless dispersion-fitness ranking scores	[6,17]
Multiobjectivisation	Design a multi-objective cost function which rewards the fittest and most spread out search agents. Use solution quality ranking map to guide agents mutation and crossover or collaboration.	Parameterless	[171]
Embedded	Combines two or more niching paradigms or ad hoc techniques in sequence to leverage different strengths.	Inherited from underlying paradigms	[175]
Ensemble	Use multiple niching paradigms concurrently, allowing competition or collaboration.	Inherited from underlying paradigms	[180,181]
Other Hybrid	Combines or integrates elements of both parallel and sequential paradigms in a unique way.	Inherited from underlying paradigms	[23,218]

summarises their most essential components.

3. Features, Trends, and Performances in Niching Paradigms

Parallel niching algorithms have undoubtedly received the most attention in the literature (see Figure 3), with 73% of theoretical works discussing them. The benefit of parallel niching algorithms lies in their ability to locate multiple optima simultaneously, unlike their sequential counterpart. In this family of methods (see Figure 4), speciation (37.4%), followed by clustering (14.8%), received the most attention, followed by crowding (8.4%), fitness sharing (6.4%), clearing (3.4%) and multiobjectivisation (3%). Figure 5 shows that in recent years, speciation, embedded hybrid methods, and clustering-based niching methods have continued to receive the most attention in the research literature.

Sequential niching algorithms have received dramatically little interest in the literature, accounting for only 2% of theoretical research works. The major challenge of the technique lies in its slow detection of basins of convergence by committing all population agents to the discovery and exploitation of promising regions one at a time. A computationally efficient adaptive radius estimation remains a challenge in this family. The hill-valley concavity test has been a viable proposition to repel search agents when approaching a peak. However, the technique can be computationally intensive, especially for problem types with a high cost in function evaluations. Nevertheless, the technique still presents some good features. Unlike parallel niching, the sequential niching peak detection capacity is not limited by the population size. Because the algorithm restarts while banning previously discovered basins of convergence, it can indefinitely suggest new peaks over time. Moreover, sequential niching exhibits a good exploitation capacity, owing to its use of the full population size.

Hybrid niching algorithms have received substantial interest (24.9%) in the literature. These techniques generally combine the strengths of different parallel niching algorithms either used in sequence (embedded) or in competition (ensemble) dynamically. Embedded techniques have been the most commonly used subparadigm in the family (16.6%), followed by ensemble methods (5.4%) and other hybrid techniques. No mention of restricted tournament selection [56,180] as a standalone niching mechanism has been recorded in our database. In as much as most hybrid methods make use of parallel niching algorithms, these algorithms can still be considered parallel niching methods. Fewer techniques, such as those in [138,179], combine parallel niching subfamilies with sequential niching to benefit from its scalability.

In terms of niching paradigm performance, fewer studies in recent years, as per our survey, have compared niching paradigms across all major families. The authors of [219] compared eight niching algorithms from six representative niching paradigms: a clustering algorithm, deterministic and probabilistic crowding, restricted tournament selection, sharing, a speciation genetic algorithm, and two clearing methods on evolutionary algorithms. In all, the niching paradigms performed well in single-dimension problems with low numbers of peaks. As the number of peaks increased, fitness sharing, deterministic crowding, and restricted tournament selection maintained reliable peak detection performance at a dimensionality of 10 with a growing number of peaks (20, 30, 40, and 50). Original clearing, speciation, and clustering had fair peak detection accuracy with an increasing number of peaks. Above 10 dimensions, only the modified clearing strategy yielded stable performance but with a tremendous computational cost. In terms of computational cost, clustering exhibited the highest computational cost, while deterministic crowding exhibited the lowest computational cost. It is worth noting, however, that dimensional scalability was performed on a single scalable function type. The study was conducted on three function types only.

The author of [220], in his study on the scalability of niching paradigms, compared two representation speciation-based methods (NichePSO and adaptive NichePSO), four variant clustering-based evolutionary algorithms, and two simple multi-restart sequential methods in terms of peak detection count [221] on three test functions at dimension counts of 10 and 30. The clustering-based paradigm ranked first in peak detection counts in its PSO variant, followed by the sequential methods and then the speciation approaches. The authors of [222] comprehensively discussed performance measures in niching algorithms and conducted a computational experiment on multimodal test functions to assess the peak detection accuracy between five speciation-based niching techniques, a multiobjective optimisation evolutionary method, and one established fitness-to-Euclidean ratio niching technique [17]. The study concluded that there was no statistically significant difference in peak detection accuracy, which speaks to their exploitation abilities. The study was, however, conducted with most problems at a dimensionality of two. These studies explored niching paradigms which perform satisfactorily well in lower dimensional spaces, and their performance in higher dimensional spaces has yet to be put to the test conclusively. More rigorous investigation should be performed on the scalability of niching algorithms in terms of peak detection ratio, niche preservation, and computational cost and across various problem types.

4. Challenges and Future Research Directions

4.1. Towards Space-Scale Niching Methods: Performance in Large Dimensional Spaces and Growing Space Deformation

Comparative studies [12,219,222] suggest that in a lower dimensional space and with fewer peaks, all niching paradigms perform fairly satisfactorily. However, the actual enigma remains in their (stable) performance in higher dimensional spaces and with a growing increase in peaks. Niching algorithms should also be assessed by their scalability (the peak detection ratio, success rate, convergence speed, and computational cost) as the problem dimension and the number of peaks increase. The non-restart nature of parallel niching methods puts a theoretical upper bound on their capacity to obtain n number of optima, albeit with a fast peak detection rate [1]. The number of optima is not known a priori, and thus a parallel niching algorithm can only discover up to p peaks, with p being the population size. Multi-restart parallel niching algorithms should be encouraged, rendering the technique embedded and parallel-sequential [138]. In addition, niching algorithms should also be assessed with benchmarking functions of diverse shapes with scalable dimensions and numbers of peaks. Established niching algorithms such as NichePSO [5] have only been tested in lower dimensional spaces. The constraints mentioned here predict that their performance in higher dimensional spaces is not guaranteed [3].

4.2. Towards Time-Scalable Niching Methods: Rewarding an Increase in Computational Resources

One major challenge of unimodal classical metaheuristics such as particle swarm optimisation, genetic algorithm, differential evolution, and similar metaheuristics leading to niching is a drastic decline in diversity as the iteration search continues. Search agents, due to social interaction and inbreeding, become homogenous, abandoning exploration for constriction into one basin of convergence. In such a set-up, an increase in computation time does not scale with an increase in optimum solution generation. The authors of [220] suggested that global optimisation methods, and niching methods in particular, should scale with time. They should return more local optima the longer they run, thus rendering extensive computation resources and rewarding optimisation. Thus, time scalability should be considered a major criterion to assess modern optimisation methods (i.e., how well they scale in peak generation when more function evaluations are provided) [13]. The current study also encourages the design of parallelisable niching methods which can benefit from modern computing architectures.

4.3. Towards Efficient and Reliable Parameterless Niching Methods

Setting the niching radius is a common issue in a category of niching paradigms (i.e., sequential niching, fitness sharing, and clearing, a category of clustering and speciation methods). Implicit niching in multiobjectivisation, deterministic crowding, and FER methods circumvent this problem [3,6,17], but with no guarantee of preservation of peaks. Also, several algorithms have relied on the use of function-evaluation-based radius-free approaches, such as the hill-valley concavity test [28]. In as much as this eliminates the need for radius estimation, several passes of the hill-valley test are more computationally intensive, especially for practical optimisation, whereby function evaluations are costly [29]. Other leading attempts have been made to estimate a single uniform niching radius, to adopt a variable niching radius, or rather to estimate the niching radius implicitly with statistical measures [5]. Tracking landscape topology and derivative information can be considered in future studies [222].

4.4. Local Exploitation Capacity and Resource Management

The number of search individuals in niche subpopulations is also a concerning parameter, especially in the proper exploitation of promising basins of convergence. Exploitation quality has been identified as a potential issue in parallel niching algorithms [12,138,223]. Further investigation of efficient local exploitation should be considered. The authors of [224] proposed a local search strategy in particle swarm optimisation which generates n additional similar particles around the pBest, thus forming a new exploitation niche. The authors of [151] proposed a local exploitation technique based on a Gaussian distribution to refine niche solutions and proposed a detection strategy of niche completion to save computational resources. Such techniques can be further investigated.

5. Conclusions

The current study comprehensively reviewed the theoretical paradigms of niching in global optimisation using data sourced from the Scopus database. Among the three main families of niching methods, parallel niching has received the most attention (73%) followed by hybrid methods (25%), with the family of hybrid-embedded methods being the most dominant one (17%). Speciation- and clustering-based parallel niching methods have been the most prominent algorithms in recent publications although not necessarily the best-performing techniques overall. In contrast, sequential niching has generated rather little interest since its inception, comprising only 2% of theoretical research efforts. However, this study still argues that the sequential niching paradigm is highly relevant for scalability in modern optimisation. The main challenge in the current state of the art lies in advancing the reliable performance of niching techniques in higher-dimensional spaces and assessing their scalability for problems with much larger numbers of peaks. The limited capacity of parallel niching methods to handle large search spaces indicates a need for more parallel algorithms with multiple restarts (parallel-sequential) to improve scalability. The favourable usage of parallel computing architectures may be beneficial. The need for computationally efficient adaptive niching radius techniques remains relevant, and the rigorous assessment of all major niching methods on scalable benchmarking test sets with diverse problem types is a worthy pursuit.