# Niching Global Optimisation: Systematic Literature Review
## 2 Niching Paradigms
### Parallel Niching Paradigms
#### 2.2.3 Restricted Tournament Selection (RTS)
\begin{table}
\begin{tabular}{c c c c c} \hline
**Authors** & **Year** & **Algorithm** & **Theoretical Ground** & **Type** \\ \hline
[142] & 2018 & KGSA & Niching GSA using k-means clustering for subpopulation formation and GSA for niche exploitation. & Clustering \\ \hline
[163] & 2018 & GATOR & Evolutionary niching in gator applies clustering-based niching techniques to predict molecular crystal structures, enhancing the discovery of diverse solutions. & Clustering \\ \hline
[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 \\ \hline
[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 \\ \hline
[12] & 2020 & EDHC-PSO & Euclidean IBest search, hierarchical clustering, and local PSO exploitation. & Clustering \\ \hline
[127] & 2020 & MMFOA & Forest optimisation adapted to multimodal optimisation using a basic sequential algorithmic scheme with a radius neighbourhood. & Clustering \\ \hline
[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 \\ \hline
[144] & 2021 & NCD-DE & Multi-population differential evolution with (sub)optimal niche centre formation using an internal genetic algorithm. & Clustering \\ \hline
[149] & 2022 & SOMDE-DS & Clustering-based differential evolution using self-organising maps and adaptive resource allocation. & Clustering \\ \hline
[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 \\ \hline
[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 \\ \hline
[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 \\ \hline \end{tabular}
\end{table} 
Table 6: _Cont._

#### 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:

\[ \begin{split}\underset{x}{\text{Min}}/\underset{x}{\text{Max}}& F(x)=(f_{1}(x),f_{2}(x),\dots f_{m}(x))\\ \text{s.t}& x=(x_{1},x_{2},\dots x_{D})\end{split}  \tag{8}\]

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:

\[\underset{x_{i}}{max}\ F_{1}=f(x_{i}) \tag{9}\]

\[\underset{x_{i}}{max}\ F_{2}=\sum_{i=1}^{j=N}\frac{1}{N}||x_{i}-x_{j}|| \tag{10}\]

Non-dominated sorting can be used to find the solution points \(x_{i}^{*}\) which are equally competing in terms of performance.