# Niching Global Optimisation: Systematic Literature Review
## 2 Niching Paradigms
### Parallel Niching Paradigms
#### 2.2.3 Restricted Tournament Selection (RTS)
```
1 Let \(X_{0}=[x^{l},x^{u}]\);
2 Set pop size N, max_iter \(K\), and \(k=0\);
3 Generate the initial population: \(x_{i}\in X_{0}\);
4 whileallagents notstalledanditer\(<K\)do
5 for\(i=1\):Ndo
6 Update search direction;
7 end for
8\(iter++\);
9
10 end for
11 Cluster agents using clustering analysis;
12 whileiter\(<K\)andall nicheheadsnotstalleddo
13 forevery nicheNchdo
14 Update local subpopulation search direction for intensification;
15 end for
16\(iter++\);
17
18 end for return niche heads;
```

**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. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Authors** & **Year** & **Algorithm** & **Theoretical Ground** & **Type** \\ \hline
[134] & 2022 & DOS & Direct search methods are used in niching strategies to locate multiple global optima without requiring niching parameters. & Speciation \\ \hline
[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 \\ \hline
[136] & 2023 & HA-NDE & History archive-assisted niching differential evolution uses variable neighbourhood search to improve exploration and maintain multiple optima. & Speciation \\ \hline
[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 \\ \hline
[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 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._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 (\(\approx\)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 IBest 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.