# Niching Global Optimisation: Systematic Literature Review
## 2 Niching Paradigms
### Parallel Niching Paradigms
#### 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. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Authors** & **Year** & **Algorithm** & **Theoretical Ground** & **Type** \\ \hline \multirow{4}{*}{[48]} & \multirow{4}{*}{2013} & \multirow{4}{*}{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. & \multirow{4}{*}{Crowding} \\ \cline{1-1} \cline{5-5}  & & & 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. & \multirow{4}{*}{Crowding} \\ \cline{1-1} \cline{5-5}  & & & Probabilistic crowding maintains population diversity by replacing individuals based on probabilistic selection rather than deterministic replacement. & \multirow{4}{*}{Crowding} \\ \cline{1-1} \cline{5-5}  & & & Modified crowd search algorithm uses niching techniques to enhance diversity and prevent premature convergence. & \multirow{4}{*}{Crowding} \\ \cline{1-1} \cline{5-5}  & & & 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. & \multirow{4}{*}{Crowding} \\ \cline{1-1} \cline{5-5}  & & & Niche differential evolution incorporates niching methods into differential evolution to maintain population diversity and balance global and local searching. & \multirow{4}{*}{Crowding} \\ \cline{1-1} \cline{5-5}  & & & Adaptive niche radius fireworks algorithm dynamically adjusts niche radius to maintain multiple solutions and improve convergence in multimodal optimisation. & \multirow{4}{*}{Crowding} \\ \cline{1-1} \cline{5-5}  & & & Niche 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. & \multirow{4}{*}{Crowding} \\ \cline{1-1} \cline{5-5}  & & & & Niche 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. & \multirow{4}{*}{Crowding} \\ \cline{1-1} \cline{5-5}  & & & & \\ \cline{1-1} \cline{5-5}  & & & & \\ \cline{1-1} \cline{5-5}  & & & & \\ \end{tabular}
\end{table} 
Table 3: _Cont._```
1 Let \(X_{0}=[x^{t},x^{u}]\);
2 Set pop size N, max_iter \(K\) and \(k=0\);
3 Generate the initial population: \(x_{i}\in X_{0}\);
4 whileallagents not stalled and iter \(<K\)do
5 fori = 1:N\({}_{p}\)do
6 Select parent \(p_{1}\) randomly from \(X\);
7 Determine neighbourhood \(N(p_{1})\) to select parent \(p_{2}\);
8 Apply crossover and mutation on \(p_{1}\) and \(p_{2}\) to produce offspring \(o\);
9 perform ad hoc replacement;
10
11 end if
12 iter++;
13
14 end for return elite agents;
```

**Algorithm 4**Typical RTS procedure.