# Initialisation Approaches for Population-Based Metaheuristic Algorithms: A Comprehensive Review
## 3 Major Initialisation Methods
### Others  
Other approaches to improve the diversity, spread, and optimality of the initial population of metaheuristic algorithms exist in the literature. This category includes approaches that used mathematical and statistical functions to aid the initial population in an exhaustive search.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Reference** & **Year** & **Initialisation Scheme** & **Optimisation Problem** \\ \hline
[86] & 2017 & Ad hoc knowledge & Energy market \\  & & Participation portfolios \\ \hline
[88] & 2020 & Ad hoc knowledge & Morphing aircraft \\ \hline
[54] & 2019 & Metropolis–Hastings (MH) and function domain \\  & & contraction technique (FDCT) & Reservoir drainage plan optimisation problem \\ \hline
[91] & 2020 & Imaging the search space & Black box setting called COCO \\ \hline
[87] & 2020 & Ad hoc knowledge & Photovoltaic energy \\  & & systems under dynamic partial shading \\ \hline
[89] & 2020 & Ad hoc knowledge & Energy-based acoustic localization \\ \hline
[92] & 2020 & Ad hoc knowledge & Nonconvex economic dispatch problem \\ \hline
[90] & 2020 & Ad hoc knowledge & PV Systems \\ \hline \hline \end{tabular}
\end{table}
Table 6: Summary of methods based on ad hoc knowledge.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Reference** & **Year** & **Initialisation Scheme** & **Optimisation Problem** \\ \hline
[94] & 2017 & Lévy flight (LF) and greedy selection & Benchmark test function \\ \hline
[95] & 2012 & Chaotic Lévy Motion & Nonlinear dynamic biological systems \\ \hline
[96] & 2016 & Lévy Motion & Steel space frames \\ \hline
[97] & 2018 & Lévy Motion & Neural network training \\ \hline
[98] & 2020 & Lévy Motion & Benchmark \\ \hline
[99] & 2018 & Lévy Motion & Engineering design problems \\ \hline
[100] & 2019 & Lévy Motion & Data clustering problems \\ \hline
[101] & 2016 & Lévy Motion & Global optimization \\ \hline
[93] & 2013 & Lévy Motion & Benchmark test function \\ \hline \hline \end{tabular}
\end{table}
Table 7: Summary of levy flight methods.  
A nonlinear simplex method was used to initialise the swarms [102]. Their results showed that the particles gravitated better towards the excellent quality solutions. An approach where a particle is placed in the centre, and the rest of the particles are spread around it in the search space was considered by [103]. Their result is promising; however, it is not entirely without bias. The use of complex-valued encoding for metaheuristic optimization research is gaining attention from researchers. A comprehensive and extensive overview of this approach is presented in [104].  
The complex-valued encoding metaheuristic algorithms have been applied significantly in function optimization, engineering optimization design, and combinatorial optimization. The regular metaheuristic algorithms are based on continuous or discrete encoding. The advantage of the complex-valued encoding metaheuristic algorithm is that it expands the search region and efficiently avoids falling into the local minimum. Finally, eight metaheuristic algorithms were enhanced using the complex-valued encoding, and they were tested using 29 benchmark test functions and five engineering optimisation design problems. The superiority of complex-valued encoding was proved by analysing and comparing the results with statistical significance, and the complex-valued encoding metaheuristic algorithm returned the best performances. We present a summary of what authors have done in this category in Table 8.