## 3 Methodology
Based on different configurations of problem dimensionality and population sizes, the FIPSaDE algorithm consistently has the highest frequency of having lowest average errors than FIPS, DE, SaDE and DE-PSO. The frequency analysis of \(h_{win}\) and the hypothesis test show that FIPSaDE performs better than its respective original versions in terms of the best and mean of \(f_{best}\) as the problems' dimensionality increases. Future research will investigate the strength of proposed algorithms with other benchmark test functions. Since the current FIPSaDE is only tested on one topology, that is, Four Clusters, the impact of the other four other FIPS topologies, namely, All, Ring, Pyramid, Square, should be investigated in the future for their effects on the hybrid's performances. Moreover, various performance metrics could be applied to strengthen the comparison among the algorithms. The study of the convergence profiles and coverage curve of the proposed algorithm as compared to other algorithms could also be investigated in the

\begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Function**} & \multicolumn{4}{c}{**3D25N**} & \multicolumn{4}{c}{**3D25N**} & \multicolumn{4}{c}{**3D25N**} \\ \cline{2-11}  & \multicolumn{2}{c}{**\(\epsilon\)-Value**} & \multicolumn{2}{c}{**\(p\)-Value**} & \multicolumn{2}{c}{**\(\epsilon\)-Value**} & \multicolumn{2}{c}{**\(p\)-Value**} & \multicolumn{2}{c}{**\(\epsilon\)-Value**} & \multicolumn{2}{c}{**\(p\)-Value**} \\ \cline{2-11}  & **FIPSaDE** & **FIPSaDE**



future. Furthermore, investigation should be conducted to broaden the comparison among the hybridization methods. Conceptualization, S.L.W., S.H.A. and T.F.N. ; Data curation, S.L.W., S.H.A., H.I. and P.R. ; Formal analysis, S.L.W., S.H.A. and P.R. ; Funding acquisition, T.F.N. ; Investigation, S.L.W. and S.H.A. ; Methodology, S.L.W., S.H.A., H.I. and T.F.N. ; Project administration, T.F.N. ; Resources, S.H.A., H.I. and P.R. ; Software, S.H.A., H.I. and P.R. ; Supervision, S.L.W., H.I. and T.F.N. ; Validation, S.L.W. and T.F.N. ; Visualization, S.L.W., S.H.A. and P.R. ; Writing--Original draft, S.L.W., S.H.A., H.I. and T.F.N. ; Writing--Review and editing, S.L.W., H.I. and T.F.N. All authors have read and agreed to the published version of the manuscript. This research was funded by the Ministry of Higher Education Malaysia under the Fundamental Research Grant Scheme (FRGS) with grant number FRGS/1/2022/ICT02/UPSI/02/1. Not applicable. The original contributions presented in the study are included in the article. Further inquires can be directed to the corresponding author. The authors declare no conflict of interest. The following abbreviations are used in this manuscript: \begin{tabular}{l l} ABC & Artificial bee colony \\ ACA & Ant colony algorithm \\ CGSS & Centre of Global Sustainability Studies \\ DE & Differential evolution \\ EC & Evolutionary computation \\ FIPS & Fully informed particle swarm \\ FIPSaDE & FIPS-SaDE \\ GUI & Graphical user interface \\ NP & nondeterministic polynomial \\ PSO & Particle swarm optimization \\ UPSI & Universiti Pendidikan Sultan Idris \\ USM & Universiti Sains Malaysia \\ SaDE & Self-adaptive differential evolution \\ \end{tabular} 

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