## 3 Proposed ATMALS-GSK Algorithm
### Atmals-Gsk
#### 3.2.6 Overall Operation of ATMALS-GSK
The Friedman test yields a \(p\)-value of \(4.11\times 10^{-10}\), indicating a significant difference in ATMALS-GSK performance compared to GSK and the components of the ATMALS-GSK algorithm. ## 5 Conclusions

This paper introduced ATMALS-GSK, an enhanced version of the GSK algorithm, empowering auto-tuning memory-based historical information and adaptive local search mechanisms. Unlike the original GSK algorithm, which relies on fixed control parameters and often struggles with premature convergence, the proposed ATMALS-GSK algorithm \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Methods** & & **R+** & **R\(-\)** & \(p\) **Value** & **+** & **=** & \(-\) & **Dec.** \\ \hline \multirow{8}{*}{ATMALS-GSK vs.} & GSK & 337 & 41 & 0.0003 & 22 & 2 & 5 & + \\ \cline{2-8}  & ATMALS-GSK-1 & 321 & 30 & 0.0002 & 22 & 3 & 4 & + \\ \cline{2-8}  & ATMALS-GSK-2 & 324 & 27 & 0.0002 & 24 & 3 & 2 & + \\ \cline{2-8}  & ATMALS-GSK-3 & 341 & 37 & 0.0003 & 23 & 2 & 4 & + \\ \cline{2-8}  & ATMALS-GSK-4 & 363 & 15 & 0.0000 & 24 & 2 & 3 & + \\ \cline{2-8}  & ATMALS-GSK-5 & 268 & 32 & 0.0007 & 19 & 5 & 5 & + \\ \hline \hline \end{tabular}
\end{table} 
Table 22: Wilcoxon signed-rank test of the ATMALS-GSK algorithm with the original GSK and five ATMALS-GSK versions over \(51\) runs for \(D=30\) on CEC 2017. Figure 15: Rank analysis of the ATMALS-GSK algorithm against original GSK and five ATMALS-GSK versions, based on the Friedman test. integrates memory-based auto-tuning and an adaptive local search strategy. The key advantage of the proposed ATMALS-GSK algorithm lies in the adaptive Gaussian-driven adjustment of its controllable parameters using a historical memory mechanism that tracks their effectiveness over time. A historical memory-powered RWS, informed by a weighted moving average, ensures that the algorithm dynamically prioritizes more successful configurations. Furthermore, the adaptive local search component focuses on fine-tuning senior solutions, enabling better exploration of the search space and avoiding getting stuck in local optima. Extensive experiments conducted on the CEC 2011 and CEC 2017 benchmark suites have demonstrated the superiority of the proposed ATMALS-GSK algorithm over the original GSK and its modified variants, as well as other recent metaheuristic algorithms. The Wilcoxon test results indicated that ATMALS-GSK surpasses the original GSK and its variants by obtaining success ratios of 75%, 74.1%, 78.4%, 66.4%, and 65.5% against GSK, AGSK, APGSK, FDBAGSK, and eGSK, respectively. Furthermore, ATMALS-GSK outperforms other metaheuristic algorithms--IADE, GJO-JOS, QSCSA, cSM, and FOWFO--achieving success ratios of 96.6%, 96.6%, 87.1%, 91.4%, and 54.3%, respectively, across all functions in overall dimensions. The Friedman test results also indicate that ATMALS-GSK ranks first across all dimensions in terms of average performance. The p-values from both tests confirm that these improvements are statistically significant. These results consistently showed improved robustness and higher solution quality across a variety of complex optimization problems. Despite these achievements, the proposed algorithm is not without limitations. The introduction of memory-based mechanisms and local search strategies inevitably adds computational overhead, which might become significant in high-dimensional or real-time applications. Additionally, while the Gaussian-based parameter tuning works well in the current setup, it might need recalibration or refinement for highly irregular or domain-specific fitness landscapes. Furthermore, the performance of ATMALS-GSK may vary based on the characteristics of the problem being solved, suggesting that further customization or hybridization with problem-specific heuristics might be beneficial. Therefore, there are several promising directions for future research. One main area involves exploring alternative memory management techniques, such as adaptive forgetting factors or reinforcement learning-inspired models, to further improve the parameter selection strategy.