The RIME-Whale Algorithm: A Synergistic Hybrid for Effective Global Optimization Problems

Metaheuristic algorithms often struggle to balance global exploration and local exploitation, which can limit their performance on complex optimization problems. Existing algorithms such as the Whale Optimization Algorithm (WOA) may risk premature convergence, while the Rime Optimization Algorithm (RIME) might benefit from enhanced exploitation strategies. To address these limitations, this paper introduces RIME-Whale, a hybrid metaheuristic algorithm. RIME-Whale synergistically integrates RIME’s Soft-Rime exploration mechanism with WOA’s Bubble-Net exploitation capabilities. The transition between these phases is adaptively managed using a control parameter derived from WOA, aiming for a superior exploration–exploitation balance throughout the optimization process. The performance of RIME-Whale was rigorously evaluated against its parent algorithms (RIME, WOA) and other established metaheuristics (Bat Algorithm – BA, JAYA, Sine Cosine Algorithm – SCA) using 23 standard benchmarks encompassing unimodal, high-dimensional multimodal, and low-dimensional multimodal characteristics. Experimental results, based on average fitness and standard deviation across 30 independent runs, demonstrate RIME-Whale’s consistent superiority across most functions. It achieved significantly better solution accuracy and convergence reliability, particularly excelling in high-precision exploitation on simpler landscapes and robust exploration on complex, multimodal problems. Statistical validation using the Wilcoxon rank-sum and Friedman tests confirmed the significance of RIME-Whale’s performance advantage: it attained the best Friedman mean rank (1.435) with the null hypothesis of equal performance rejected at p=1.65×10-16. Furthermore, complexity analysis showed that these performance gains were achieved efficiently, without substantial computational overhead compared to WOA, BA, JAYA, and SCA, and with improved efficiency over RIME. In addition, the practical applicability of RIME-Whale was validated on a real-world software engineering task, the software module clustering (SMC) problem, where it attained the highest modularization quality on five of eleven benchmark software systems against state-of-the-art clustering methods. The findings highlight the effectiveness of the hybridization strategy, positioning RIME-Whale as a powerful and computationally efficient tool for tackling diverse global optimization challenges.