An enhanced hybrid optimization model for renewable energy storage: Integrating GWO and WOA, with Lévy mechanisms

This study addresses renewable-energy storage scheduling—a high-dimensional, multimodal optimization task—by proposing an enhanced Grey Wolf–Whale Optimization Algorithm (EGW–WOA). The method fuses GWO’s hierarchical leadership with WOA’s spiral exploitation and augments them with Lévy flights and progress-triggered chaotic re-initialisation. Across 100 Monte-Carlo trials, EGW–WOAreduced 24 h operating cost to 2 . 94 × 1 0 5 ± 7 . 97 × 1 0 4 , improving over WOA by 16.62%, GA by 10.15%, FPA by 63.6%, and HS by 80.76%, with a 100% feasibility rate. It achieved the lowest dispersion (Std = 7 . 97 × 1 0 4 ; Max–Min spread = 3 . 82 × 1 0 5 ), shaved peak-demand charges by ≈ 9%, and limited depth-of-discharge swings to < 35 %, projecting a 12%–18% life extension. A 50-iteration run completed in 38.6 s on a 3.4 GHz CPU—over 20 × faster than a comparable MILP baseline—demonstrating suitability for near-real-time PV–wind microgrid control. Within the scope of Sustainable Computing: Informatics and Systems , this work delivers a reproducible, open-source optimization engine with non-parametric statistical validation and edge-suitable runtimes, linking algorithmic advances to system-level sustainability metrics (LCOS, demand charges). The results show how algorithm–system co-design can lower operating cost and risk while preserving battery health in cyber–physical energy systems. • The proposed Enhanced Grey Wolf–Whale Optimization Algorithm (EGW–WOA) achieved statistically significant improvements (Wilcoxon, Holm-adjusted p < 0 . 05 ) over HS, FPA, FSS, Mayfly, APO, WOA, TTA, HOA, PFA across 100 independent trials. • Against GA and CPSO , EGW–WOAdelivered lower mean cost but the differences were not statistically significant after Holm correction ( p Holm ≥ 0 . 05 ). • EGW–WOAprovided the lowest average operational cost and the tightest spread among the retained metaheuristics, confirming strong robustness for renewable-energy storage optimization. • A 100-trial benchmarking protocol and non-parametric statistics were employed to ensure reliable comparisons. • Future work will extend comparisons to additional constrained and emerging metaheuristics (e.g., CPSO variants, APO variants) under standardized multi-objective benchmarks.