Hybrid Grey Wolf Optimizers with Probabilistic Spiral Updating for Global Optimization

The Grey Wolf Optimizer (GWO) is a widely used meta-heuristic optimization algorithm; however, its standard linear encircling mechanism often leads to premature convergence to local optima in complex search spaces, and the equal weighting of its top three leaders limits fine-tuned exploitation. To overcome these specific limitations, two hybrid variants of the Grey Wolf Optimization algorithm, named HGWO-S and HGWO-SW, are proposed. The HGWO-S variant probabilistically integrates a spiral position update mechanism based on the Whale Optimization Algorithm (WOA) during the exploitation phase, while the HGWO-SW variant extends HGWO-S by replacing the standard GWO equally weighted position averaging formulation with a coefficient-weighted position averaging formulation. The effectiveness of the proposed algorithms was evaluated using 23 classical benchmark functions, and the results were compared with several algorithms from the literature under standardized experimental conditions. Among the proposed variants, HGWO-SW exhibited competitive performance, demonstrating the best or equivalent average results in 14 of the 23 benchmark functions. Furthermore, both algorithms were successfully validated on two classical engineering design problems, while HGWO-SW was uniquely applied to a slotted rectangular microstrip antenna optimization, demonstrating robust performance across diverse practical design tasks. Consequently, the proposed HGWO-SW algorithm provides an effective approach for solving complex optimization problems.