Hierarchical multi step Gray Wolf optimization algorithm for energy systems optimization

Gray Wolf Optimization (GWO), inspired by the social hierarchy and cooperative hunting behavior of gray wolves, is a widely used metaheuristic algorithm for solving complex optimization problems in various domains, including engineering design, image processing, and machine learning. However, standard GWO can suffer from premature convergence and sensitivity to parameter settings. To address these limitations, this paper introduces the Hierarchical Multi-Step Gray Wolf Optimization (HMS-GWO) algorithm. HMS-GWO incorporates a novel hierarchical decision-making framework that more closely mimics the observed hierarchical behavior of wolf packs, enabling each wolf type (Alpha, Beta, Delta, and Omega) to execute a structured multi-step search process. This hierarchical approach enhances exploration and exploitation, improves solution diversity, and prevents stagnation. The performance of HMS-GWO is evaluated on a benchmark suite of 23 functions, showing a 99% accuracy, with a computational time of 3 s and a stability score of 0.9. Compared to other advanced optimization techniques such as standard GA, PSO, MMSCC-GWO, WCA, and CCS-GWO, HMS-GWO demonstrates significantly better performance, including faster convergence and improved solution accuracy. While standard GWO suffers from premature convergence, HMS-GWO mitigates this issue by employing a multi-step search process and better solution diversity. These results confirm that HMS-GWO outperforms other techniques in terms of both convergence speed and solution quality, making it a promising approach for solving complex optimization problems across various domains with enhanced robustness and efficiency.