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.

The efficiency of photovoltaic (PV) systems significantly decreases under partial shading conditions (PSC), leading to challenges in accurately tracking the maximum power point (MPP). This paper presents an enhanced Artificial Neural Network (ANN) to improve the performance of MPP tracking (MPPT) in PV systems subject to PSC. The proposed algorithm is based on an advanced ANN model trained with widely known analytical and metaheuristic algorithms, providing higher accuracy and faster convergence than existing methods. Furthermore, the ANN model was developed and trained using an extensive dataset that includes diverse shading scenarios, irradiation levels, and temperature conditions, with metaheuristic algorithms playing a key role in enhancing its training process. The performance of the proposed system has been evaluated through extensive simulations and sensitivity analyses. The results demonstrate that the improved ANN-based MPPT algorithm consistently outperforms existing MPPT techniques, including the Perturb and Observe (P&O) and Grey Wolf Optimization (GWO), Harris Hawks Optimization (HHO), and Particle Swarm Optimization (PSO) methods. The proposed approach achieves higher efficiency, faster response times, and improved stability under dynamic shading conditions. Specifically, its superior efficiency reaches up to 99.98% under clear sky conditions (CSC) and up to 99.97% under PSC, as verified through extensive simulations using MPPT efficiency metrics. This advancement holds significant potential for optimizing the energy yield of PV systems, promoting more reliable and efficient renewable energy solutions, especially when operating in challenging environmental conditions.