Advancements in Multi-Objective Grey Wolf Optimization: Improvements and Applications With Angle Quantization

Abstract

Multi-objective Grey Wolf Optimizer (MOGWO) has emerged as a significant metaheuristic algorithm for solving complex optimization problems across various domains. Despite its effectiveness, MOGWO faces a critical limitation: lack of direction awareness in the search process, which negatively impacts the diversity and distribution of solutions along the Pareto front. This paper introduces Multi-Objective Grey Wolf Optimizer based on Angle Quantization and Crowding Distance (MOGWO-AQCD), a novel approach that addresses this limitation by integrating angle quantization for direction-aware search with crowding distance mechanisms for improved diversity preservation. Through comprehensive experimental evaluation on benchmark functions including Schaffer, Fonseca-Fleming, Kursawe, and the ZDT suite, we demonstrate that MOGWO-AQCD consistently outperforms the original MOGWO across all performance metrics, with statistically significant improvements in convergence, diversity, and hypervolume. Performance improvements are particularly pronounced for problems with challenging characteristics such as disconnected Pareto fronts (35.4% improvement in Generational Distance for ZDT3) and multiple local optima (37.8% improvement for ZDT4). Our systematic review of existing MOGWO variants reveals that while numerous modifications have been proposed, none explicitly addresses the direction awareness gap that our approach targets. This work provides both theoretical contributions through the novel integration of angle quantization with wolf hierarchy-based optimization and practical benefits through enhanced Pareto front approximations that can be applied across diverse fields including wireless communications, energy systems, and engineering design.