An Experimental Study of Strategies to Control Diversity in Grouping Mutation Operators: An Improvement to the Adaptive Mutation Operator for the GGA-CGT for the Bin Packing Problem

Grouping Genetic Algorithms (GGAs) are among the most outstanding methods for solving NP-hard combinatorial optimization problems by efficiently grouping sets of items. Their performance depends on problem-specific heuristics and a balance between exploration and exploitation. The mutation operator plays a crucial role in exploring new solutions, but improper mutation control can lead to premature convergence. This work introduces adaptive mutation strategies for the GGA-CGT applied to the One-Dimensional Bin Packing Problem (1D-BPP). These strategies control the level of change that will be introduced to each solution dynamically by using feedback on population diversity, enabling better exploration. The proposed approach resulted in a 4.08% increase in optimal solutions (2227 across all classes) and a severe reduction in the average of individuals with equal fitness (from over 50% to less than 1%), enhancing diversity and avoiding local optima. The adaptive strategies were particularly effective in problem instances with larger item weights, where improvements were the most significant. Furthermore, statistical analysis confirmed the adaptive mutation approach’s superior performance compared with the original one. These findings demonstrate the potential of adaptive mechanisms to improve genetic algorithms, offering a robust strategy for tackling complex optimization problems.