An adaptive Bi-population and harmonic distance of density differences for multi-objective evolutionary algorithm

In multi-objective optimization problems, maintaining the trade-off between convergence and diversity is regarded as a pivotal challenge in algorithm design. Because the inherent contradiction between the two often leads to degradation in algorithm performance. Therefore, an adaptive bi-population and harmonic distance of density differences for multi-objective evolutionary algorithm (ABP-HDD) is proposed. In ABP-HDD, an adaptive bi-population partitioning strategy based on hyper-dominance degree assessment is proposed. The population is adaptively divided into two interactive components: an elite-oriented subpopulation responsible for exploiting high-quality regions and ensuring convergence, and a potential-exploration subpopulation tasked with exploring sparse or undiscovered regions to maintain diversity. These two subpopulations dynamically share information during the evolutionary process, where individuals are continuously re-evaluated and reallocated based on their current hyper-dominance degree. This collaborative mechanism enhances the rationality of individual allocation and global exploration while preventing the population from prematurely converging to local optimal solution. Besides, a new environment selection strategy, which harmonic average distance of density differences (HDD) strategy, is proposed to prevent premature convergence in the potential-exploration subpopulation. The HDD strategy assesses population diversity by calculating density differences between individuals. It can effectively distinguish solutions from different distribution areas in high-dimensional space, thereby better balancing exploration and exploitation in environmental selection. Finally, the experimental results show that ABP-HDD can achieve better results on 48 test functions and has certain competitiveness.