ENSGA-II: Efficient non-dominated sorting genetic algorithm framework with finite-difference diversity for router placement optimization

This study proposes an efficient non-dominated sorting genetic algorithm II ( ENSGA-II ) for router placement optimization in industrial wireless mesh networks. Unlike conventional NSGA-II , which relies on a first-order crowding distance, ENSGA-II incorporates a finite-difference–based diversity measure to better reflect the geometric characteristics of the Pareto front. Evaluation using Hypervolume (HV), Inverted Generational Distance (IGD), and IGD + shows that ENSGA-II achieves more accurate and stable Pareto-front approximations than NSGA-II , SPEA2 , MOEA/D , and HHO .