Reinvestigation of evolutionary many-objective optimization: Focus on the Pareto knee front

Abstract Approximating the entire Pareto front (PF) in many-objective optimization is challenging but often unnecessary because a decision maker is usually only interested in a small portion of the PF. Assuming no preference, we argue that a more appropriate way to address many-objective optimization problems (MaOPs) is to find Pareto-optimal knee solutions—solutions where small improvements in one objective will lead to severe degradation in at least one other objective. Herein, we propose such a method, which uses a distance-based indicator to first identify knee points (knee-detection phase) and then uses a refined fitness assignment strategy to select solutions near the knee points (knee-selection phase). The proposed method is integrated into two traditional algorithms, resulting in k-NSGA-II and k-MOEA/D. We discuss the effects of the parameter that controls the width of the knee region(s) and then analyze the effects of different methods for identifying knee points in the knee-detection phase. Finally, we examine the performances of k-NSGA-II and k-MOEA/D on a set of knee benchmark problems. The experimental results show that k-NSGA-II is competitive on knee test problems with 2 and 4 objectives, while k-MOEA/D performs better than k-NSGA-II with 6 and 8 objectives.