MaNSGA-II: Many-Objective NSGA-II

The elitist non-dominated sorting genetic algorithm (NSGA-II), proposed first in 2000, has spurred ample interests in shaping the research and application of evolutionary multi-objective optimization (EMO) field. While NSGA-II was developed for solving two and three-objective problems, the idea for an adequate emphasis for non-dominated and diverse solutions was borrowed to develop evolutionary many-objective optimization (EMaO) algorithms, capable of handling more than three objectives. In this paper, we modify original NSGA-II's domination and diversity preservation operators to propose a many-objective version of NSGA-II using a cone-domination concept to eliminate dominance resistant solutions which cause hindrance of an evolving population to converge to the Pareto-optimal front and an efficient high-dimensional distance-based selection operator capable of emphasizing a well-spread high-dimensional solutions. We compare the proposed MaNSGA-II with frequently-used EMO and EMaO algorithms on artificial and real-world motivated problems. Remarkably, MaNSGA-II performs well on all problems. On real-world motivated problems, MaNSGA-II performs the best, thereby making MaNSGA-II a worthwhile EMaO algorithm to be considered further. The results of this and a few earlier preliminary studies are extremely encouraging and contrary to decades of general belief, show promise for non-decomposition-based and free-form evolutionary approaches for solving many-objective optimization problems. We hope that this extensive and conclusive study will spur a renewed interest on non-decomposition-based EMO approaches.