Eliminating Non-dominated Sorting from NSGA-III

Balija Santoshkumar, Kalyanmoy Deb, Lei Chen

Abstract: The series of non-dominated sorting based genetic algorithms (NSGA-series) has clearly shown their niche in solving multi- and many-objective optimization problems since mid-nineties. Of them, NSGA-III was designed to solve problems having three or more objectives efficiently. It is well established that with an increase in number of objectives, an increasingly large proportion of a random population stays non-dominated, thereby making only a few population members to remain dominated. Thus, in many-objective optimization problems, the need for a non-dominated sorting (NDS) procedure is questionable, except in early generations. In support of this argument, it can also be noted that most other popular evolutionary multi- and many-objective optimization algorithms do not use the NDS procedure. In this paper, we investigate the effect of NDS procedure on the performance of NSGA-III. From simulation results on two to 10-objective problems, it is observed that an elimination of the NDS procedure from NSGA-III must accompany a penalty boundary intersection (PBI) type niching method to indirectly emphasize best non-dominated solutions. Elimination of the NDS procedure from NSGA-III will open up a number of avenues for NSGA-III to be modified for different scenarios, such as, for parallel implementations, surrogate-assisted applications, and others, more easily.