An Improved Selection Operator for Multi-objective Optimization

Abstract

Non-dominated sorting genetic algorithm II (NSGA-II) obtains a great success for solving multi-objective optimization problems (MOPs). It uses a tournament selection operator (TSO) to select the suitable individuals for the next generation. However, TSO selects individuals based on the non-dominated rank and the crowding distance of each individual, which exhausts a lot of computational burden. In order to relieve the heavy computational burden, this paper proposes an improved selection operator (ISO) that is based on two selection schemes, i.e., a rank-based selection (S-Rank) and a random-based selection (S-Rand). S-Rank is a scheme that selects individuals based on its non-dominated ranks, in which if the individuals have the different non-dominated ranks, the individuals with lower (better) ranks will be selected for the next generation. On the contrary, if the individuals have the same rank, we first select an objective randomly from all objectives, and then select the individual with the better fitness on this objective to enter the next generation. This is the S-Rand scheme that can increase the diversity of individuals (solutions) due to the random selection of objective. The proposed ISO only calculates the crowding distance of the last (selected) rank individual, and avoids the calculation of the crowding distance of all individuals. The performance of ISO is tested on two different benchmark sets: the ZDT test set and the UF test set. Experimental results show that ISO effectively reduces the computational burden and enhance the selection diversity by the aid of S-Rank and S-Rand.