A New Adaptive Operator Selection for NSGA-III Applied to CEC 2018 Many-Objective Benchmark

Abstract

As well as new algorithms are constantly proposed, new test functions for these algorithms are also designed. In this paper we explore 15 new benchmark functions proposed for CEC-2018 Multiobjective Evolutionary Algorithms (MOEA) Competition for many-objective optimization. The functions have diverse properties which cover a good representation of various real-world scenarios. We propose many-objective approaches that were designed considering three schemes to perform adaptive operator selection with NSGA-III algorithm: Thompson Sampling, Probability Matching and Adaptive Pursuit. They select from a pool of candidates composed by DE mutations and a Genetic Algorithm crossover. Thompson Sampling is a multi-armed bandit approach, i.e., it was designed to deal with the exploration versus exploitation dilemma intrinsic to the adaptive operator selection problem. Its use in a many objective evolutionary algorithm is innovative and constitutes the main contribution of this work. As the CEC-2018 is composed by complex, potentially nonlinear functions, we also perform the analysis of the effects of the insertion of a nonlinear operator within the candidate pool of operators. Statistical analysis of the experiments were performed with Mann-Whitney and Friedman tests. The IGD indicator was used to infer the quality of the solutions. The results indicate the use of Thompson Sampling as an adaptive operator selection is promising and increases the optimization performance of NSGA-III. They also indicate that the use of the nonlinear operator is capable of improving the results of all adaptive versions.