U-NSGA-III: A Unified Evolutionary Optimization Procedure for Single, Multiple, and Many Objectives: Proof-of-Principle Results

Abstract

Evolutionary algorithms (EAs) have been systematically developed to solve mono-objective, multi-objective and many-objective problems, respectively, over the past few decades. Despite some efforts in unifying different types of mono-objective evolutionary and non-evolutionary algorithms, there does not exist too many studies to unify all three types of optimization problems together. In this study, we propose an unified evolutionary optimization algorithm U-NSGA-III, based on recently-proposed NSGA-III procedure for solving all three classes of problems. The $\text{ U-NSGA-III }$ algorithm degenerates to an equivalent and efficient population-based optimization procedure for each class, just from the description of the number of specified objectives of a problem. The algorithm works with usual EA parameters and no additional tunable parameters are needed. The performance of $\text{ U-NSGA-III }$ is compared with a real-coded genetic algorithm for mono-objective problems, with NSGA-II for two-objective problems, and with NSGA-III for three or more objective problems. Results amply demonstrate the merit of our proposed unified approach, encourage its further application, and motivate similar studies for a richer understanding of the development of optimization algorithms.