U-NSGA-III: A Unified Evolutionary Algorithm for Single, Multiple, and Many-Objective Optimization

Evolutionary algorithms (EAs) have been systematically developed to solve mono-objective, multi-objective and many-objective optimization problems, in this order, over the past few decades. Despite some efforts in unifying different types of mono-objective evolutionary and non-evolutionary algorithms, there does not exist many studies to unify all three types of optimization problems together. Such a unified optimization algorithm will allow a user to work with a single code or software enabling one-time implementation of a suitable solution representation, objective and constraint function coding and operator updates, if any, to achieve optimizations with different objective dimensions. In this study, for the first time, we propose a unified evolutionary optimization algorithm U-NSGA-III, based on the recentlyproposed NSGA-III procedure, developed for solving many-objectives problems, for solving all three classes of problems specified above. Our proposed implementation is such that the 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. To demonstrate the working of U-NSGA-III, extensive simulations are performed on unconstrained and constrained test problems having single, two, multi and many-objectives, taken from the literature and on two engineering optimization design problems. The performance of U-NSGA-III is compared with a real-coded genetic algorithm for mono-objective problems, with well-known NSGA-II for two-objective problems, and with recently proposed NSGA-III for three to 15-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.