EF1-NSGA-III: An evolutionary algorithm based on the first front to obtain non-negative and non-repeated extreme points

Abstract

Multi-Objective and Many-objective Optimization problems have been extensively solved through evolutionary algorithms over a few decades. Despite the fact that NSGA-II and NSGA-III are frequently employed as a reference for a comparative evaluation of new evolutionary algorithms, the latter is proprietary. In this paper, we used the basic framework of the NSGA-II, which is very similar to the NSGA-III, with significant changes in its selection operator. We took the first front generated at the non-dominating sort procedure to obtain nonnegative and nonrepeated extreme points. This opensource version of the NSGA-III is called EF1-NSGA-III, and its implementation does not start from scratch; that would be reinventing the wheel. Instead, we took the NSGA-II code from the authors in the repository of the Kanpur Genetic Algorithms Laboratory to extend the EF1-NSGA-III. We then adjusted its selection operator from diversity, based on the crowding distance, to the one found on reference points and preserved its parameters. After that, we continued with the adaptive EF1-NSGA-III (A-EF1-NSGA-III), and the efficient adaptive EF1-NSGA-III (A2-EF1-NSGA-III), while also contributing to explain how to generate different types of reference points. The proposed algorithms resolve optimization problems with constraints of up to 10 objective functions. We tested them on a wide range of benchmark problems, and they showed notable improvements in terms of convergence and diversity by using the Inverted Generational Distance (IGD) and the HyperVolume (HV) performance metrics. The EF1-NSGA-III aims to resolve the power consumption for Centralized Radio Access Networks and the BiObjective Minimum DiameterCost Spanning Tree problems.