NSGA-III

This paper presents a fast and open source extension based on the NSGA-II code stored in the repository of the Kanpur Genetic Algorithms Laboratory (KanGAL) and the adjustment of the selection operator. It slightly modifies existing well-established genetic algorithms for many-objective optimization called the NSGA-III, the adaptive NSGA-III (A-NSGA-III), and the efficient adaptive NSGA-III, (A$^2$-NSGA-III). The proposed method is tested on a range of benchmark problems and showcases notable performance improvement.NSGA-II and NSGA-III are frequently employed as a reference for a comparative evaluation of new evolutionary algorithms.However, the latter is proprietary and many researchers have been forced to implement it from scratch with lower performance. Our NSGA-III variations consider static and dynamic reference points where individuals in the first front are contemplated to obtain extreme points that are neither negatives nor repeated. Those algorithms resolve binary and real, constrained and non-constrained Multi-Objective and Many-objective problems. Additionally, when efficient adaptive NSGA-III is employed to solve the Car-Side Impact problem and the Water problem, we find not only visually well-distributed solutions, but also in terms of the Hyper-volume metric compared to the A-NSGA-III and the NSGA-III.