Influence of Reference Points on a Many-Objective Optimization Algorithm

Many-Objective Optimization Problems (MaOPs) are problems that have more than three objective functions to be optimized. Most Multi-Objective Evolutionary Algorithms scales poorly when the number of objective function increases. To face this limitation, new strategies have been proposed. One of them is the use of reference points to enhance the search of the algorithms. NSGA-III is a reference point based algorithm that has been successfully applied to solve MaOPs. NSGA-III uses a set of reference points placed on a normalized hyperplane which is equally inclined to all objective axes and has an intercept at 1 on each axis. Despite the good results of NSGA-III, the shape of the hyper-plane is not deeply explored in literature. This work studies the influence of the set of reference points on Many-Objective Optimization. Here, it is proposed three new transformations of the reference points set used by NSGA-III. Besides, the Vector Guided Adaptation procedure is also applied to modify original NSGA-III hyper-plane. Furthermore, an adaptation of NSGA-III algorithm is proposed and it is performed a set of experiments to evaluate the transformation procedures. Original and adapted versions of NSGA-III are faced over several benchmarking problems observing both convergence and diversity through the analysis of statistical tests.