Manifold dimension reduction based clustering for multi-objective evolutionary algorithm

Real world optimization problems always possess multiple objectives which are conflict in nature. Multi-objective evolutionary algorithms (MOEAs), which provide a group of solutions in region of Pareto front, increasingly draw researchers attention for their excellent performance. In this regard, solutions with a wide diversity would be more favored as they give decision makers more choices to evaluate upon their problems. Based on the insight of investigating the evolution, the Pareto front often lies in a manifold space, not Euclidian space. However, most MOEAs utilize Euclidian distance as a sole mechanism to keep a wide range of diversity for solutions, which is not suitable somewhat from this aspect. To this end, manifold dimension reduction algorithm which has the ability to map solutions in the same front of objective space into Euclidian space is adapted in further. And then, general clustering algorithm are utilized. At the end, we use this technology to replace the crowding distance technology in NSGA-II to choose individuals when there is not enough slots in mating selection process. Based on a range of experiments over benchmark problems against state-of-the-art, it is fully expected benefit of performance improvement will be more significant when applied in many objectives optimization problems. This will be pursuit in our future study.