Adaptive ∈-ranking on MNK-Landscapes

This work proposes an adaptive isin-ranking method to enhance Pareto based selection, aiming to develop effective many objective evolutionary optimization algorithm. isin-ranking fine grains ranking of solutions after they have been ranked by Pareto dominance, using a randomized sampling procedure combined with isin-dominance to favor a good distribution of the samples. In essence, sampled solutions keep their initial rank and solutions located within the virtually expanded dominance regions of the sampled solutions are demoted to an inferior rank. The parameter isin that determines the expanded regions of dominance of the sampled solutions is adapted to each generation so that the number of highest ranked solutions is kept close to a desired number expressed as a fraction of the population size. We enhanced NSGA-II with the proposed method and verify its performance on MNK-Landscapes. Experimented results show that the adaptive method works effectively and that convergence and diversity of the solutions found can improve remarkably on MNK-Landscapes with 3 les M les 10 objectives.