Adaptive epsilon-Ranking on MNK-Landscapes

Abstract

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.