An improved secondary ranking for many objective optimization problems

Many objective optimization refers to optimization problems for which the number of objectives is significantly greater than conventionally studied 2 or 3. For such problems, large number of solutions become non-dominated, which reduces the convergence pressure of the Evolutionary Algorithms~(EAs) towards the Pareto Optimal Front. Recently, alternate secondary ranking schemes for have been suggested for NSGA-II in lieu of crowding distance to expedite its convergence for many objective problems. In this paper, we improvise upon an existing scheme~(epsilon dominance). The proposed approach is found to perform better than the other substitute distance assignment methods for the problems studied in this paper. A new diversity metric has also been proposed, which can be used in order to compare the performance of the various EAs.