WEIGHTED DIVERSITY MEASURE TO IMPROVE CONVERGENCE IN A CLASS OF MANY-OBJECTIVE OPTIMIZATION PROBLEMS

Abstract

The main difficulty with many-objective optimization problems is that at any instant (generation), the entire population belongs to the same-rank non-dominated front. The result is that there is no selection pressure for convergence to the true Pareto-optimal front (P.O.F.). In such a case, (a) the primary selection based on Pareto-dominance ranking ceases to be effective. (b) The role of the secondary selection based on diversity preservation becomes more crucial. While a lot of approaches aiming to increase the selection pressure to the P.O.F. by modifying Pareto-dominance have been reported in literature, the issue of enhancing the role of diversity preservation remains unaddressed. This report proposes a method to improve the selection pressure to the P.O.F. by way of modifying the crowding distance (diversity preservation) operator in NSGAII for those many-objective problems which have redundant objectives. The earlier proposed principal component analysis based dimensionality reduction procedures [I], [2] are used to identify the redundant objectives. This information is used to so scale the crowding distance measure that an NSGA-11 run results in the true P.O.F., for problems which could not be otherwise solved. Extensive experiments performed on DTLZ5-(l.M) problems [1] demonstrate (0 that, the proposed method offers on the fly dimensionality reduction in true sense, and. (ii,) that, significantly improved convergence in important objectives can be achieved at the cost of the loss in diversity in redundant objectives