NAEMO: Neighborhood-sensitive archived evolutionary many-objective optimization algorithm

Abstract

Abstract One of the prominent strategies to address many-objective optimization problems involves using the reference direction based algorithms. However, literature severely lacks formal mathematical analysis to establish the reason behind superior performance of such methods. In this work, the neighborhood property of the many-objective optimization problems is recognized and is used to propose the neighborhood-sensitive archived evolutionary many-objective optimization (NAEMO) algorithm. In NAEMO, mating occurs within a local neighborhood and every reference direction continues to retain at least one associated candidate solution. Such preservation of candidate solutions leads to a monotonic improvement in diversity which has been theoretically and experimentally studied. Moreover, to combine the advantages of various mutation strategies, probabilistic mutation switching concept is introduced and to keep the archive size under control, periodic filtering modules are integrated with the NAEMO framework. Experimental results reveal that, in terms of inverted generational distance, hypervolume values and purity metric, NAEMO outperforms several state-of-the-art algorithms viz. NSGA-III, MOEA/D, θ-DEA, MOEA/DD, GrEA, HypE, MOPSO and dMOPSO on DTLZ1-4 test problems for up to 15 objectives. Further experiments show that NAEMO is competitive to M2M-based algorithms where the difficult regions of IMB problems have also been explored. These experiments make NAEMO a robust algorithm, which is additionally supported by theoretical foundations. The source code of NAEMO is available at http://worksupplements.droppages.com/naemo .