A Decomposition Based Evolutionary Algorithm for Many Objective Optimization with Systematic Sampling and Adaptive Epsilon Control

Abstract

Decomposition based evolutionary approaches such as MOEA/D and its variants have been quite successful in solving various classes of two and three objective optimization problems. While there have been some attempts to modify the dominance based approaches such as NSGA-II and SPEA2 to deal with many-objective optimization, there are few attempts to extend the capability of decomposition based approaches. The performance of a decomposition based approach is dependent on (a) the mechanism of reference points generation i.e. one which needs to be scalable and computationally efficient (b) the method to simultaneously deal with conflicting requirements of convergence and diversity and finally (c) the means to use the information of neighboring subproblems efficiently. In this paper, we introduce a decomposition based evolutionary algorithm, wherein the reference points are generated via systematic sampling and an adaptive epsilon scheme is used to manage the balance between convergence and diversity. To deal with constraints efficiently, an adaptive epsilon formulation is adopted. The performance of the algorithm is highlighted using standard benchmark problems i.e. DTLZ1 and DTLZ2 for 3, 5, 8, 10 and 15 objectives, the car side impact problem, the water resource management problem and the constrained ten-objective general aviation aircraft (GAA) design problem. The study clearly highlights that the proposed algorithm is better or at par with recent reference direction based approaches.