Explicit and Implicit Parallelisms in Decomposition Based Evolutionary Many-Objective Optimization Algorithms

Over the past two decades, evolutionary multiobjective optimization (EMO) algorithms have demonstrated their ability to find and maintain multiple trade-off solutions in two and three-objective problems. This is because their operators are able to establish an implicit parallel search within an evolving population around multiple optimal regions of the search space simultaneously. For many-objective optimization problems involving a large-dimensional objective space, the extent of parallelism present in early EMO methods was found to be too generic. Decompositionbased EMO algorithms which divide the overall computing task into a number of sub-tasks of focusing within a region of the search space have found to be successful in solving many-objective problems. In this paper, we term this external control of an algorithm’s parallelism as ‘explicit parallelism’ set by the algorithm developer. Although such a decomposition concept compromises on the implicit parallelism aspect of an EMO algorithm, an externally defined coordination among different subtasks is able to bring back the requisite parallelism needed to solve them. In this paper, we consider three decomposition-based EMO algorithms – MOEA/D, M2M, and NSGA-III – to investigate the effect of user-controlled explicit parallelism mechanism on their search operators. For this purpose, we first consider a number of M2M variants with differing levels of explicit parallelism and identify the most-balanced algorithm between explicit and implicit parallelisms by applying them on a number of standard many-objective unscaled and scaled ∗L. Chen and H.-L. Liu are with Guangdong University of Technology, Guangzhou, China, e-mail: chenaction@126.com, hlliu@gdut.edu.cn. †K. Deb is with Department of Electrical and Computer Engineering and BEACON Center for the Study of Evolution in Action (NSF DBI-0939454), Michigan State University, 428 S. Shaw Lane, 2120 EB, East Lansing, MI 48824, USA, e-mail: kdeb@egr.msu.edu ‡The visit of the first author to Michigan State University was supported by China Scholarship Council. This material is based in part upon work supported by the National Science Foundation under Cooperative Agreement No. DBI-0939454. test problems (DTLZ and WFG problems). Results from our extensive study indicate that by relaxing the decomposition effect, thereby re-establishing an appropriate parallel search within M2M operators, the performance of the resulting M2M variants can be improved. Motivated by the M2M-variant study, we repeat the procedure on NSGA-III and MOEA/D operators and observe interesting but unique balancing acts between explicit and implicit parallelisms that each of the algorithms requires. We also investigate the effect of normalization of objectives in improving the performance of MOEA/D and M2M methods and report much improved performances than the original methods. The overall approach helps to develop more efficient algorithms than the original methods. The principles of this study can be used to improve the performance other EMO methods.