Decomposition-Based-Sorting and Angle-Based-Selection for Evolutionary Multiobjective and Many-Objective Optimization

• Published in: IEEE transactions on cybernetics Vol. 47; no. 9; pp. 2824 - 2837
• Main Authors: Cai, Xinye, Yang, Zhixiang, Fan, Zhun, Zhang, Qingfu
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.09.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Angle-based-selection (ABS); Classification; Computational efficiency; Computing time; Convergence; decomposition-based-sorting (DBS); diversity; Evolutionary algorithms; evolutionary multiobjective optimization; many-objective optimization; Mopping; Multiple objective analysis; Optimization; Satellite broadcasting; Shape optimization; Sociology; Sorting algorithms; Statistics; Synthetic aperture sonar
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2016.2586191

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem (MOP) into a number of scalar optimization subproblems and then solves them in parallel. In many MOEA/D variants, each subproblem is associated with one and only one solution. An underlying assumption is that each subproblem has a different Pareto-optimal solution, which may not be held, for irregular Pareto fronts (PFs), e.g., disconnected and degenerate ones. In this paper, we propose a new variant of MOEA/D with sorting-and-selection (MOEA/D-SAS). Different from other selection schemes, the balance between convergence and diversity is achieved by two distinctive components, decomposition-based-sorting (DBS) and angle-based-selection (ABS). DBS only sorts L closest solutions to each subproblem to control the convergence and reduce the computational cost. The parameter L has been made adaptive based on the evolutionary process. ABS takes use of angle information between solutions in the objective space to maintain a more fine-grained diversity. In MOEA/D-SAS, different solutions can be associated with the same subproblems; and some subproblems are allowed to have no associated solution, more flexible to MOPs or many-objective optimization problems (MaOPs) with different shapes of PFs. Comprehensive experimental studies have shown that MOEA/D-SAS outperforms other approaches; and is especially effective on MOPs or MaOPs with irregular PFs. Moreover, the computational efficiency of DBS and the effects of ABS in MOEA/D-SAS are also investigated and discussed in detail.