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Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 1435463, 18 pages
Research Article

An Indicator and Decomposition Based Steady-State Evolutionary Algorithm for Many-Objective Optimization

1Department of Information Science and Engineering, Northeastern University, Shenyang 110819, China
2School of Information Science and Engineering, Central South University (CSU), Changsha 410083, China
3School of Mechanical Engineering, Shenyang Jianzhu University, Shenyang 110168, China

Correspondence should be addressed to Fei Li

Received 6 August 2017; Revised 11 December 2017; Accepted 22 January 2018; Published 11 March 2018

Academic Editor: Giuseppe Vairo

Copyright © 2018 Fei Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An indicator based selection method is a major ingredient in the formulation of indicator based evolutionary multiobjective optimization algorithms. The existing classical indicator based selection methodologies have demonstrated an excellent performance to solve low-dimensional optimization problems. However, the indicator based evolutionary multiobjective optimization algorithms encounter enormous challenges in high-dimensional objective space. Our main purpose is to explore how to extend the indicator to handle many-objective optimization problems. After analyzing the indicator, the objective space partition strategy, and the decomposition method, we propose a steady-state evolutionary algorithm based on the indicator and the decomposition method, named, -MOEA/D, to obtain well-converged and well-distributed Pareto front. The main contribution of this paper contains two aspects. (1) The convergence and diversity for the indicator based selection are analyzed. Two improper selection situations will be properly solved via applying the decomposition method. (2) According to the position of a new individual in the steady-state evolutionary algorithm, two different objective space partition strategies and the corresponding selection methods are proposed. Extensive experiments are conducted on a variety of benchmark test problems, and the experimental results demonstrate that the proposed algorithm has competitive performance in comparison with several tailored algorithms for many-objective optimization.