Chinese Journal of Computers   Full Text
Title	A Differential Evolution Based on Double Populations for Constrained Multi-Objective Optimization Problem
Authors	MENG Hong-Yun1) ZHANG Xiao-Hua2) LIU San-Yang1)
Address	1)(Department of Applied Mathematics, Xidian University, Xi’an 710071) 2)(Institute of Intelligent Information Processing, Xidian University, Xi’an 710071)
Year	2008
Issue	No.2(228—235)
Abstract &   Background	Abstract An improved differential evolution approach is given first, and a new algorithm based on double populations for Constrained Multi-objective Optimization Problem(CMOP) is presented. In the proposed algorithm, two populations are adopted, one is for the feasible solutions found during the evolution, and the other is for infeasible solutions with better performance which are allowed to participate in the evolution with the advantage of avoiding difficulties such as constructing penalty function and deleting infeasible solutions directly. In addition, the time complexity of the proposed algorithm, NSGA-Ⅱand SPEA are compared, which show the best is NSGA-Ⅱ, followed by SPEA and the proposed algorithm simultaneously. The experiments on benchmarks indicate that the proposed algorithm is superior to NSGA-Ⅱin the measure of GD and SP. keywords differential evolution; constrained optimization problem; multi-objective optimization problem background Constrained optimization, both for nonlinear programming and multi-objective optimization, is a very important problem and has a variety of applications in engineering, management, mathematics and other fields. A common way to constrained optimization problem is to deal with constraints by penalty function, with the disadvantage and difficulty in choosing the penalty factors. In this paper, the authors propose a differential evolution based on double populations for constrained multi-objective optimization problem. By using the definitions and the mechanism in the paper, an effective evolutionary algorithm for constrained multi-objective optimization problem is given and the time complexity is discussed and compared with the state of the art—NSGA-Ⅱand SPEA, which shows the time complexity of the proposed algorithm is as the same magnitude as SPEA and is higher than that of NSGA-Ⅱ, while simulations illustrate that the proposed algorithm is superior to NSGA-Ⅱin the measure of GD and SP. However, it is worthy to note that the time complexity of our algorithm will decrease greatly if a strategy like NSGA-Ⅱis taken for updating optimal population gbest.