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Journal of Information Science and Engineering, Vol. 29 No. 5, pp. 811-834 (September 2013)


A Multi-Algorithm Balancing Convergence and Diversity for Multi-Objective Optimization*


DATONG XIE1,2, LIXIN DING1, YURONG HU1, SHENWEN WANG1,3, CHENGWANG XIE4 AND LEI JIANG1,5
1State Key Lab of Software Engineering
School of Computer
Wuhan University
Wuhan, 430000 P.R. China
2Department of Information Management Engineering
Fujian Commercial College
Fuzhou, 350000 P.R. China
3Department of Information Engineering
Shijiazhuang University of Economics
Shijiazhuang, 050000 P.R. China
4School of Software
East China Jiao Tong University
Nanchang, 330000 P.R. China
5Key Laboratory of Knowledge Processing and Networked Manufacture
Hunan University of Science and Technology
Xiangtan, 411201 P.R. China

As a population-based method, evolutionary algorithms have been extensively used to solve multi-objective optimization problems. However, most of the current multi-objective evolutionary algorithms (MOEAs) cannot strike a good balance between the closeness to the true Pareto front and the uniform distribution of non-dominated solutions. In this paper, we present a multi-algorithm, MABNI, which is based on two popular MOEAs, NSGA-II and IBEA. The proposed algorithm is inspired from the strengths and weaknesses of the two algorithms, e.g., the former can preserve extreme solutions effectively but has a worse diversity while the latter shows a better convergence and makes non-dominated solutions more evenly distributed but easily suffers losses of extreme solutions. In MABNI, modified NSGA-II and IBEA run alternatively and the update principle for the archive population is based on the distances to nearest neighbors. Furthermore, accompanied with preservation of extreme points, an improved differential evolution is employed to speed the search. The performance of MABNI is examined on ZDT-series and DTLZ-series test instances in terms of the selected performance indicators. Compared with NSGA-II and IBEA, the results indicate that MABNI can reach a better balance between convergence and diversity for the approximation of the true Pareto front and obtain more stable results.

Keywords: multi-algorithm, multi-objective optimization, evolutionary algorithm, nearest neighbor, extreme solution

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Received March 13, 2012; revised August 23, 2012; accepted October 22, 2012.
Communicated by Zhi-Hua Zhou.
* This work is supported by the National Natural Science Foundation of China (No. 60975050), the Fundamental Research Funds for the Central Universities (No. 6081014), the National Natural Science Foundation of China (No. 61165004), the Natural Science Foundation of Fujian Province (No. 2012J01248), the social science and humanity on Young Fund of the Ministry of Education, China (No. 12YJCZH084).