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The Scientific World Journal
Volume 2015, Article ID 439307, 10 pages
Research Article

A Novel Multiobjective Evolutionary Algorithm Based on Regression Analysis

1School of Computer, China University of Geosciences, Wuhan 430074, China
2Department of Mechanical & Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, UK

Received 23 June 2014; Revised 15 September 2014; Accepted 30 December 2014

Academic Editor: Shifei Ding

Copyright © 2015 Zhiming Song 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.


As is known, the Pareto set of a continuous multiobjective optimization problem with objective functions is a piecewise continuous ()-dimensional manifold in the decision space under some mild conditions. However, how to utilize the regularity to design multiobjective optimization algorithms has become the research focus. In this paper, based on this regularity, a model-based multiobjective evolutionary algorithm with regression analysis (MMEA-RA) is put forward to solve continuous multiobjective optimization problems with variable linkages. In the algorithm, the optimization problem is modelled as a promising area in the decision space by a probability distribution, and the centroid of the probability distribution is ()-dimensional piecewise continuous manifold. The least squares method is used to construct such a model. A selection strategy based on the nondominated sorting is used to choose the individuals to the next generation. The new algorithm is tested and compared with NSGA-II and RM-MEDA. The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages. At the same time, MMEA-RA has higher efficiency than the other two algorithms. A few shortcomings of MMEA-RA have also been identified and discussed in this paper.