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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 584909, 12 pages
Research Article

Using Objective Clustering for Solving Many-Objective Optimization Problems

School of Computer Science and Technology, Xidian University, Xi'an 710071, China

Received 18 January 2013; Accepted 13 April 2013

Academic Editor: Andy Song

Copyright © 2013 Xiaofang Guo 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.


Many-objective optimization problems involving a large number (more than four) of objectives have attracted considerable attention from the evolutionary multiobjective optimization field recently. With the increasing number of objectives, many-objective optimization problems may lead to stagnation in search process, high computational cost, increased dimensionality of Pareto-optimal front, and difficult visualization of the objective space. In this paper, a special kind of many-objective problems which has redundant objectives and which can be degenerated to a lower dimensional Pareto-optimal front has been investigated. Different from the works in the previous literatures, a novel metric, interdependence coefficient, which represents the nonlinear relationship between pairs of objectives, is introduced in this paper. In order to remove redundant objectives, PAM clustering algorithm is employed to identify redundant objectives by merging the less conflict objectives into the same cluster, and one of the least conflict objectives is removed. Furthermore, the potential of the proposed algorithm is demonstrated by a set of benchmark test problems scaled up to 20 objectives and a practical engineering design problem.