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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 841780, 15 pages
Research Article

A Hybrid Multiobjective Differential Evolution Algorithm and Its Application to the Optimization of Grinding and Classification

1School of Information Science and Engineering, Central South University, Changsha 410083, China
2Department of Mathematics & Statistics, Curtin University, Perth, WA 6845, Australia

Received 19 July 2013; Accepted 5 September 2013

Academic Editor: Dewei Li

Copyright © 2013 Yalin Wang 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.


The grinding-classification is the prerequisite process for full recovery of the nonrenewable minerals with both production quality and quantity objectives concerned. Its natural formulation is a constrained multiobjective optimization problem of complex expression since the process is composed of one grinding machine and two classification machines. In this paper, a hybrid differential evolution (DE) algorithm with multi-population is proposed. Some infeasible solutions with better performance are allowed to be saved, and they participate randomly in the evolution. In order to exploit the meaningful infeasible solutions, a functionally partitioned multi-population mechanism is designed to find an optimal solution from all possible directions. Meanwhile, a simplex method for local search is inserted into the evolution process to enhance the searching strategy in the optimization process. Simulation results from the test of some benchmark problems indicate that the proposed algorithm tends to converge quickly and effectively to the Pareto frontier with better distribution. Finally, the proposed algorithm is applied to solve a multiobjective optimization model of a grinding and classification process. Based on the technique for order performance by similarity to ideal solution (TOPSIS), the satisfactory solution is obtained by using a decision-making method for multiple attributes.