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Mathematical Problems in Engineering
Volume 2015, Article ID 940592, 10 pages
Research Article

Pareto-Ranking Based Quantum-Behaved Particle Swarm Optimization for Multiobjective Optimization

1Institute of Educational Informatization, Jiangnan University, Wuxi 214122, China
2Institute of Electrical Automation, Jiangnan University, Wuxi 214122, China

Received 27 April 2015; Accepted 25 June 2015

Academic Editor: Fabio Tramontana

Copyright © 2015 Na Tian and Zhicheng Ji. 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.


A study on pareto-ranking based quantum-behaved particle swarm optimization (QPSO) for multiobjective optimization problems is presented in this paper. During the iteration, an external repository is maintained to remember the nondominated solutions, from which the global best position is chosen. The comparison between different elitist selection strategies (preference order, sigma value, and random selection) is performed on four benchmark functions and two metrics. The results demonstrate that QPSO with preference order has comparative performance with sigma value according to different number of objectives. Finally, QPSO with sigma value is applied to solve multiobjective flexible job-shop scheduling problems.