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Shock and Vibration
Volume 2017 (2017), Article ID 8204867, 16 pages
Research Article

An Improved Multiobjective Particle Swarm Optimization Algorithm Using Minimum Distance of Point to Line

1Department of Vehicle Engineering, Taiyuan University of Technology, Shanxi, China
2Department of Mechanical Engineering, Taiyuan University of Science Technology, Shanxi, China
3Centre for Efficiency and Performance Engineering, University of Huddersfield, Queensgate, Huddersfield HD1 3DH, UK

Correspondence should be addressed to Tie Wang

Received 12 February 2017; Revised 9 May 2017; Accepted 15 May 2017; Published 25 September 2017

Academic Editor: Toshiaki Natsuki

Copyright © 2017 Zhengwu Fan 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.


In a multiobjective particle swarm optimization algorithm, selection of the global best particle for each particle of the population from a set of Pareto optimal solutions has a significant impact on the convergence and diversity of solutions, especially when optimizing problems with a large number of objectives. In this paper, a new method is introduced for selecting the global best particle, which is minimum distance of point to line multiobjective particle swarm optimization (MDPL-MOPSO). Using the basic concept of minimum distance of point to line and objective, the global best particle among archive members can be selected. Different test functions were used to test and compare MDPL-MOPSO with CD-MOPSO. The result shows that the convergence and diversity of MDPL-MOPSO are relatively better than CD-MOPSO. Finally, the proposed multiobjective particle swarm optimization algorithm is used for the Pareto optimal design of a five-degree-of-freedom vehicle vibration model, which resulted in numerous effective trade-offs among conflicting objectives, including seat acceleration, front tire velocity, rear tire velocity, relative displacement between sprung mass and front tire, and relative displacement between sprung mass and rear tire. The superiority of this work is demonstrated by comparing the obtained results with the literature.