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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 2013673, 15 pages
Research Article

GPU-Based Parallel Particle Swarm Optimization Methods for Graph Drawing

1College of Management Science and Engineering, Shandong Normal University, Jinan, Shandong, China
2College of Business, The University of Texas at San Antonio, San Antonio, TX, USA

Correspondence should be addressed to Jianhua Qu

Received 17 March 2017; Accepted 15 June 2017; Published 30 July 2017

Academic Editor: Filippo Cacace

Copyright © 2017 Jianhua Qu 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.


Particle Swarm Optimization (PSO) is a population-based stochastic search technique for solving optimization problems, which has been proven to be effective in a wide range of applications. However, the computational efficiency on large-scale problems is still unsatisfactory. A graph drawing is a pictorial representation of the vertices and edges of a graph. Two PSO heuristic procedures, one serial and the other parallel, are developed for undirected graph drawing. Each particle corresponds to a different layout of the graph. The particle fitness is defined based on the concept of the energy in the force-directed method. The serial PSO procedure is executed on a CPU and the parallel PSO procedure is executed on a GPU. Two PSO procedures have different data structures and strategies. The performance of the proposed methods is evaluated through several different graphs. The experimental results show that the two PSO procedures are both as effective as the force-directed method, and the parallel procedure is more advantageous than the serial procedure for larger graphs.