Abstract
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.
Highlights
Graphs are often used to depict objects and to represent the relationship between objects
As a population-based metaheuristic, Particle Swarm Optimization (PSO) has the advantages of robustness, effectiveness, and simplicity compared to other swarm intelligent approaches such as genetic algorithms and ant colony optimization [10,11,12]
These results show that the two PSO procedures can converge after a number of iterations
Summary
Graphs are often used to depict objects and to represent the relationship between objects. Eades [4] proposed a force-directed heuristic method for graph drawing. Many other methods have been proposed [5, 6] Among these methods, the force-directed method is popular, which uses a heuristic cost or energy function to map the layout of a graph to a real number. The force-directed method is used to draw undirected graphs with straight-line edges. A Particle Swarm Optimization (PSO) procedure is proposed to solve the graph drawing problem. Some methods proposed in the literature focus on the communication strategies or the neighborhood topologies [23,24,25] These methods are all more efficient than serial PSO procedures and are implemented on distributed systems.
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