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Particle Swarm Optimization With Crossover and Mutation Operators Using the Diversity Criteria

[+] Author Affiliations
Guang Dong, John Cooper

Tesla Motors Inc., Fremont, CA

Paper No. DETC2013-13593, pp. V03AT03A010; 10 pages
doi:10.1115/DETC2013-13593
From:
  • ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 3A: 39th Design Automation Conference
  • Portland, Oregon, USA, August 4–7, 2013
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5588-1
  • Copyright © 2013 by ASME

abstract

Particle Swarm Optimization is a population based globalized search algorithm that mimics the behavior of swarms. It belongs to the larger class of evolutionary algorithms as widely used stochastic technique in the global optimization field. Since the PSO is population based, it requires no auxiliary information, such as the gradient of the problem.

It is known that each particle in the PSO uses only two pieces of information, called the personal best position and the global best position, to update its moving velocity and position by generations. One disadvantage of this algorithm is that it can be easily trapped into some local optimal solutions because of the premature convergence. This may be an issue when solving complex multi-modal functions with multiple local minimums. Hence, the global optimization algorithm should have the ability to prevent being trapped into local optima by keeping wide search space and maintaining the population diversity. In order to improve the performance of the PSO for complex global optimization problems, this paper introduces both crossover and mutation operators to the basic PSO algorithm. The proposed algorithm uses the mechanism that all the particles in the current iteration will have crossover and mutation operations if the diversity criteria of the particles is reduced to be smaller than a predefined limit value. Therefore, the PSO using both crossover and mutation operators can maintain the diversity of population and enhance the search ability as to get better results while solving complex problems. This study adopts the average distance around the swarm center as the diversity measure, and extends the distance metrics to both L1 norm distance and L norm distance.

To verify the usability and effectiveness of the proposed algorithm, it is applied to 12 widely used nonlinear benchmark functions. These examples show that the proposed PSO with crossover and mutation operators using the diversity criteria has better optimization performance than the basic PSO by maintaining the swarm diversity. Moreover, the PSO using the L1 norm distance diversity gives better results than both L2 and L norm distance for most cases.

Copyright © 2013 by ASME

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