A Multi-objective Particle Swarm Optimizer Enhanced with a Differential Evolution Scheme

  • Jorge Sebastian Hernández-Domínguez
  • Gregorio Toscano-Pulido
  • Carlos A. Coello Coello
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7401)

Abstract

Particle swarm optimization (PSO) and differential evolution (DE) are meta-heuristics which have been found to be very successful in a wide variety of optimization tasks. The high convergence rate of PSO and the exploratory capabilities of DE make them highly viable candidates to be used for solving multi-objective optimization problems (MOPs). In previous studies that we have undertaken [2], we have observed that PSO has the ability to launch particles in the direction of a leader (i.e., a non-dominated solution) with a high selection pressure. However, this high selection pressure tends to move the swarm rapidly towards local optima. DE, on the other hand, seems to move solutions at smaller steps, yielding solutions close to their parents while exploring the search space at the same time. In this paper, we present a multi-objective particle swarm optimizer enhanced with a differential evolution scheme which aims to maintain diversity in the swarm while moving at a relatively fast rate. The goal is to avoid premature convergence without sacrificing much the convergence rate of the algorithm. In order to design our hybrid approach, we performed a series of experiments using the ZDT test suite. In the final part of the paper, our proposed approach is compared (using 2000, 3500, and 5000 objective function evaluations) with respect to four state-of-the-art multi-objective evolutionary algorithms, obtaining very competitive results.

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References

  1. 1.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA–II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  2. 2.
    Dominguez, J.S.H., Pulido, G.T.: A comparison on the search of particle swarm optimization and differential evolution on multi-objective optimization. In: 2011 IEEE Congress on Evolutionary Computation (CEC), pp. 1978–1985 (June 2011)Google Scholar
  3. 3.
    Durillo, J.J., García-Nieto, J., Nebro, A.J., Coello Coello, C.A., Luna, F., Alba, E.: Multi-Objective Particle Swarm Optimizers: An Experimental Comparison. In: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, J.-K., Sevaux, M. (eds.) EMO 2009. LNCS, vol. 5467, pp. 495–509. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    Kennedy, J., Eberhart, R.: Particle Swarm Optimization. In: IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948 (1995)Google Scholar
  5. 5.
    Nebro, A.J., Durillo, J.J., Garcia-Nieto, J., Coello Coello, C.A., Luna, F., Alba, E.: SMPSO: A New PSO-based Metaheuristic for Multi-objective Optimization. In: 2009 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making (MCDM 2009), March 30-April 2, pp. 66–73. IEEE Press, Nashville (2009) ISBN 978-1-4244-2764-2CrossRefGoogle Scholar
  6. 6.
    Price, K., Storn, R.: Differential Evolution - a simple evolution strategy for fast optimization (April 1997)Google Scholar
  7. 7.
    Reyes Sierra, M., Coello Coello, C.A.: Improving PSO-Based Multi-objective Optimization Using Crowding, Mutation and ε-Dominance. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 505–519. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Robič, T., Filipič, B.: DEMO: Differential Evolution for Multiobjective Optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 520–533. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Veldhuizen, D.A.V., Lamont, G.B.: On Measuring Multiobjective Evolutionary Algorithm Performance. In: 2000 Congress on Evolutionary Computation, vol. 1, pp. 204–211. IEEE Service Center, Piscataway (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jorge Sebastian Hernández-Domínguez
    • 1
  • Gregorio Toscano-Pulido
    • 1
  • Carlos A. Coello Coello
    • 2
  1. 1.Information Technology LaboratoryCINVESTAV - Tamaulipas, Parque Científico y Tecnológico TECNOTAMTamaulipasMéxico
  2. 2.Evolutionary Computation Group, Depto. de ComputaciónCINVESTAV-IPNMéxico, D.F.México

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