Particle Swarm Optimization with Gravitational Interactions for Multimodal and Unimodal Problems

  • Juan J. Flores
  • Rodrigo López
  • Julio Barrera
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6438)


Evolutionary computation is inspired by nature in order to formulate metaheuristics capable to optimize several kinds of problems. A family of algorithms has emerged based on this idea; e.g. genetic algorithms, evolutionary strategies, particle swarm optimization (PSO), ant colony optimization (ACO), etc. In this paper we show a population-based metaheuristic inspired on the gravitational forces produced by the interaction of the masses of a set of bodies. We explored the physics knowledge in order to find useful analogies to design an optimization metaheuristic. The proposed algorithm is capable to find the optima of unimodal and multimodal functions commonly used to benchmark evolutionary algorithms. We show that the proposed algorithm works and outperforms PSO with niches in both cases. Our algorithm does not depend on a radius parameter and does not need to use niches to solve multimodal problems. We compare with other metaheuristics respect to the mean number of evaluations needed to find the optima.


Optimization gravitational interactions evolutionary computation metaheuristic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Stretching technique for obtain global minimizers through particle swarm optimization. In: Proceedings of the Particle Swarm Optimization Workshop (2001)Google Scholar
  2. 2.
    Dorigo, M., Maniezzo, V., Colorni, A.: Distributed Optimization by Ant Colonies. Elsevier Publishing, Amsterdam (1992)Google Scholar
  3. 3.
    Barrera, J., Coello, C.A.C.: A particle swarm optimization method for multimodal optimization based on electrostatic interaction (2009)Google Scholar
  4. 4.
    Goldberg David, E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Pub. Co., Reading (1989)zbMATHGoogle Scholar
  5. 5.
    Rashedi, E., Nezamabadi-pour, H., Saryazdi, S.: GSA: A Gravitational Search Algorithm (2009)Google Scholar
  6. 6.
    Ingo, R.: Evolutionsstrategie 1994. Frommann Holzboog (1994)Google Scholar
  7. 7.
    Plagianakos, V.P., Magoulas, G.M., Parsopoulos, K.E., Vrahatis, M.N.: Improving particle swarm optimizer by function stretching. Nonconvex Optimization and Applications 54Google Scholar
  8. 8.
    Kennedy, J., Eberhart, R.: Swarm Intelligence. Evolutionary Computation. Morgan Kaufmann Publisher, San Francisco (2001)Google Scholar
  9. 9.
    Li, X.: A multimodal particle swarm optimizer based on fitness euclidean-distance ratio. In: Proceedings of the 9t annual conference on Genetin and evolutionary computation (GECCO 2007), pp. 78–85 (2007)Google Scholar
  10. 10.
    Newton, I.: Newtons Principia Mathematica. Fsica. Ediciones Altaya, S.A., 21 edition (1968)Google Scholar
  11. 11.
    Robert, H., David, R.: Physics Part I. Physics. John Wiley and Sons Inc., Chichester (1966)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Juan J. Flores
    • 1
  • Rodrigo López
    • 1
  • Julio Barrera
    • 2
  1. 1.División de Estudios de Posgrado, Facultad de Ingeniería EléctricaUniversidad Michoacana de San Nicolás de HidalgoMexico
  2. 2.CINVESTAV-IPN, Departamento de ComputaciónEvolutionary Computation GroupMéxico, D.F.México

Personalised recommendations