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Initial Particles Position for PSO, in Bound Constrained Optimization

  • Emilio Fortunato Campana
  • Matteo Diez
  • Giovanni Fasano
  • Daniele Peri
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7928)

Abstract

We consider the solution of bound constrained optimization problems, where we assume that the evaluation of the objective function is costly, its derivatives are unavailable and the use of exact derivative-free algorithms may imply a too large computational burden. There is plenty of real applications, e.g. several design optimization problems [1,2], belonging to the latter class, where the objective function must be treated as a ‘black-box’ and automatic differentiation turns to be unsuitable. Since the objective function is often obtained as the result of a simulation, it might be affected also by noise, so that the use of finite differences may be definitely harmful.

In this paper we consider the use of the evolutionary Particle Swarm Optimization (PSO) algorithm, where the choice of the parameters is inspired by [4], in order to avoid diverging trajectories of the particles, and help the exploration of the feasible set. Moreover, we extend the ideas in [4] and propose a specific set of initial particles position for the bound constrained problem.

Keywords

Bound Constrained Optimization Discrete Dynamic Linear Systems Free and Forced Responses Particles Initial Position 

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References

  1. 1.
    Mohammadi, B., Pironneau, O.: Applied Shape Optimization for Fluids. Clarendon Press, Oxford (2001)Google Scholar
  2. 2.
    Haslinger, J., Mäkinen, R.A.E.: Introduction to Shape Optimization. In: Advances in Design and Control. SIAM, Philadelphia (2003)Google Scholar
  3. 3.
    Pinter, J.D.: Global Optimization in Action. In: Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications. Kluwer Academic Publishers, The Netherlands (1996)Google Scholar
  4. 4.
    Campana, E.F., Fasano, G., Pinto, A.: Dynamic analysis for the selection of parameters and initial population, in particle swarm optimization. Journal of Global Optimization 48, 347–397 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Campana, E.F., Fasano, G., Peri, D.: Globally Convergent Modifications of Particle Swarm Optimization for Unconstrained Optimization. In: Olsson, A.E. (ed.) Particle Swarm Optimization: Theory, Techniques and Applications. Advances in Engineering Mechanics, pp. 97–118. Nova Publishers Inc., South Africa (2011)Google Scholar
  6. 6.
    Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings of the 1995 IEEE International Conference on Neural Networks IV, pp. 1942–1948. IEEE Service Center, Piscataway (1995)Google Scholar
  7. 7.
    Clerc, M., Kennedy, J.: The Particle Swarm - Explosion, Stability, and Convergence in a Multidimensional Complex Space. IEEE Transactions on Evolutionary Computation 6, 58–73 (2002)CrossRefGoogle Scholar
  8. 8.
    Sarachik, P.E.: Principles of linear systems, Cambridge University Press, Cambridge (1997)Google Scholar
  9. 9.
    Zheng, Y.L., Ma, L.H., Zhang, L.Y., Qian, J.X.: On the convergence analysis and parameter selection in particle swarm optimization. In: Proceedings of the Second International Conference on Machine Learning and Cybernetics, Xi’an, November 2-5 (2003)Google Scholar
  10. 10.
    Bernstein, D.S.: Matrix Mathematics: Theory, Facts, and Formulas, 2nd edn. Princeton University Press, NJ (2009)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Emilio Fortunato Campana
    • 1
  • Matteo Diez
    • 1
  • Giovanni Fasano
    • 2
  • Daniele Peri
    • 1
  1. 1.National Research Council-Maritime Research Centre (CNR-INSEAN)RomeItaly
  2. 2.Department of ManagementUniversity Ca’Foscari of VeniceItaly

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