Skip to main content

An Effective and Efficient Two Stage Algorithm for Global Optimization

  • Conference paper
Advances in Machine Learning and Cybernetics

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3930))

Abstract

A two stage algorithm, consisting of gradient technique and particle swarm optimization (PSO) method for global optimization is proposed. The gradient method is used to find a local minimum of objective function efficiently, and PSO with potential parallel search is employed to help the minimization sequence to escape from the previously converged local minima to a better point which is then given to the gradient method as a starting point to start a new local search. The above search procedure is applied repeatedly until a global minimum of the objective function is found. In addition, a repulsion technique and partially initializing population method are also incorporated in the new algorithm to increase its global search ability. Global convergence is proven, and tests on benchmark problems show that the proposed method is more effective and reliable than the existing optimization methods.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ge, R.: A Filled Function Method for Finding a Gobal Minimizer of a Function of Several Variables. Mathematical Programming 46, 191–204 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  2. Levy, A., Montalvo, A.: The Tunneling Algorithm for the Global Minimization of Functions. SIAM Journal of Scientific and Statistical Computing 6, 15–29 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  3. Holland, J.H.: Genetic algorithms. Scientific American 4, 44–50 (1992)

    Google Scholar 

  4. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by Simulated Annealing. Science 220, 671–680 (1983)

    Article  MathSciNet  Google Scholar 

  5. Eberhart, R.C., Kennedy, J.: A New Optimizer Using Particle Swarm Theory. In: Proc. 6th Symp., Micro Machine and Human Science, Nagoya, Japan, pp. 39–43 (1995)

    Google Scholar 

  6. Kennedy, J., Eberhart, R.C.: Particle Swarm Optimization. In: Proc. of IEEE International Conference on Neural Networks, Piscataway, NJ, pp. 1942–1948 (1995)

    Google Scholar 

  7. Shi, Y., Eberhart, R.C.: A Modified Particle Swarm Optimizer. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 1998), Piscataway, NJ, pp. 69–73 (1998)

    Google Scholar 

  8. Noel, M.M., Jannett, T.C.: Simulation of a New Hybrid Particle Swarm Optimization Algorithm. In: Proceedings of the Thirty-Sixth Southeastern Symposium on System Symposium, pp. 150–153 (2004)

    Google Scholar 

  9. RoyChowdhury, P., Singh, Y.P., Chansarkar, R.A.: Hybridization of Gradient Descent Algorithms with Dynamic Tunneling Methods for Global Optimization. IEEE Transactions on Systems, Man, and Cybernetics 30, 384–390 (2000)

    Article  Google Scholar 

  10. Yiu, K.F.C., Liu, Y., Teo, K.L.: A hybrid Descent Method for Global Optimization. Journal of Global Optimization 28, 229–238 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. Deb, K.: Optimization for Engineering Design, Algorithms and Examples. Prentice-Hall, New Delhi (1995)

    Google Scholar 

  12. Parsopoulos, K.E., Vrahatis, M.N.: On the Computation of All Global Optimizers Through Particle Swarm Optimization. IEEE Transactions on Evolutionary Computation 8, 211–223 (2004)

    Article  Google Scholar 

  13. Cvijovic, D., Klinowski, J.: Taboo search, An Approach to the Multiple Minima Problem. Science 267, 664–666 (1995)

    Article  MathSciNet  Google Scholar 

  14. Bilbro, G.L., Snyder, W.E.: Optimization of Functions With Many Minima. Transaction on Systems, Man, and Cybern. 21(7), 840–849 (1991)

    Article  MathSciNet  Google Scholar 

  15. Anerssen, R.S., Jennings, L.S., Ryan, D.M.: Optimization. University of Queensland Press, St. Lucia (1972)

    Google Scholar 

  16. Dekkers, A., Aarts, E.: Global Optimization and Simulated Annealing. Mathematical Programming 50, 367–393 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  17. Barhen, J., Protopopescu, V., Reister, D.: TRUST: A Deterministic Algorithm for Global Optimization. Science 276, 1094–1097 (1997)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, YJ., Zhang, JS., Zhang, YF. (2006). An Effective and Efficient Two Stage Algorithm for Global Optimization. In: Yeung, D.S., Liu, ZQ., Wang, XZ., Yan, H. (eds) Advances in Machine Learning and Cybernetics. Lecture Notes in Computer Science(), vol 3930. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11739685_51

Download citation

  • DOI: https://doi.org/10.1007/11739685_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33584-9

  • Online ISBN: 978-3-540-33585-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics