Skip to main content
Log in

A Theoretical Approach to Restart in Global Optimization

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

While searching for the global minimum of a cost function we haveoftento decide if a restart from a different initial point would bemoreadvantageous than continuing current optimization. This is aparticularcase of the efficiency comparison between repeatedminimizations and singleextended search having the same total length.

A theoretical approach forthe treatment of this general problem formsthe subject of the present paper.A fundamental role is played by theprobability of reaching the globalminimum, whose asymptoticalbehavior allows to provide useful information onthe efficiency ofrepeated trials.

The second part of this work is devoted toa detailed analysis of threeoptimization algorithms whose evolution isindependent of the costfunction to be minimized: pure random search, grid search and randomwalk. These three examples give an interesting validationof thetheoretical results and provide a general procedure which can beemployed in the study of more complex optimization problems.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aluffi-Pentini, F., Parisi, V. and Zirilli, F. (1985), Global Optimization and Stochastic Differential Equations, Journal of Optimization Theory and Applications 47, 1–16.

    Google Scholar 

  • Baba, N. (1979), Global Optimization of Functions by the Random Optimization Method, International Journal of Control 30, 1061–1065.

    Google Scholar 

  • Bazaraa, M.S. and Shetty, C.M. (1979), Nonlinear Programming: Theory and Algorithms, JohnWiley & Sons, New York.

    Google Scholar 

  • Boender, C.G.E., Rinnooy Kan, A.H.G., Stougie, L. and Timmer, G. (1982), A Stochastic Method for Global Optimization, Mathematical Programming 22, 125–140.

    Google Scholar 

  • Corana, A., Marchesi, M., Martini, C. and Ridella, S. (1988), Minimizing Multimodal Functions of Continuous Variables with the Simulated Annealing Algorithm, ACM Transactions on Mathematical Software 13, 262–280.

    Google Scholar 

  • Devroye, L.P. (1976), On the Convergence of Statistical Search, IEEE Transactions on Systems, Man, and Cybernetics SMC-6, 46–56.

    Google Scholar 

  • Dorea, C.C.Y. (1983), Expected Number of Steps of a Random Optimization Method, Journal of Optimization Theory and Applications 39, 165–171.

    Google Scholar 

  • Feller, W. (1968), An Introduction to Probability Theory and Its Applications, vol. 1, John Wiley & Sons, New York, 3rd ed.

    Google Scholar 

  • Kirkpatrick, S., Gelatt, C.D. and Vecchi, M.P. (1983), Optimization by Simulated Annealing, Science {vn220}, 671–680.

    Google Scholar 

  • Kolen, J.F. (1988), Faster Learning through a Probabilistic Approximation Algorithm, Proceedings of the IEEE Second International Conference on Neural Networks, vol. I, 449–454.

    Google Scholar 

  • Muselli, M. and Ridella, S. (1992), Global Optimization of Functions with the Interval Genetic Algorithm, Complex Systems 6, 193–212.

    Google Scholar 

  • Solis, F.J. and Wets, R.J-B. (1981), Minimization by Random Search Techniques, Mathematics of Operation Research 6, 19–30.

    Google Scholar 

  • Törn, A. and Žilinskas, A. (1989), Global Optimization, Springer-Verlag, Berlin.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Muselli, M. A Theoretical Approach to Restart in Global Optimization. Journal of Global Optimization 10, 1–16 (1997). https://doi.org/10.1023/A:1008238928345

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008238928345

Navigation