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On Optimization and Extreme Value Theory

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Abstract

We present a statistical study of the distribution of the objective value of solutions (outcomes) obtained by stochastic optimizers. Our results are based on three optimization procedures: random search and two evolution strategies. We study the fit of the outcomes to an extreme value distribution, namely the Weibull distribution through parametric estimation. We discuss the interpretation of the parameters of the estimated extreme value distribution in the context of the optimization problem and suggest that they can be used to characterize the performance of the optimizer.

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References

  • T. Bäck, F. Hoffmeister, and H.-P. Schwefel. “A Survey of Evolution Strategies. Genetic Algorithms”, in Proceedings of the Fourth International Conference at San Diego, Ca., Morgan Kaufmann: San Mateo, Ca., pp. 2–9, 1991.

    Google Scholar 

  • P. Embrechts, C. Klüppelberg, and T. Mikosch, Modelling Extremal Events for Insurance and Finance, Springer-Verlag: Berlin, 1997.

    Google Scholar 

  • M. Falk, J. Hüsler, and R. D. Reiss, Laws of small numbers: extremes and rare events, DMV-Seminar Series 23, Birkhäuser: Basel and Boston, 1994.

    Google Scholar 

  • C. M. Fonseca and P. J. Fleming, “On the performance and comparison of stochastic multiobjective optimizers”, Lecture Notes in Computer Science, vol. 1141, Springer, pp. 584–593, 1996.

  • M. R. Leadbetter, G. Lindgren, and H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer-Verlag: New York, 1983.

    Google Scholar 

  • R. Lockhart and M. Stephens, “Estimation and tests of fit for the three-parameter Weibull distribution,” J.R. Statist. Soc. B, vol. 56, pp. 491–500, 1994.

    Google Scholar 

  • R.-D. Reiss and M. Thomas, Statistical Analysis of Extreme Values with Application to Insurance, Finance, Hydrology and other fields, Birkhäuser: Basel, 1997.

    Google Scholar 

  • R. L. Smith, “Extreme value theory based on the largest annual events”, J. Hydrology vol. 86, pp. 27–43, 1986.

    Google Scholar 

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Authors and Affiliations

  1. Dept. Math. Statistics, University of Bern, Sidlerstr. 5, CH-3012, Bern, Switzerland

    Jürg Hüsler & Andreia Hall

  2. Department of Mathematics, 3810-193, Aveiro, Portugal

    Pedro Cruz

  3. ECEH, University of the Algarve, Campus de Gambelas, 8000, Faro, Portugal

    Carlos M. Fonseca

Authors
  1. Jürg Hüsler
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  2. Pedro Cruz
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  3. Andreia Hall
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  4. Carlos M. Fonseca
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Hüsler, J., Cruz, P., Hall, A. et al. On Optimization and Extreme Value Theory. Methodology and Computing in Applied Probability 5, 183–195 (2003). https://doi.org/10.1023/A:1024505701928

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