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Simple Random Sampling Estimation of the Number of Local Optima

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Parallel Problem Solving from Nature – PPSN XIV (PPSN 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9921))

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Abstract

We evaluate the performance of estimating the number of local optima by estimating their proportion in the search space using simple random sampling (SRS). The performance of this method is compared against that of the jackknife method. The methods are used to estimate the number of optima in two landscapes of random instances of some combinatorial optimisation problems. SRS provides a cheap, unbiased and accurate estimate when the proportion is not exceedingly small. We discuss choices of confidence interval in the case of extremely small proportion. In such cases, the method more likely provides an upper bound to the number of optima and can be combined with other methods to obtain a better lower bound. We suggest that SRS should be the first choice for estimating the number of optima when no prior information is available about the landscape under study.

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Authors and Affiliations

  1. School of Computer Science, University of Birmingham, Birmingham, B15 2TT, UK

    Khulood Alyahya & Jonathan E. Rowe

Authors
  1. Khulood Alyahya
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  2. Jonathan E. Rowe
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Corresponding author

Correspondence to Khulood Alyahya .

Editor information

Editors and Affiliations

  1. University of Manchester, Manchester, United Kingdom

    Julia Handl

  2. Edinburgh Napier University, Edinburgh, United Kingdom

    Emma Hart

  3. Aston University, Birmingham, United Kingdom

    Peter R. Lewis

  4. University of Manchester, Manchester, United Kingdom

    Manuel López-Ibáñez

  5. University of Stirling, Stirling, United Kingdom

    Gabriela Ochoa

  6. Edinburgh Napier University, Edinburgh, United Kingdom

    Ben Paechter

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© 2016 Springer International Publishing AG

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Alyahya, K., Rowe, J.E. (2016). Simple Random Sampling Estimation of the Number of Local Optima. In: Handl, J., Hart, E., Lewis, P., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds) Parallel Problem Solving from Nature – PPSN XIV. PPSN 2016. Lecture Notes in Computer Science(), vol 9921. Springer, Cham. https://doi.org/10.1007/978-3-319-45823-6_87

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  • DOI: https://doi.org/10.1007/978-3-319-45823-6_87

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45822-9

  • Online ISBN: 978-3-319-45823-6

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