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Sample size calculations for the experimental comparison of multiple algorithms on multiple problem instances

Author

Listed:
  • Felipe Campelo

    (Aston University
    Universidade Federal de Minas Gerais)

  • Elizabeth F. Wanner

    (Aston University
    CEFET-MG)

Abstract

This work presents a statistically principled method for estimating the required number of instances in the experimental comparison of multiple algorithms on a given problem class of interest. This approach generalises earlier results by allowing researchers to design experiments based on the desired best, worst, mean or median-case statistical power to detect differences between algorithms larger than a certain threshold. Holm’s step-down procedure is used to maintain the overall significance level controlled at desired levels, without resulting in overly conservative experiments. This paper also presents an approach for sampling each algorithm on each instance, based on optimal sample size ratios that minimise the total required number of runs subject to a desired accuracy in the estimation of paired differences. A case study investigating the effect of 21 variants of a custom-tailored Simulated Annealing for a class of scheduling problems is used to illustrate the application of the proposed methods for sample size calculations in the experimental comparison of algorithms.

Suggested Citation

  • Felipe Campelo & Elizabeth F. Wanner, 2020. "Sample size calculations for the experimental comparison of multiple algorithms on multiple problem instances," Journal of Heuristics, Springer, vol. 26(6), pages 851-883, December.
    • Handle: RePEc:spr:joheur:v:26:y:2020:i:6:d:10.1007_s10732-020-09454-w
    DOI: 10.1007/s10732-020-09454-w
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    References listed on IDEAS

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    1. J. N. Hooker, 1994. "Needed: An Empirical Science of Algorithms," Operations Research, INFORMS, vol. 42(2), pages 201-212, April.
    2. Felipe Campelo & Fernanda Takahashi, 2019. "Sample size estimation for power and accuracy in the experimental comparison of algorithms," Journal of Heuristics, Springer, vol. 25(2), pages 305-338, April.
    3. Marie Coffin & Matthew J. Saltzman, 2000. "Statistical Analysis of Computational Tests of Algorithms and Heuristics," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 24-44, February.
    4. Vallada, Eva & Ruiz, Rubén, 2011. "A genetic algorithm for the unrelated parallel machine scheduling problem with sequence dependent setup times," European Journal of Operational Research, Elsevier, vol. 211(3), pages 612-622, June.
    5. Catherine C. McGeoch, 1996. "Feature Article---Toward an Experimental Method for Algorithm Simulation," INFORMS Journal on Computing, INFORMS, vol. 8(1), pages 1-15, February.
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