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Laplace’s rule of succession: a simple and efficient way to compare metaheuristics

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Abstract

Metaheuristics are algorithms that are used to solve difficult optimization problems. They are typically stochastic approaches; hence, proper statistical tests are needed to compare them. However, choosing an appropriate statistical test is not trivial given that each test requires some assumptions to be true before the test can be used. Moreover, the p-values associated with a statistical test is usually difficult to interpret. In this paper, we propose the use of Laplace’s rule of succession to compare different metaheuristic approaches. The rule is simple, intuitive and easy to compute. It can be used alone or to complement a statistical test. The process of using the rule for comparison purposes is clearly explained and applied to a typical scenario encountered in the field of metaheuristics. In this scenario, an improved variant of an existing metaheuristic algorithm is proposed. To evaluate the performance of the two algorithms, Laplace’s rule and a traditional statistical test are used. Analysis of the results and how to interpret them are provided. The results show that Laplace’s rule is consistent with the used statistical test. Furthermore, the rule is easier to compute and interpret.

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Notes

  1. A Notebook document with the code and results can be requested from the corresponding author.

  2. The classical Pearson’s correlation coefficient evaluates how much the relationship is linear. Actually, it is also strong on this small benchmark set and these algorithms A and B. However, the Spearman’s rank correlation is more general and robust.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive and helpful comments and suggestions. This work was supported by Gulf University for Science and Technology (Kuwait) under Grant 251896.

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Authors and Affiliations

  1. Centre for Applied Mathematics and Bioinformatics, and Computer Science Department, Gulf University for Science & Technology, Mubarak Al-Abdullah, Kuwait

    Mahamed Ghasib Hussein Omran

  2. Laboratory of Images Signals and Intelligent Systems (LiSSi), University of Paris-Est Créteil (UPEC), Créteil, France

    Maurice Clerc

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  1. Mahamed Ghasib Hussein Omran
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  2. Maurice Clerc
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Correspondence to Mahamed Ghasib Hussein Omran.

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Omran, M.G.H., Clerc, M. Laplace’s rule of succession: a simple and efficient way to compare metaheuristics. Neural Comput & Applic 35, 11807–11814 (2023). https://doi.org/10.1007/s00521-023-08322-5

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