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Rao algorithms based on elite local search method

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Abstract

The Rao algorithms, which have been proposed for solving complex and continuous optimization problems lately, are described as metaphor-less optimization algorithms because they do not contain algorithm-specific parameters. The Rao algorithms have variants called Rao-1, Rao-2 and Rao-3, respectively, depending on different population updating procedures. In Rao 1–3 algorithms, random interactions between candidate solutions and the best and worst solution in the whole population for solving optimizations problems were determined as the basic principle. Although this situation makes the Rao 1–3 algorithms increase the speed of convergence, it can cause the diversity of candidate solutions to decrease and the local search capacity to reduce. In this study, a new elite local search procedure was added to the population updating procedure of Rao algorithms to expand the capacity of Rao 1–3 algorithms and develop their solutions. The proposed method was called ELSRao-1, ELSRao-2 and ELSRao-3. Fifteen unconstrained unimodal, fifteen unconstrained multimodal functions and twenty-nine unconstrained CEC 2017 benchmark test functions were used to analyze the performance of the proposed ELSRao 1–3 algorithms. Jaya, dragonfly algorithm, arithmetic optimization algorithm, whale optimization algorithm and standard Rao 1–3 algorithms which are all state-of-the-art algorithms were used to compare the superiority and success of the proposed ELSRao 1–3 algorithms in benchmark functions. Friedman's mean rank test and Tukey–Kramer post hoc test were applied for statistical analysis. According to the experimental studies and statistical analysis, it was concluded that the proposed ELSRao 1–3 algorithms proved to be efficient and robust in the solution to unconstrained optimization problems.

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Source code can be found at https://github.com/mftefek/ElitLocalSearchProsedure.

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Authors and Affiliations

  1. Departmant of Computer Engineering, Osmaniye Korkut Ata University, Osmaniye, Turkey

    Mehmet Fatih Tefek

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  1. Mehmet Fatih Tefek
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M.F.T.: Methodology. Writing—original draft. Conceptualization. Validation. Writing—review & editing.

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Correspondence to Mehmet Fatih Tefek.

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Appendix

Appendix

Tables used to explain the ELSRao-1 method: (Tables 10, 11, 12).

Table 10 Demonstration of the application of the proposed ELSRao-1 in the first iteration to the F1 (sphere) function implementation
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Table 11 Demonstration of the application of the proposed ELSRao-1 in 10th iteration to the F1 (sphere) function implementation
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Table 12 Demonstration of the application of the proposed ELSRao-1 in 20th iteration to the F1 (sphere) function implementation
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Experimental study results: (Tables 13, 14, 15).

Table 13 Experimental study results of unimodal benchmark function (F1–F15)
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Table 14 Experimental study results of multimodal benchmark functions (F16–F30)
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Table 15 Experimental study results of unconstrained CEC 2017 functions
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Tukey–Kramer post hoc test statistical analyzes: (Tables 16, 17, 18).

Table 16 Tukey–Kramer Post hoc test analysis results of ELSRao-1 and other algorithms for unimodal benchmark functions
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Table 17 Tukey–Kramer Post hoc test analysis results of ELSRao-1 and other algorithms for multimodal benchmark functions
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Table 18 Tukey–Kramer Post hoc test analysis results of ELSRao-1 and other algorithms for CEC 2017 benchmark functions
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Tefek, M.F. Rao algorithms based on elite local search method. Neural Comput & Applic 35, 4435–4465 (2023). https://doi.org/10.1007/s00521-022-07932-9

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