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Nature-Inspired Metaheuristic Search Algorithms for Optimizing Benchmark Problems: Inclined Planes System Optimization to State-of-the-Art Methods

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A Correction to this article was published on 21 November 2022

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Abstract

In the literature, different types of inclined planes system optimization (IPO) algorithms have been proposed and evaluated in various applications. Due to the large number of variants and applications, this work provides an overview of IPO’s state-of-the-art in terms of variants presented, applications, statistical evaluation, and analysis. In addition, the performance of IPO variants are evaluated and compared. The results are benchmarked against other algorithms. Final evaluation based on statistical analysis and a new and effective ranking methodology indicates the optimal performance and relative success of all IPO variants and their performance in comparison with other recent diverse metaheuristic search competitors, including reinforcement learning, evolution-based, swarm-based, physics-based, and human-based. The performance of IPO variants shown that the use of bio-operators to improve the standard version is more successful than other applied approaches. So that, the successful performance of SIPO + M with a minimum overall ranking of 0.73 has been ahead of all versions, and the complexity of IPO equations has also been led to a high time loss and achieving a maximum overall ranking of 2.07. Among other algorithms, it shown that versions without control parameters perform exploration and exploitation processes intelligently and more successful. For example, POA-I, POA-II, SLOA, OPA, and CMBO are among the methods that achieved the best performance, with minimum overall ranking values of 0.363, 0.384, 0.387, 0.424, and 0.933, respectively.

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Acknowledgments

Ali Mohammadi would like to sincerely thank his family and wife for their support and kindness during the preparation and submission to acceptance of this research work. He wishes the best for his life together. Also, the authors are grateful to all supporters and colleagues in partner universities.

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All source codes are fully and publicly available at https://github.com/ali-ece

Appendix

Appendix

As a reference for readers to access the codes of various IPO methods, the source codes of all versions of IPO, MIPO, SIPO, MOIPO, MOMIPO, and MOSIPO in MATLAB can be downloaded and used for free and publicly through the following link: https://github.com/ali-ece.

See Table 20.

Table 20 Benchmark functions [7, 43, 167]

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Mohammadi, A., Sheikholeslam, F. & Mirjalili, S. Nature-Inspired Metaheuristic Search Algorithms for Optimizing Benchmark Problems: Inclined Planes System Optimization to State-of-the-Art Methods. Arch Computat Methods Eng 30, 331–389 (2023). https://doi.org/10.1007/s11831-022-09800-0

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