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A novel meta-heuristic algorithm for solving numerical optimization problems: Ali Baba and the forty thieves

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Abstract

This paper presents a novel meta-heuristic algorithm called Ali Baba and the forty thieves (AFT) for solving global optimization problems. Recall the famous tale of Ali Baba and the forty thieves, where Ali Baba once saw a gang of forty thieves enter a strange cave filled with all kinds of treasures. The strategies pursued by the forty thieves in the search for Ali Baba inspired us to design ideas and underlie the basic concepts to put forward the mathematical models and implement the exploration and exploitation processes of the proposed algorithm. The performance of the AFT algorithm was assessed on a set of basic benchmark test functions and two more challenging benchmarks called IEEE CEC-2017 and IEEE CEC-C06 2019 benchmark test functions. These benchmarks cover simple and complex test functions with various dimensions and levels of complexity. An extensive comparative study was performed between the AFT algorithm and other well-studied algorithms, and the significance of the results was proved by statistical test methods. To study the potential performance of AFT, its further development is discussed and carried out from five aspects. Finally, the applicability of the AFT algorithm was subsequently demonstrated in solving five engineering design problems. The results in both benchmark functions and engineering problems show that the AFT algorithm has stronger performance than other competitors’ algorithms.

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  1. Al-Balqa Applied University, Al-Salt, Jordan

    Malik Braik & Mohammad Hashem Ryalat

  2. Yarmouk University, Irbid, Jordan

    Hussein Al-Zoubi

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  1. Malik Braik
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  2. Mohammad Hashem Ryalat
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Appendices

Appendix A. Unimodal, multimodal and fixed-dimension multimodal functions

A detailed description of the unimodal benchmark functions (\(\hbox {F}_1\)–\(\hbox {F}_7\)), multimodal benchmark functions (\(\hbox {F}_8\)–\(\hbox {F}_{{13}}\)) and fixed-dimension multimodal benchmark functions (\(\hbox {F}_{{14}}\)–\(\hbox {F}_{{23}}\)) is tabulated in Table 33.

Table 33 Characteristics of the unimodal, multimodal and fixed-dimension multimodal functions used in this work
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Appendix B. IEEE CEC-2017 test suite

A description of the IEEE CEC-2017 benchmark test functions is shown in Table 34.

Table 34 Characteristics of the IEEE CEC-2017 benchmark test functions
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Appendix C. IEEE CEC-C06 2019 benchmark test functions

A description of the IEEE CEC-C06 2019 benchmark functions is given in Table 35.

Table 35 Characteristics of the IEEE CEC-C06 2019 benchmark functions
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Braik, M., Ryalat, M.H. & Al-Zoubi, H. A novel meta-heuristic algorithm for solving numerical optimization problems: Ali Baba and the forty thieves. Neural Comput & Applic 34, 409–455 (2022). https://doi.org/10.1007/s00521-021-06392-x

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