Soft Computing

, Volume 23, Issue 24, pp 13489–13512 | Cite as

Adaptive \(\beta -\)hill climbing for optimization

  • Mohammed Azmi Al-BetarEmail author
  • Ibrahim Aljarah
  • Mohammed A. Awadallah
  • Hossam Faris
  • Seyedali Mirjalili
Methodologies and Application


In this paper, an adaptive version of \(\beta -\)hill climbing is proposed. In the original \(\beta -\)hill climbing, two control parameters are utilized to strike the right balance between a local-nearby exploitation and a global wide-range exploration during the search: \({\mathcal {N}}\) and \(\beta \), respectively. Conventionally, these two parameters require an intensive study to find their suitable values. In order to yield an easy-to-use optimization method, this paper proposes an efficient adaptive strategy for these two parameters in a deterministic way. The proposed adaptive method is evaluated against 23 global optimization functions. The selectivity analysis to determine the optimal progressing values of \({\mathcal {N}}\) and \(\beta \) during the search is carried out. Furthermore, the behavior of the adaptive version is analyzed based on various problems with different complexity levels. For comparative evaluation, the adaptive version is initially compared with the original one as well as with other local search-based methods and other well-regarded methods using the same benchmark functions. Interestingly, the results produced are very competitive with the other methods. In a nutshell, the proposed adaptive \(\beta -\)hill climbing is able to achieve the best results on 10 out of 23 test functions. For more validation, the test functions established in IEEE-CEC2015 are used with various scaling values. The comparative results show the viability of the proposed adaptive method.


Metaheuristics \(\beta \)-hill climbing Global optimization Control parameters 


Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Ethical approval

This article does not contain any studies with animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Information Technology, Al-Huson University CollegeAl-Balqa Applied UniversityIrbidJordan
  2. 2.King Abdullah II School for Information TechnologyThe University of JordanAmmanJordan
  3. 3.Department of Computer ScienceAl-Aqsa UniversityGazaPalestine
  4. 4.Institute for Integrated and Intelligent SystemsGriffith UniversityBrisbaneAustralia

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