Advertisement

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

Abstract

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.

Keywords

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

Notes

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.

References

  1. Abualigah LM, Khader AT, Al-Betar MA(2017a) \(\beta \)-hill climbing technique for the text document clustering. In: New trends in information technology NTIT2017 conference, Amman, Jordan. IEEE, pp 1–6Google Scholar
  2. Abualigah LM, Khadery AT, Al-Betar MA, Alyasseri ZAA, Alomari OA,Hanandehk ES(2017b) Feature selection with \(\beta \)-hill climbing search for text clustering application. In: Second palestinian international conference on information and communication technology (PICICT 2017), Gaza, Palestine. IEEE, pp 22–27Google Scholar
  3. Al-Betar MA, Awadallah MA, Bolaji AL, Alijla BO (2017) \(\beta \)-hill climbing algorithm for sudoku game. In: Second Palestinian international conference on information and communication technology (PICICT 2017), Gaza, Palestine. IEEE, pp 84–88Google Scholar
  4. Al-Betar MA, Khader AT, Doush IA (2014) Memetic techniques for examination timetabling. Ann Oper Res 218(1):23–50MathSciNetCrossRefGoogle Scholar
  5. Al-Betar MA (2017) \(\beta \)-hill climbing: an exploratory local search. Neural Comput Appl 28(1):153–168Google Scholar
  6. Al-Dujaili A, Subramanian K, Suresh S (2015) Humancog: a cognitive architecture for solving optimization problems. In: 2015 IEEE congress on, evolutionary computation (CEC). IEEE, pp 3220–3227Google Scholar
  7. Aleti A, Moser I (2016) A systematic literature review of adaptive parameter control methods for evolutionary algorithms. ACM Comput Surv (CSUR) 49(3):56CrossRefGoogle Scholar
  8. Alsukni E, Arabeyyat OS, Awadallah MA, Alsamarraie L, Abu-Doush I, Al-Betar MA (2017) Multiple-reservoir scheduling using B-hill climbing algorithm. J Intell Syst.  https://doi.org/10.1515/jisys-2017-0159
  9. Alyasseri ZAA, Khader AT, Al-Betar MA (2017) Optimal EEG signals denoising using hybrid \(\beta \)-hill climbing algorithm and wavelet transform. In: ICISPC ’17, Penang, Malaysia. ACM, pp 5–11Google Scholar
  10. Alyasseri ZAA, Khader AT, Al-Betar MA, Awadallah MA (2018) Hybridizing \(\beta \)-hill climbing with wavelet transform for denoising ECG signals. Inf Sci 429:229–246Google Scholar
  11. Angeline PJ, Angeline PJ (1995) Adaptive and self-adaptive evolutionary computations. In: Computational intelligence: a dynamic systems perspective. IEEE Press, pp 152–163Google Scholar
  12. Awad N, Ali MZ, Reynolds RG (2015) A differential evolution algorithm with success-based parameter adaptation for cec2015 learning-based optimization. In: 2015 IEEE congress on, evolutionary computation (CEC). IEEE, pp 1098–1105Google Scholar
  13. Awadallah MA, Al-Betar MA, Bolaji AL, Alsukhni EM, Al-Zoubi H (2018) Natural selection methods for artificial bee colony with new versions of onlooker bee. Soft ComputGoogle Scholar
  14. Aydilek İB (2018) A hybrid firefly and particle swarm optimization algorithm for computationally expensive numerical problems. Appl Soft Comput 66:232–249CrossRefGoogle Scholar
  15. Aydın D, Sffltzle T (2015) A configurable generalized artificial bee colony algorithm with local search strategies. In: 2015 IEEE congress on, evolutionary computation (CEC). IEEE, pp 1067–1074Google Scholar
  16. Blum C, Roli A (2003) Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput Surv (CSUR) 35(3):268–308CrossRefGoogle Scholar
  17. BoussaïD I, Lepagnot J, Siarry P (2013) A survey on optimization metaheuristics. Inf Sci 237:82–117MathSciNetCrossRefGoogle Scholar
  18. Corana A, Marchesi M, Martini C, Ridella S (1987) Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm corrigenda for this article is available here. ACM Trans Math Softw (TOMS) 13(3):262–280CrossRefGoogle Scholar
  19. Cui L, Li G, Luo Y, Chen F, Ming Z, Lu N, Lu J (2018) An enhanced artificial bee colony algorithm with dual-population framework. Swarm Evolut Comput 43:184–206CrossRefGoogle Scholar
  20. Dragoi E-N, Dafinescu V (2016) Parameter control and hybridization techniques in differential evolution: a survey. Artif Intell Rev 45(4):447–470CrossRefGoogle Scholar
  21. Eiben ÁE, Hinterding R, Michalewicz Z (1999) Parameter control in evolutionary algorithms. IEEE Trans Evolut Comput 3(2):124–141CrossRefGoogle Scholar
  22. El-Abd M (2015) Hybrid cooperative co-evolution for the cec15 benchmarks. In: 2015 IEEE congress on, evolutionary computation (CEC). IEEE, pp 1053–1058Google Scholar
  23. Feo TA, Resende MGC (1995) Greedy randomized adaptive search procedures. J Global Optim 6(2):109–133MathSciNetCrossRefGoogle Scholar
  24. Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Oper Res 13(5):533–549MathSciNetCrossRefGoogle Scholar
  25. Guo S-M, Tsai JS-H, Yang C-C, Hsu P-H (2015) A self-optimization approach for l-shade incorporated with eigenvector-based crossover and successful-parent-selecting framework on cec 2015 benchmark set. In: 2015 IEEE congress on, evolutionary computation (CEC). IEEE, pp 1003–1010Google Scholar
  26. Guo Z, Liu G, Li D, Wang S (2017) Self-adaptive differential evolution with global neighborhood search. Soft Comput 21(13):3759–3768CrossRefGoogle Scholar
  27. Guo Z, Yang H, Wang S, Zhou C, Liu X (2018) Adaptive harmony search with best-based search strategy. Soft Comput 22(4):1335–1349CrossRefGoogle Scholar
  28. Hansen P, Mladenovi’c N (1999) An introduction to variable neighborhood search. In: Voß S, Martello S, Osman IH, Roucairol C (eds) Metaheuristics: advances and trends in local search paradigms for optimization, chapter 30. Kluwer Academic Publishers, Dordrecht, pp 433–458CrossRefGoogle Scholar
  29. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(1):671–680MathSciNetCrossRefGoogle Scholar
  30. Leboucher C, Shin H-S, Chelouah R, Le Menec S, Siarry P, Formoso M, Tsourdos A, Kotenkoff A (2018) An enhanced particle swarm optimisation method integrated with evolutionary game theory. IEEE Transactions on Games, pp 1–11Google Scholar
  31. Liang J, Qu B, Suganthan P, Chen Q (2014) Problem definitions and evaluation criteria for the cec 2015 competition on learning-based real-parameter single objective optimization. Technical Report201411A, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, SingaporeGoogle Scholar
  32. Liang J, Guo L, Liu R, Qu B (2015) A self-adaptive dynamic particle swarm optimizer. In: 2015 IEEE Congress on, Evolutionary Computation (CEC). IEEE, pp 3206–3213Google Scholar
  33. Lourenço HR, Martin OC, Stützle T (2003) Iterated local search. In: Glover F, Kochenberger GA (eds) Handbook of Metaheuristics. International series in operations research & management science, vol 57. Springer, Boston, MA, pp 320–353Google Scholar
  34. Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579MathSciNetzbMATHGoogle Scholar
  35. Mezura-Montes E, Palomeque-Ortiz AG (2009) Self-adaptive and deterministic parameter control in differential evolution for constrained optimization. Springer, Berlin, pp 95–120Google Scholar
  36. Mirjalili S, Lewis A (2013) S-shaped versus v-shaped transfer functions for binary particle swarm optimization. Swarm Evolut Comput 9:1–14CrossRefGoogle Scholar
  37. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67CrossRefGoogle Scholar
  38. Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27(2):495–513CrossRefGoogle Scholar
  39. Molga M, Smutnicki C (2005) Test functions for optimization needs. In: Test functions for optimization needsGoogle Scholar
  40. Noorbin SFEH, Alfi A (2018) Adaptive parameter control of search group algorithm using fuzzy logic applied to networked control systems. Soft Computing 22(23):7939–7960CrossRefGoogle Scholar
  41. Osman IH, Laporte G (1996) Metaheuristics: A bibliography. Ann Oper Res 63(5):511–623CrossRefGoogle Scholar
  42. Poláková R, Tvrdík J, Bujok P (2015) Cooperation of optimization algorithms: a simple hierarchical model. In: 2015 IEEE congress on, evolutionary computation (CEC), IEEE, pp 1046–1052Google Scholar
  43. Rueda JL, Erlich I (2015) Testing mvmo on learning-based real-parameter single objective benchmark optimization problems. In: 2015 IEEE congress on, evolutionary computation (CEC), IEEE, pp 1025–1032Google Scholar
  44. Sallam KM, Sarker RA, Essam DL, Elsayed SM (2015) Neurodynamic differential evolution algorithm and solving cec2015 competition problems. In: 2015 IEEE congress on, evolutionary computation (CEC), IEEE, pp 1033–1040Google Scholar
  45. Sörensen K (2015) Metaheuristics-the metaphor exposed. Int Trans Oper Res 22(1):3–18MathSciNetCrossRefGoogle Scholar
  46. Suganthan P, Hansen N, Liang J, Deb K, CY, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real parameter optimization. In: Technical report, Nanyang Technological University, NanyangGoogle Scholar
  47. Tanweer MR, Suresh S, Sundararajan N (2017) Development of a higher order cognitive optimization algorithm. In: 2017 IEEE congress on evolutionary computation (CEC), pp 2752–2758Google Scholar
  48. Wang H, Zhou X, Sun H, Yu X, Zhao J, Zhang H, Cui L (2017) Firefly algorithm with adaptive control parameters. Soft Comput 21(17):5091–5102CrossRefGoogle Scholar
  49. Wessing S, Preuss M, Rudolph G (2011) When parameter tuning actually is parameter control. In: Proceedings of the 13th annual conference on Genetic and evolutionary computation, ACM, pp 821–828Google Scholar
  50. Xue Y, Jiang J, Zhao B, Ma T (2018) A self-adaptive artificial bee colony algorithm based on global best for global optimization. Soft Comput 22(9):2935–2952CrossRefGoogle Scholar
  51. Yu C, Kelley LC, Tan Y (2015) Dynamic search fireworks algorithm with covariance mutation for solving the CEC 2015 learning based competition problems. In: 2015 IEEE congress on, evolutionary computation (CEC), IEEE, pp 1106–1112Google Scholar
  52. Zhao H, Zhang C, Ning J (2019) A best firework updating information guided adaptive fireworks algorithm. Neural Comput Appl 31(1):79–99CrossRefGoogle Scholar
  53. Zheng Y-J, Wu X-B (2015) Tuning maturity model of ecogeography-based optimization on cec 2015 single-objective optimization test problems. In: 2015 IEEE congress on, evolutionary computation (CEC), IEEE, pp 1018–1024Google Scholar

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

Personalised recommendations