Skip to main content
SpringerLink
Log in

\(\beta\)-Hill climbing: an exploratory local search

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Hill climbing method is an optimization technique that is able to build a search trajectory in the search space until reaching the local optima. It only accepts the uphill movement which leads it to easily get stuck in local optima. Several extensions to hill climbing have been proposed to overcome such problem such as Simulated Annealing, Tabu Search. In this paper, an extension version of hill climbing method has been proposed and called \(\beta\)-hill climbing. A stochastic operator called \(\beta\)-operator is utilized in hill climbing to control the balance between the exploration and exploitation during the search. The proposed method has been evaluated using IEEE-CEC2005 global optimization functions. The results show that the proposed method is a very efficient enhancement to the hill climbing providing powerful results when it compares with other advanced methods using the same global optimization functions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. The downhill move is used for minimization problem.

References

  1. Al-Betar MA, Khader AT, Awadallah MA, Abdalkareem ZA (2015) Island-based harmony search for optimization problems. Expert Syst Appl 42:2026–2035

    Article  Google Scholar 

  2. Al-Betar MA, Khader AT, Awadallah MA, Alawan MH, Zaqaibeh B (2013) Cellular harmony search for optimization problems. J Appl Math. doi:10.1155/2013/139464

    MathSciNet  Google Scholar 

  3. Al-Betar MA, Khader AT, Doush IA (2014) Memetic techniques for examination timetabling. Ann OR 218(1):23–50

    Article  MathSciNet  MATH  Google Scholar 

  4. Auger A, Hansen N (2005) Performance evaluation of an advanced local search evolutionary algorithm. In: The 2005 IEEE Congress on Evolutionary Computation (CEC’2005), vol 2. IEEE, pp 1777–1784

  5. Auger A, Hansen N (2005) A restart CMA evolution strategy with increasing population size. In: The 2005 IEEE Congress on Evolutionary Computation (CEC’2005), vol 2. IEEE, pp 1769–1776

  6. Azar AT, Vaidyanathan S (2015) Computational intelligence applications in modeling and control, vol 575. Springer, Berlin. doi:10.1007/978-3-319-11017-2

    Google Scholar 

  7. Ballester PJ, Stephenson J, Carter JN, Gallagher K (2005) Real-parameter optimization performance study on the CEC-2005 benchmark with SPC-PNX. In: The 2005 IEEE Congress on Evolutionary Computation (CEC’2005), vol 1. IEEE, pp 498–505

  8. Blum C, Roli A (2003) Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput Surv 35(3):268–308

    Article  Google Scholar 

  9. Corana A, Marchesi M, Martini C, Ridella S (1987) Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm. ACM Trans Math Softw (TOMS) 13(3):262–280

    Article  MathSciNet  MATH  Google Scholar 

  10. Feo TA, Resende MGC (1995) Greedy randomized adaptive search procedures. J Glob Optim 6(2):109–133

    Article  MathSciNet  MATH  Google Scholar 

  11. García-Martínez C, Lozano M (2005) Hybrid real-coded genetic algorithms with female and male differentiation. In: The 2005 IEEE Congress on Evolutionary Computation (CEC’2005), vol 1. IEEE, pp 896–903

  12. Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Oper Res 13(5):533–549

    Article  MathSciNet  MATH  Google Scholar 

  13. Glover F, Laguna M (1997) Tabu search. Kluwer, Dordrecht

    Book  MATH  Google Scholar 

  14. Hansen P, Mladenovic N (1999) An introduction to variable neighborhood search. In: Vo S, Martello S, Osman I, Roucairol C (eds) Metaheuristics: advances and trends in local search paradigms for optimization, chap 30. Kluwer, Dordrecht, pp 433–458

    Chapter  Google Scholar 

  15. Hansen P, Mladenovic N (2001) Variable neighborhood search: principles and applications. Eur J Oper Res 130(3):449–467

    Article  MathSciNet  MATH  Google Scholar 

  16. Hassanien A, Tolba M, Azar A (2014) Advanced machine learning technologies and applications. In: Second international conference, AMLTA, vol 488. Springer. doi:10.1007/978-3-319-13461-1

  17. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(1):671–680

    Article  MathSciNet  MATH  Google Scholar 

  18. Lewis R (2008) A survey of metaheuristic-based techniques for university timetabling problems. OR Spectr 30:167–190

    Article  MathSciNet  MATH  Google Scholar 

  19. Liang JJ, Suganthan PN (2005) Dynamic multi-swarm particle swarm optimizer with local search. In: The 2005 IEEE Congress on Evolutionary Computation (CEC’2005), vol 1. IEEE, pp 522–528

  20. Loureno HR, Martin OC, Sttzle T (2002) Iterated local search. In: Glover F, Kochenberger G (ed) Handbook of metaheuristics. International series in operations research and management science, vol 57. Kluwer, Dordrecht, pp 321–353

  21. Molina D, Herrera F, Lozano M (2005) Adaptive local search parameters for real-coded memetic algorithms. In: The 2005 IEEE Congress on Evolutionary Computation (CEC’2005), vol 1. IEEE, pp 888–895

  22. Osman I, Laporte G (1996) Metaheuristics: a bibliography. Ann Oper Res 63(5):511–623

    Article  MATH  Google Scholar 

  23. Posik P (2005) Real-parameter optimization using the mutation step co-evolution. In: The 2005 IEEE Congress on Evolutionary Computation (CEC’2005), vol 1. IEEE, pp 872–879

  24. Qin AK, Suganthan PN (2005) Self-adaptive differential evolution algorithm for numerical optimization. In: The 2005 IEEE Congress on Evolutionary Computation (CEC’2005), vol 2. IEEE, pp 1785–1791

  25. Ronkkonen J, Kukkonen S, Price KV (2005) Real-parameter optimization with differential evolution. In: The 2005 IEEE Congress on Evolutionary Computation (CEC’2005), vol 1. IEEE, pp 506–513

  26. Sinha A, Tiwari S, Deb K (2005) A population-based, steady-state procedure for real-parameter optimization. In: The 2005 IEEE Congress on Evolutionary Computation (CEC’2005), vol 1. IEEE, pp 514–521

  27. Suganthan P, Hansen N, Liang J, Deb K, Chen Y-P, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real parameter optimization. Technical report, Nanyang Technological University

  28. Suman B, Kumar P (2006) A survey of simulated annealing as a tool for single and multiobjective optimization. J Oper Res Soc 57:1143–1160

    Article  MATH  Google Scholar 

  29. Črepinšek M, Liu SH, Mernik M (2013) Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput Surv 45(3):35:1–35:33

    MATH  Google Scholar 

  30. Yuan B, Gallagher M (2005) Experimental results for the special session on real-parameter optimization at CEC 2005: a simple, continuous EDA. In: The 2005 IEEE Congress on Evolutionary Computation (CEC’2005), vol 2. IEEE, pp 1792–1799

  31. Zhu Q, Azar AT (2015) Complex system modelling and control through intelligent soft computations, vol 319. Springer, Berlin. doi:10.1007/978-3-319-12883-2

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Technology, Al-Huson University College, Al-Balqa Applied University, P.O. Box 50, Al-Huson, Irbid, Jordan

    Mohammed Azmi Al-Betar

Authors
  1. Mohammed Azmi Al-Betar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammed Azmi Al-Betar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Al-Betar, M.A. \(\beta\)-Hill climbing: an exploratory local search. Neural Comput & Applic 28 (Suppl 1), 153–168 (2017). https://doi.org/10.1007/s00521-016-2328-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-016-2328-2

Keywords

Search

Navigation