Skip to main content
SpringerLink
Log in

A novel cuckoo search algorithm with adaptive discovery probability based on double Mersenne numbers

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

Abstract

Cuckoo search algorithm is one of the most prominent meta-heuristic optimization algorithms which is applied to various applications. The discovery probability is the one and the only tuning parameter of the cuckoo search algorithm. The physical meaning of this parameter contradicts its implementation in the standard algorithm. Therefore, this study concerns the correction to the definition and implementation of the cuckoo search algorithm to resolve this conflict. Moreover, a novel algorithm called double exponential cuckoo search is proposed, in which the discovery probability became adaptive based on the concept of the double Mersenne numbers. The proposed algorithm is compared to nine other variants to find the best variant that makes the discovery probability adaptive. All the variants are compared and tested on 30 and 50 dimensions of CEC2017 benchmark functions. The results have been statistically proved using the sign test, Wilcoxon signed-rank test, and Friedman test. Moreover, multiple graphical methods are also used to visualize the median performance such as Violin plots and mean convergence graphs. Simulation results prove the superior performance of the proposed algorithm over all other variants.

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
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: 2009 World congress on nature & biologically inspired computing (NaBIC). IEEE, pp 210–214

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

    Article  Google Scholar 

  3. Storn R, Price K (1996) Minimizing the real functions of the ICEC’96 contest by differential evolution. In: Proceedings of IEEE international conference on evolutionary computation. IEEE, pp 842–844

  4. Koza JR (1994) Genetic programming II: automatic discovery of reusable subprograms. Cambridge, MA, USA 13(8):32

    MATH  Google Scholar 

  5. Holland J (1975) Adaptation in natural and artificial systems: an introductory analysis with application to biology. Control and artificial intelligence. University of Michigan Press, Ann Arbor

    MATH  Google Scholar 

  6. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60

    Article  Google Scholar 

  7. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671

    Article  MathSciNet  Google Scholar 

  8. Glover F (1977) Heuristics for integer programming using surrogate constraints. Decis Sci 8(1):156

    Article  Google Scholar 

  9. Al-Betar MA (2017) \(\beta \)-Hill climbing: an exploratory local search. Neural Comput Appl 28(1):153

    Article  Google Scholar 

  10. Koziel S, Yang XS (2011) Computational optimization, methods and algorithms, vol 356. Springer, Berlin

    Book  Google Scholar 

  11. Bolaji AL, Al-Betar MA, Awadallah MA, Khader AT, Abualigah LM (2016) A comprehensive review: Krill Herd algorithm (KH) and its applications. Appl Soft Comput 49:437

    Article  Google Scholar 

  12. Yang XS (2008) N.I.M. Algorithms. Luniver press, Beckington, pp 242–246

    Google Scholar 

  13. Kennedy J, Eberhart R (1995) Particle swarm optimization (PSO). In: Proc. IEEE international conference on neural networks, Perth, Australia, pp 1942–1948

  14. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Tech. rep., Technical report-tr06, Erciyes university, engineering faculty, computer...

  15. Feng Y, Wang GG, Deb S, Lu M, Zhao XJ (2017) Solving 0–1 knapsack problem by a novel binary monarch butterfly optimization. Neural Comput Appl 28(7):1619

    Article  Google Scholar 

  16. Biswas P, Pal BB (2019) A fuzzy goal programming method to solve congestion management problem using genetic algorithm. Decis Mak Appl Manag Eng 2(2):36

    Article  Google Scholar 

  17. Saji Y, Riffi ME (2016) A novel discrete bat algorithm for solving the travelling salesman problem. Neural Comput Appl 27(7):1853

    Article  Google Scholar 

  18. Dalfard VM, Kaveh M, Nosratian NE (2013) Two meta-heuristic algorithms for two-echelon location-routing problem with vehicle fleet capacity and maximum route length constraints. Neural Comput Appl 23(7):2341

    Article  Google Scholar 

  19. Chung H, Shin KS (2020) Genetic algorithm-optimized multi-channel convolutional neural network for stock market prediction. Neural Comput Appl 32(12):7897

    Article  Google Scholar 

  20. Shareh MB, Bargh SH, Hosseinabadi AAR, Slowik A (2020) An improved bat optimization algorithm to solve the tasks scheduling problem in open shop. Neural Comput Appl 1–15

  21. Yang XS, Deb S (2010) Engineering optimisation by cuckoo search. arXiv preprint arXiv:1005.2908

  22. Pare S, Kumar A, Bajaj V, Singh GK (2016) A multilevel color image segmentation technique based on cuckoo search algorithm and energy curve. Appl Soft Comput 47:76

    Article  Google Scholar 

  23. Liu X, Fu H (2014) PSO-based support vector machine with Cuckoo search technique for clinical disease diagnoses. Sci World J

  24. Goel S, Sharma A, Bedi P (2011) Cuckoo Search Clustering Algorithm: a novel strategy of biomimicry. In: 2011 World congress on information and communication technologies. IEEE, pp 916–921

  25. Sekhar P, Mohanty S (2016) An enhanced cuckoo search algorithm based contingency constrained economic load dispatch for security enhancement. Int J Electr Power Energy Syst 75:303

    Article  Google Scholar 

  26. Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17

    Article  Google Scholar 

  27. Devabalaji K, Yuvaraj T, Ravi K (2016) An efficient method for solving the optimal sitting and sizing problem of capacitor banks based on cuckoo search algorithm. Ain Shams Eng J

  28. Valian E, Mohanna S, Tavakoli S (2011) Improved cuckoo search algorithm for global optimization. Int J Commun Inf Technol 1(1):31

    MATH  Google Scholar 

  29. Mishra SK (2012) Global optimization of some difficult benchmark functions by cuckoo-host co-evolution meta-heuristics. Available at SSRN 2128079

  30. Huang H, Hu P (2016) A self-adaptive mutation cuckoo search algorithm. In: 2016 12th World congress on intelligent control and automation (WCICA). IEEE, pp 1064–1068

  31. Dhabal S, Tagore S, Mukherjee D (2016) An improved cuckoo search algorithm for numerical optimization. In: 2016 International conference on computer, electrical & communication engineering (ICCECE). IEEE, pp 1–7

  32. Chi R, Su YX, Zhang DH, Chi XX (2016) Adaptive cuckoo search algorithm for continuous function optimization problems. In: 2016 12th World congress on intelligent control and automation (WCICA). IEEE, pp 672–676

  33. Rakhshani H, Rahati A (2017) Snap-drift cuckoo search: a novel cuckoo search optimization algorithm. Appl Soft Comput 52:771

    Article  Google Scholar 

  34. Cheng J, Wang L, Jiang Q, Xiong Y (2018) A novel cuckoo search algorithm with multiple update rules. Appl Intell 48(11):4192

    Article  Google Scholar 

  35. Mareli M, Twala B (2018) An adaptive cuckoo search algorithm for optimisation. Appl Comput Inform 14(2):107

    Article  Google Scholar 

  36. Reda M, Haikal AY, Elhosseini MA, Badawy M (2019) An innovative damped cuckoo search algorithm with a comparative study against other adaptive variants. IEEE Access 7(1):119272

    Article  Google Scholar 

  37. Davies GH (1970) The life of birds, parenthood. http://www.pbs.org/lifeofbirds/home/index.html

  38. Khan K, Sahai A (2013) Neural-based cuckoo search of employee health and safety (HS). Int J Intell Syst Appl 5(2):76

    Google Scholar 

  39. Yang XS, Press L (2010) Nature-inspired metaheuristic algorithms, 2nd edn. Luniver Press

  40. Brown CT, Liebovitch LS, Glendon R (2007) Lévy flights in Dobe Ju/’hoansi foraging patterns. Hum Ecol 35(1):129

    Article  Google Scholar 

  41. Pavlyukevich I (2007) Cooling down Lévy flights. J Phys A Math Theor 40(41):12299

    Article  Google Scholar 

  42. Pavlyukevich I (2007) Lévy flights, non-local search and simulated annealing. J Comput Phys 226(2):1830

    Article  MathSciNet  Google Scholar 

  43. Reynolds AM, Frye MA (2007) Free-flight odor tracking in Drosophila is consistent with an optimal intermittent scale-free search. PLoS ONE 2(4):e354

    Article  Google Scholar 

  44. Roy S, Chaudhuri SS (2013) Cuckoo search algorithm using Lévy flight: a review. Int J Mod Educ Comput Sci 5(12):10

    Article  Google Scholar 

  45. Wang L, Yin Y, Zhong Y (2015) Cuckoo search with varied scaling factor. Front Comput Sci 9(4):623

    Article  Google Scholar 

  46. Pandey AC, Rajpoot DS, Saraswat M (2017) Hybrid step size based cuckoo search. In: 2017 Tenth international conference on contemporary computing (IC3). IEEE, pp 1–6

  47. Zielinski S (2015) Cuckoos may have a long-lasting impact on other birds. https://www.sciencenews.org/blog/wild-things/cuckoos-may-have-long-lasting-impact-other-birds. [Online; posted July 8, 2015]

  48. Medina I, Langmore NE (2015) The costs of avian brood parasitism explain variation in egg rejection behaviour in hosts. Biol Let 11(7):20150296

    Article  Google Scholar 

  49. Pappas T (1989) Mersenne’s number. The joy of mathematics. Wide World Publishing/Tetra, San carlos

    Google Scholar 

  50. Uhler HS (1952) A brief history of the investigations on Mersenne numbers and the latest immense primes. Scripta Mathematica 181(122–131):4

    MathSciNet  MATH  Google Scholar 

  51. Selfridge J, Hurwitz A (1964) Fermat numbers and Mersenne numbers. Math Comput 18(85):146

    Article  MathSciNet  Google Scholar 

  52. Solinas JA et al (1999) Generalized mersenne numbers. Citeseer, Princeton

    Google Scholar 

  53. Caldwell CK (2014) Mersenne primes: history, theorems and lists. Prime Pages

  54. Awad N, Ali M, Liang J, Qu B, Suganthan P (2016) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective real-parameter numerical optimization. Tech. Rep.

  55. Thrun MC, Gehlert T, Ultsch A (2020) Analyzing the fine structure of distributions. PLoS ONE 15(10):e0238835

    Article  Google Scholar 

  56. Hoffmann H et al (2015) violin. m-Simple violin plot using matlab default kernel density estimation. INRES (University of Bonn), Katzenburgweg, Germany

Download references

Acknowledgements

Our previous study [36] was proposed to find the best variant that makes the Lévy flight step size parameter adaptive. Thirteen different variants are tested on the well-known CEC2017 benchmark functions with 30 dimensions. In this study, we are going to follow the same procedure but with a different important parameter which is called the probability of discovery. The objective is to find the best algorithm that makes this parameter adaptive. A new adaptive variant is proposed and is compared against nine different variants. All these algorithms are tested on the well-known CEC2017 benchmark functions [54]. These benchmark functions are known for their high complexity and are usually used to measure the performance of meta-heuristic optimization techniques. Therefore, the proposed algorithm is tested on these functions with 10, 30, and 50 dimensions.

Author information

Authors and Affiliations

  1. Computers and Control Systems Engineering Department, Faculty of Engineering, Mansoura University, Mansoura, Egypt

    Mohamed Reda, Mostafa Elhosseini, Amira Haikal & Mahmoud Badawy

  2. College of Computer Science and Engineering in Yanbu, Taibah University, Medina, Saudi Arabia

    Mostafa Elhosseini

  3. Computer Science and Information Department, Taibah University, Medina, Saudi Arabia

    Mahmoud Badawy

Authors
  1. Mohamed Reda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mostafa Elhosseini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Amira Haikal
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mahmoud Badawy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mahmoud Badawy.

Ethics declarations

Conflict of interest

There is no conflict of interest between the authors to publish this manuscript.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Reda, M., Elhosseini, M., Haikal, A. et al. A novel cuckoo search algorithm with adaptive discovery probability based on double Mersenne numbers. Neural Comput & Applic 33, 16377–16402 (2021). https://doi.org/10.1007/s00521-021-06236-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-021-06236-8

Keywords

Search

Navigation