Skip to main content
SpringerLink
Log in

Emperor Penguins Colony: a new metaheuristic algorithm for optimization

  • Research Paper
  • Published:
Evolutionary Intelligence Aims and scope Submit manuscript

Abstract

A metaheuristic is a high-level problem independent algorithmic framework that provides a set of guidelines or strategies to develop heuristic optimization algorithms. Metaheuristic algorithms attempt to find the best solution out of all possible solutions of an optimization problem. A very active area of research is the design of nature-inspired metaheuristics. Nature acts as a source of concepts, mechanisms and principles for designing of artificial computing systems to deal with complex computational problems. In this paper, a new metaheuristic algorithm, inspired by the behavior of emperor penguins which is called Emperor Penguins Colony (EPC), is proposed. This algorithm is controlled by the body heat radiation of the penguins and their spiral-like movement in their colony. The proposed algorithm is compared with eight developed metaheuristic algorithms. Ten benchmark test functions are applied to all algorithms. The results of the experiments to find the optimal result, show that the proposed algorithm is better than other metaheuristic algorithms.

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

Available in: https://www.bas.ac.uk/

Fig. 2

Available in Gilbert et al. [37]

Fig. 3

Original image is in landscapes & cycles: An environmentalist’s journey to climate skepticism by Jim Steele

Fig. 4

Image and graph created by Gerum and Zitterbart and available in paper with title “The origin of traveling waves in an emperor penguin huddle”, published by the open access new journal of physics [35]

Fig. 5

Original image taken by Stephanie Jenouvrier, Woods Hole Oceanographic Institution

Fig. 6
Fig. 7

Original image taken by Fred https://www.Olivier/naturepl.com

Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. He S. Wu Q, Saunders J (2009) Group search optimizer: an optimization algorithm inspired by animal searching behavior. IEEE Trans Evol Comput 13(5):973–990

    Google Scholar 

  2. Rajabioun R (2011) Cuckoo optimization algorithm. Appl Soft Comput 11(8):5508–5518

    Google Scholar 

  3. Gandomi A. Yang X, Alavi A (2011) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35

    Google Scholar 

  4. Talbi EG (2009) Metaheuristics: from design to implementation, vol. 74. Wiley, Hoboken

    MATH  Google Scholar 

  5. Jain M, Singh V, Rani A (2019) A novel nature-inspired algorithm for optimization: squirrel search algorithm. Swarm Evol Comput 44:148–175

    Google Scholar 

  6. Sivanandam SN, Deepa SN (2007) Introduction to genetic algorithms. Springer Science & Business Media, Berlin

    MATH  Google Scholar 

  7. Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359

    MathSciNet  MATH  Google Scholar 

  8. Kennedy J (2017) Particle swarm optimization. In: Sammut C, Webb GI (eds) Encyclopedia of machine learning and data mining. Springer, US, pp 760–766

    Google Scholar 

  9. Dorigo M, Birattari M (2011) Ant colony optimization. In: Sammut C, Webb GI (eds) Encyclopedia of machine learning. Springer, Boston, MA, pp 36–39

    Google Scholar 

  10. Kirkpatrick S. Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680

    MathSciNet  MATH  Google Scholar 

  11. Yang XS, Deb S (2009) Cuckoo search via lévy flights. In: 2009 world congress on nature & biologically inspired computing (NaBIC)

  12. Yang XS (2010) a new metaheuristic bat-inspired algorithm. In: nature inspired cooperative strategies for optimization (NICSO 2010) pp 65–74

  13. Yang XS (2009) Firefly algorithms for multimodal optimization. In: International symposium on stochastic algorithms. LNCS, vol 5792. Springer, Berlin, Heidelberg, pp 169–178

    Google Scholar 

  14. Geem ZW. Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68.

    Google Scholar 

  15. Glover F (1989) Tabu search—part I. ORSA J Comput 1(3):190–206.

    MathSciNet  MATH  Google Scholar 

  16. Glover F (1990) Tabu search—part II. ORSA J Comput 2(1):4–32

    MathSciNet  MATH  Google Scholar 

  17. Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In: 2007 IEEE congress on evolutionary computation

  18. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39(3):459–471

    MathSciNet  MATH  Google Scholar 

  19. Gandomi A, Alavi A (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17(12):4831–4845

    MathSciNet  MATH  Google Scholar 

  20. Mehrabian AR, Lucas C (2006) A novel numerical optimization algorithm inspired from weed colonization. Ecol Inf 1(4):355–366

    Google Scholar 

  21. Eusuff M. Lansey K, Pasha F (2006) Shuffled frog-leaping algorithm: a memetic meta-heuristic for discrete optimization. Eng Optim 38(2):129–154

    MathSciNet  Google Scholar 

  22. Hosseini HS (2007) Problem solving by intelligent water drops. In: 2007 IEEE congress on evolutionary computation. pp 3226–3231

  23. Mirjalili S. Mirjalili S, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Google Scholar 

  24. Jain M, Maurya S, Rani A, Singh V (2018) Owl search algorithm: a novel nature-inspired heuristic paradigm for global optimization. J Intell Fuzzy Syst 34:1573–1582

    Google Scholar 

  25. Zhao W. Wang L, Zhang Z (2018) Atom search optimization and its application to solve a hydrogeologic parameter estimation problem. Knowl Based Syst

  26. Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191 and

    Google Scholar 

  27. Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98

    Google Scholar 

  28. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67 and

    Google Scholar 

  29. Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249

    Google Scholar 

  30. Saremi SH, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47 and

    Google Scholar 

  31. Schwaller MR. Olson CE. Ma Z. Zhu Z, Dahmer P (1989) A remote sensing analysis of Adélie penguin rookeries. Remote Sens Environ 28:199–206

    Google Scholar 

  32. Kooyman GL, Kooyman TG (1995) Diving behavior of emperor penguins nurturing chicks at Coulman Island, Antarctica. The Condor 97(2):536–549

    Google Scholar 

  33. Maho YL (1977) The emperor penguin: a strategy to live and breed in the cold: morphology, physiology, ecology, and behavior distinguish the polar emperor penguin from other penguin species, particularly from its close relative, the king penguin. Am Sci 65(6):680–693

    Google Scholar 

  34. Fretwell PT, Trathan PN (2009) Penguins from space: faecal stains reveal the location of emperor penguin colonies. Glob Ecol Biogeogr 18(5):543–552

    Google Scholar 

  35. Gerum RC, Fabry B, Metzner C, Beaulieu M, Ancel A, Zitterbart DP (2013) The origin of traveling waves in an emperor penguin huddle. New J Phys 15(12):1–17

    Google Scholar 

  36. Kooyman GL, Campbell WB (1971) Diving behavior of the emperor Penguin, Aptenodytes forsteri. The Auk 88(4):775–795

    Google Scholar 

  37. Gilbert C, Robertson G, Maho YL, Naito Y, Ancel A (2006) Huddling behavior in emperor penguins: dynamics of huddling. Physiol Behav 88( 4–5):479–488

    Google Scholar 

  38. Maho YL, Delclitte P, Chatonnet J (1976) Thermoregulation in fasting emperor penguins under natural conditions. Am J Physiol Leg Content 231(3):913–922

    Google Scholar 

  39. Forero MG, Tella JL, Hobson KA, Bertellotti M, Blanco G (2002) Conspecific food competition explains variability in colony size: a test in Magellanic penguins. Ecology 83(12):3466–3475

    Google Scholar 

  40. Rolland C, Danchin E, de Fraipont M (1998) The evolution of coloniality in birds in relation to food, habitat, predation, and life-history traits: a comparative analysis. Am Nat 151(6):514–529

    Google Scholar 

  41. Ancel A, Visser H, Handrich Y, Masman D, Maho YL (1997) Energy saving in huddling penguins. Nature 385(6614):304–305

    Google Scholar 

  42. Ancel A, Beaulieu M, Gilbert C (2013) The different breeding strategies of penguins: a review. Comptes Rendus Biol 336(1):1–12

    Google Scholar 

  43. Gilbert C, Robertson G, Maho YL, Ancel A (2007) How do weather conditions affect the huddling behaviour of emperor penguins?. Polar Biology 31(2):163–169

    Google Scholar 

  44. Truszkowski W, Rouff C, Hinchey MG (2003) Innovative concepts for agent-based systems. Springer, Berlin

    MATH  Google Scholar 

  45. Dhiman G, Kumar V (2018) Emperor penguin optimizer: a bio-inspired algorithm for engineering problems. Knowl Based Syst 159:20–50

    Google Scholar 

  46. Pinshow B, Fedak M. Battles D, Schmidt-Nielsen K (1976) Energy expenditure for thermoregulation and locomotion in emperor penguins. Am J Physiol Leg Content 231(3):903–912

    Google Scholar 

  47. Du N, Fan J, Wu H, Chen S, Liu Y (2007) An improved model of heat transfer through penguin feathers and down. J Theor Biol 248(4):727–735

    MathSciNet  Google Scholar 

  48. Geankoplis CJ (2003) Transport processes and separation process principles: (includes unit operations). Prentice Hall Professional Technical Reference, Upper Saddle River

    Google Scholar 

  49. McCafferty DJ, Gilbert C, Paterson W, Pomeroy PP, Thompson D, Currie JI, Ancel A (2011) Estimating metabolic heat loss in birds and mammals by combining infrared thermography with biophysical modelling. Comp Biochem Physiol Part A Mol Integr Physiol 158(3):337–345

    Google Scholar 

  50. Hammel HT (1956) Infrared emissivities of some arctic fauna. J Mammal 37(3):375

    Google Scholar 

  51. Pascal LMA, Courtois H, Hekking FWJ (2011) Circuit approach to photonic heat transport. Phys Rev B 83(12):125113.1–125113.7

    Google Scholar 

  52. Gang C (1996) Heat transfer in micro-and nanoscale photonic devices. Annu Rev of Heat Transf 7(7):1–57

    Google Scholar 

  53. Taler J, Duda P (2006) Solving direct and inverse heat conduction problems. Springer, Berlin

    MATH  Google Scholar 

  54. Simon V (2010) Adaptations in the animal kingdom. Xlibris, Bloomington

    Google Scholar 

  55. Weisstein EW Logarithmic spiral. From MathWorld—a Wolfram Web Resource. http://mathworld.wolfram.com/LogarithmicSpiral.html. Accessed 4 June 2002

  56. Surjanovic S, Bingham D (2013) Virtual Library of simulation experiments: test functions and datasets. Retrieved October 23, 2017, from http://www.sfu.ca/~ssurjano. Accessed 23 Oct 2017

  57. Adorio EP, Diliman U (2005) Mvf-multivariate test functions library in c for unconstrained global optimization. Metro Manila, Quezon City, pp 100–104

    Google Scholar 

  58. Molga M, Smutnicki C (2005) Test functions for optimization needs. Test functions for optimization needs

  59. Back T (1996) Evolutionary algorithms in theory and practice. Oxford University Press, Oxford

    MATH  Google Scholar 

  60. Picheny V, Wagner T, Ginsbourger D (2013) A benchmark of kriging-based infill criteria for noisy optimization”. Struct Multidiscip Optim 48(3):607–626

    Google Scholar 

  61. Pohlheim H (2007) Examples of objective functions. Retrieved 4(10)

  62. Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evolut Comput 1(1):3–18 and

    Google Scholar 

  63. Mendenhall W, Beaver RJ, Barbara MB (2012) Introduction to probability and statistics. Cengage Learning, Boston

    MATH  Google Scholar 

  64. Littlefair G (2005) Free search—a comparative analysis. Inf Sci 172(1–2):173–193

    MathSciNet  Google Scholar 

  65. Vasileva V, Penev K (2017) Free search and particle swarm optimisation applied to global optimisation numerical tests from two to hundred dimensions. In: Sgurev V, Yager R, Kacprzyk J, Atanassov K (eds) Recent contributions in intelligent systems. Studies in computational intelligence, vol 657. Springer, Cham, pp 313–337

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering, Karaj Branch, Islamic Azad University, Karaj, Iran

    Sasan Harifi, Madjid Khalilian & Javad Mohammadzadeh

  2. Department of Industrial Engineering, Karaj Branch, Islamic Azad University, Karaj, Iran

    Sadoullah Ebrahimnejad

Authors
  1. Sasan Harifi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Madjid Khalilian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Javad Mohammadzadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sadoullah Ebrahimnejad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Madjid Khalilian.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s Note

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

Appendix A

Appendix A

The results of applying the PSO and DE algorithms on test functions for 100, 500 and 1000 dimensions.

See Table 10.

Table 10 Mean of best function values obtained for 100 iterations by PSO and DE with high dimensions
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Harifi, S., Khalilian, M., Mohammadzadeh, J. et al. Emperor Penguins Colony: a new metaheuristic algorithm for optimization. Evol. Intel. 12, 211–226 (2019). https://doi.org/10.1007/s12065-019-00212-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12065-019-00212-x

Keywords

Search

Navigation