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Evolutionary Intelligence

, Volume 12, Issue 2, pp 211–226 | Cite as

Emperor Penguins Colony: a new metaheuristic algorithm for optimization

  • Sasan Harifi
  • Madjid KhalilianEmail author
  • Javad Mohammadzadeh
  • Sadoullah Ebrahimnejad
Research Paper

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.

Keywords

Metaheuristic Optimization Emperor penguins colony algorithm EPC algorithm Optimization techniques Nature-inspired Benchmark test functions 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 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):973–990Google Scholar
  2. 2.
    Rajabioun R (2011) Cuckoo optimization algorithm. Appl Soft Comput 11(8):5508–5518Google Scholar
  3. 3.
    Gandomi A. Yang X, Alavi A (2011) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35Google Scholar
  4. 4.
    Talbi EG (2009) Metaheuristics: from design to implementation, vol. 74. Wiley, HobokenzbMATHGoogle Scholar
  5. 5.
    Jain M, Singh V, Rani A (2019) A novel nature-inspired algorithm for optimization: squirrel search algorithm. Swarm Evol Comput 44:148–175Google Scholar
  6. 6.
    Sivanandam SN, Deepa SN (2007) Introduction to genetic algorithms. Springer Science & Business Media, BerlinzbMATHGoogle Scholar
  7. 7.
    Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359MathSciNetzbMATHGoogle Scholar
  8. 8.
    Kennedy J (2017) Particle swarm optimization. In: Sammut C, Webb GI (eds) Encyclopedia of machine learning and data mining. Springer, US, pp 760–766Google Scholar
  9. 9.
    Dorigo M, Birattari M (2011) Ant colony optimization. In: Sammut C, Webb GI (eds) Encyclopedia of machine learning. Springer, Boston, MA, pp 36–39Google Scholar
  10. 10.
    Kirkpatrick S. Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680MathSciNetzbMATHGoogle Scholar
  11. 11.
    Yang XS, Deb S (2009) Cuckoo search via lévy flights. In: 2009 world congress on nature & biologically inspired computing (NaBIC)Google Scholar
  12. 12.
    Yang XS (2010) a new metaheuristic bat-inspired algorithm. In: nature inspired cooperative strategies for optimization (NICSO 2010) pp 65–74Google Scholar
  13. 13.
    Yang XS (2009) Firefly algorithms for multimodal optimization. In: International symposium on stochastic algorithms. LNCS, vol 5792. Springer, Berlin, Heidelberg, pp 169–178Google Scholar
  14. 14.
    Geem ZW. Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68.Google Scholar
  15. 15.
    Glover F (1989) Tabu search—part I. ORSA J Comput 1(3):190–206.MathSciNetzbMATHGoogle Scholar
  16. 16.
    Glover F (1990) Tabu search—part II. ORSA J Comput 2(1):4–32MathSciNetzbMATHGoogle Scholar
  17. 17.
    Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In: 2007 IEEE congress on evolutionary computationGoogle Scholar
  18. 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):459–471MathSciNetzbMATHGoogle Scholar
  19. 19.
    Gandomi A, Alavi A (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17(12):4831–4845MathSciNetzbMATHGoogle Scholar
  20. 20.
    Mehrabian AR, Lucas C (2006) A novel numerical optimization algorithm inspired from weed colonization. Ecol Inf 1(4):355–366Google Scholar
  21. 21.
    Eusuff M. Lansey K, Pasha F (2006) Shuffled frog-leaping algorithm: a memetic meta-heuristic for discrete optimization. Eng Optim 38(2):129–154MathSciNetGoogle Scholar
  22. 22.
    Hosseini HS (2007) Problem solving by intelligent water drops. In: 2007 IEEE congress on evolutionary computation. pp 3226–3231Google Scholar
  23. 23.
    Mirjalili S. Mirjalili S, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61Google Scholar
  24. 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 34:1573–1582Google Scholar
  25. 25.
    Zhao W. Wang L, Zhang Z (2018) Atom search optimization and its application to solve a hydrogeologic parameter estimation problem. Knowl Based SystGoogle Scholar
  26. 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 andGoogle Scholar
  27. 27.
    Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98Google Scholar
  28. 28.
    Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67 andGoogle Scholar
  29. 29.
    Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249Google Scholar
  30. 30.
    Saremi SH, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47 andGoogle Scholar
  31. 31.
    Schwaller MR. Olson CE. Ma Z. Zhu Z, Dahmer P (1989) A remote sensing analysis of Adélie penguin rookeries. Remote Sens Environ 28:199–206Google Scholar
  32. 32.
    Kooyman GL, Kooyman TG (1995) Diving behavior of emperor penguins nurturing chicks at Coulman Island, Antarctica. The Condor 97(2):536–549Google Scholar
  33. 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):680–693Google Scholar
  34. 34.
    Fretwell PT, Trathan PN (2009) Penguins from space: faecal stains reveal the location of emperor penguin colonies. Glob Ecol Biogeogr 18(5):543–552Google Scholar
  35. 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):1–17Google Scholar
  36. 36.
    Kooyman GL, Campbell WB (1971) Diving behavior of the emperor Penguin, Aptenodytes forsteri. The Auk 88(4):775–795Google Scholar
  37. 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):479–488Google Scholar
  38. 38.
    Maho YL, Delclitte P, Chatonnet J (1976) Thermoregulation in fasting emperor penguins under natural conditions. Am J Physiol Leg Content 231(3):913–922Google Scholar
  39. 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):3466–3475Google Scholar
  40. 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):514–529Google Scholar
  41. 41.
    Ancel A, Visser H, Handrich Y, Masman D, Maho YL (1997) Energy saving in huddling penguins. Nature 385(6614):304–305Google Scholar
  42. 42.
    Ancel A, Beaulieu M, Gilbert C (2013) The different breeding strategies of penguins: a review. Comptes Rendus Biol 336(1):1–12Google Scholar
  43. 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):163–169Google Scholar
  44. 44.
    Truszkowski W, Rouff C, Hinchey MG (2003) Innovative concepts for agent-based systems. Springer, BerlinzbMATHGoogle Scholar
  45. 45.
    Dhiman G, Kumar V (2018) Emperor penguin optimizer: a bio-inspired algorithm for engineering problems. Knowl Based Syst 159:20–50Google Scholar
  46. 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):903–912Google Scholar
  47. 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):727–735MathSciNetGoogle Scholar
  48. 48.
    Geankoplis CJ (2003) Transport processes and separation process principles: (includes unit operations). Prentice Hall Professional Technical Reference, Upper Saddle RiverGoogle Scholar
  49. 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):337–345Google Scholar
  50. 50.
    Hammel HT (1956) Infrared emissivities of some arctic fauna. J Mammal 37(3):375Google Scholar
  51. 51.
    Pascal LMA, Courtois H, Hekking FWJ (2011) Circuit approach to photonic heat transport. Phys Rev B 83(12):125113.1–125113.7Google Scholar
  52. 52.
    Gang C (1996) Heat transfer in micro-and nanoscale photonic devices. Annu Rev of Heat Transf 7(7):1–57Google Scholar
  53. 53.
    Taler J, Duda P (2006) Solving direct and inverse heat conduction problems. Springer, BerlinzbMATHGoogle Scholar
  54. 54.
    Simon V (2010) Adaptations in the animal kingdom. Xlibris, BloomingtonGoogle Scholar
  55. 55.
    Weisstein EW Logarithmic spiral. From MathWorld—a Wolfram Web Resource. http://mathworld.wolfram.com/LogarithmicSpiral.html. Accessed 4 June 2002
  56. 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. 57.
    Adorio EP, Diliman U (2005) Mvf-multivariate test functions library in c for unconstrained global optimization. Metro Manila, Quezon City, pp 100–104Google Scholar
  58. 58.
    Molga M, Smutnicki C (2005) Test functions for optimization needs. Test functions for optimization needsGoogle Scholar
  59. 59.
    Back T (1996) Evolutionary algorithms in theory and practice. Oxford University Press, OxfordzbMATHGoogle Scholar
  60. 60.
    Picheny V, Wagner T, Ginsbourger D (2013) A benchmark of kriging-based infill criteria for noisy optimization”. Struct Multidiscip Optim 48(3):607–626Google Scholar
  61. 61.
    Pohlheim H (2007) Examples of objective functions. Retrieved 4(10)Google Scholar
  62. 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 andGoogle Scholar
  63. 63.
    Mendenhall W, Beaver RJ, Barbara MB (2012) Introduction to probability and statistics. Cengage Learning, BostonzbMATHGoogle Scholar
  64. 64.
    Littlefair G (2005) Free search—a comparative analysis. Inf Sci 172(1–2):173–193MathSciNetGoogle Scholar
  65. 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 313–337Google Scholar

Copyright information

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

Authors and Affiliations

  • Sasan Harifi
    • 1
  • Madjid Khalilian
    • 1
    Email author
  • Javad Mohammadzadeh
    • 1
  • Sadoullah Ebrahimnejad
    • 2
  1. 1.Department of Computer Engineering, Karaj BranchIslamic Azad UniversityKarajIran
  2. 2.Department of Industrial Engineering, Karaj BranchIslamic Azad UniversityKarajIran

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