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Applied Intelligence

, Volume 48, Issue 9, pp 2580–2612 | Cite as

Electromagnetism-like mechanism with collective animal behavior for multimodal optimization

  • Jorge Gálvez
  • Erik Cuevas
  • Omar Avalos
  • Diego Oliva
  • Salvador Hinojosa
Article
  • 460 Downloads

Abstract

Evolutionary Computation Algorithms (ECA) are conceived as alternative methods for solving complex optimization problems through the search for the global optimum. Therefore, from a practical point of view, the acquisition of multiple promissory solutions is especially useful in engineering, since the global solution may not always be realizable due to several realistic constraints. Although ECAs perform well on the detection of the global solution, they are not suitable for finding multiple optima in a single execution due to their exploration-exploitation operators. This paper proposes a new algorithm called Collective Electromagnetism-like Optimization (CEMO). Under CEMO, a collective animal behavior is implemented as a memory mechanism simulating natural animal dominance over the population to extend the original Electromagnetism-like Optimization algorithm (EMO) operators to efficiently register and maintain all possible Optima in an optimization problem. The performance of the proposed CEMO is compared against several multimodal schemes over a set of benchmark functions considering the evaluation of multimodal performance indexes typically found in the literature. Experimental results are statistically validated to eliminate the random effect in the obtained solutions. The proposed method exhibits higher and more consistent performance against the rest of the tested multimodal techniques.

Keywords

Evolutionary computation algorithms Multimodal optimization Collective animal behavior Collective electromagnetism-like mechanism optimization 

Notes

Compliance with ethical standards

Conflict of interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

References

  1. 1.
    Yang X-S (2010) Wiley InterScience (Online service), Engineering optimization?: an introduction with metaheuristic applications. Wiley, New YorkCrossRefGoogle Scholar
  2. 2.
    Pardalos PM, Romeijn HE, Tuy H (2000) Recent developments and trends in global optimization. J Comput Appl Math 124:209–228MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Floudas CA, Akrotirianakis IG, Caratzoulas S, Meyer CA, Kallrath J (2005) Global optimization in the 21st century: advances and challenges. Comput Chem Eng 29(6):1185–1202CrossRefGoogle Scholar
  4. 4.
    Cuevas E, Gálvez J, Hinojosa S, Avalos O, Zaldívar D, Pérez-cisneros M (2014) A comparison of evolutionary computation techniques for IIR model identification, vol 2014Google Scholar
  5. 5.
    Lera D, Sergeyev YD (2010) Lipschitz and Hölder global optimization using space-filling curves. Appl Numer Math 160(1–2):115–129CrossRefzbMATHGoogle Scholar
  6. 6.
    Holland JH (1975) Adaptation in natural and artificial systems. University Michigan Press, Ann ArborGoogle Scholar
  7. 7.
    Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, BostonzbMATHGoogle Scholar
  8. 8.
    Karaboga D (2005) An idea based on honey bee swarm for numerical optimization, Comput. Eng. Dep. Eng. Fac. Erciyes University, KayseriGoogle Scholar
  9. 9.
    Dorigo M, Stützle T (2003) The ant colony optimization metaheuristic: algorithms, applications, and advances. In: Handbook of metaheuristics boston: kluwer academic publishers, pp 250–285Google Scholar
  10. 10.
    Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings IEEE international conference on neural networks, vol 4, pp 1942–1948Google Scholar
  11. 11.
    Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: A gravitational search algorithm. Inf Sci (Ny) 179(13):2232–2248CrossRefzbMATHGoogle Scholar
  12. 12.
    Birbil SI, Fang S-C (2003) An electromagnetism-like mechanism for global optimization. J Glob Optim 25:263–282MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Storn R, Price K (1997) Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Hansen N, Kern S (2004) Evaluating the CMA evolution strategy on multimodal test functions. In: Proceedings 8th international conference on parallel problem solving from nature - PPSN VIII, vol. 3242/2004, no 0, pp 282–291Google Scholar
  15. 15.
    Das S, Maity S, Qu B-Y, Suganthan PN (2011) Real-parameter evolutionary multimodal optimization — A survey of the state-of-the-art. Swarm Evol Comput 1(2):71–88CrossRefGoogle Scholar
  16. 16.
    Wong K-C, Wu C-H, Mok RKP, Peng C, Zhang Z (2012) Evolutionary multimodal optimization using the principle of locality. Inf Sci (Ny) 194:138–170CrossRefGoogle Scholar
  17. 17.
    Jong D, Alan K (1975) An analysis of the behavior of a class of genetic adaptive systems. University of Michigan, Ann ArborGoogle Scholar
  18. 18.
    Goldberg DE, Richardson I (1987) Genetic algorithm with sharing for multimodal function optimization. In: Proceedings 2nd international conference on generic algorithm, pp 41–49Google Scholar
  19. 19.
    Petrowski A (1996) A clearing procedure as a niching method for genetic algorithms. In: Proceedings of IEEE international conference on evolutionary computation ICEC-96, pp 798–803Google Scholar
  20. 20.
    Li J-P, Balazs ME, Parks GT, Clarkson PJ (2002) A species conserving genetic algorithm for multimodal function optimization. Evol Comput 10(3):207–234CrossRefGoogle Scholar
  21. 21.
    Thomsen R (2004) Multimodal optimization using crowding-based differential evolution. In: Proceedings of congress on evolutionary computation (CEC ’04), pp 1382–1389Google Scholar
  22. 22.
    Vollmer DT, Soule T, Manic M (2010) A distance measure comparison to improve crowding in multi-modal optimization problems. In: Proceedings - ISRCS 2010 - 3rd international symposium on resilient control system, pp 31–36Google Scholar
  23. 23.
    Mahfoud SW (1995) Niching methods for genetic algorithms, Ph.D. thesisGoogle Scholar
  24. 24.
    Yazdani S, Nezamabadi-pour H, Kamyab S (2014) A gravitational search algorithm for multimodal optimization. Swarm Evol Comput 14:1–14CrossRefGoogle Scholar
  25. 25.
    Liang JJ, Qu BY, Mao XB, Niu B, Wang DY (2014) Differential evolution based on fitness Euclidean-distance ratio for multimodal optimization. Neurocomputing 137:252–260CrossRefGoogle Scholar
  26. 26.
    Biswas S, Das S, Kundu S, Patra GR (2014) Utilizing time-linkage property in DOPs: An information sharing based Artificial Bee Colony algorithm for tracking multiple optima in uncertain environments. Soft Comput 18(6):1199–1212CrossRefGoogle Scholar
  27. 27.
    Sacco WF, Henderson N, Rios-Coelho AC (2014) Topographical clearing differential evolution: A new method to solve multimodal optimization problems. Prog Nucl Energy 71:269–278CrossRefGoogle Scholar
  28. 28.
    Liang Y, Leung K-S (2011) Genetic Algorithm with adaptive elitist-population strategies for multimodal function optimization. Appl Soft Comput 11(2):2017–2034CrossRefGoogle Scholar
  29. 29.
    Gao W, Yen GG, Liu S (2014) A cluster-based differential evolution with self-adaptive strategy for multimodal optimization. IEEE Trans Cybern 44(8):1314–1327CrossRefGoogle Scholar
  30. 30.
    Ursem RK (1999) Multinational evolutionary algorithms. In: Proceedings of the 1999 congress on evolutionary computation-CEC99 (Cat. No. 99TH8406), pp 1633–1640Google Scholar
  31. 31.
    Yao J, Kharma N, Zhu YQ (2006) On clustering in evolutionary computation. In: IEEE international conference on evolutionary computation, pp 1752–1759Google Scholar
  32. 32.
    Li L, Tang K (2015) History-based topological speciation for multimodal optimization. IEEE Trans Evol Comput 19(1):136–150MathSciNetCrossRefGoogle Scholar
  33. 33.
    Chen G, Low CP, Yang Z (2009) Preserving and exploiting genetic diversity in evolutionary programming algorithms. IEEE Trans Evol Comput 13(3):661–673CrossRefGoogle Scholar
  34. 34.
    Yang Q, Member S, Chen W, Yu Z, Gu T (2017) Adaptive multimodal continuous ant colony optimization. IEEE Trans Evol Comput 21(2):191–205CrossRefGoogle Scholar
  35. 35.
    Biswas S, Kundu S, Das S (2014) An improved parent-centric mutation with normalized neighborhoods for inducing niching behavior in differential evolution. IEEE Trans Cybern 44(10):1726–1737CrossRefGoogle Scholar
  36. 36.
    Hui S, Suganthan PN (2016) Ensemble and arithmetic recombination-based speciation differential evolution for multimodal optimization. IEEE Trans Cybern 46(1):64–74CrossRefGoogle Scholar
  37. 37.
    Lacroix B, Molina D, Herrera F (2016) Region-based memetic algorithm with archive for multimodal optimisation. Inf Sci (Ny) 367:719–746CrossRefGoogle Scholar
  38. 38.
    Yao Jie, Kharma N, Grogono P (2010) Bi-objective multipopulation genetic algorithm for multimodal function optimization. IEEE Trans Evol Comput 14(1):80–102CrossRefGoogle Scholar
  39. 39.
    Deb K, Saha A (2012) Multimodal optimization using a bi-objective evolutionary algorithm. Evol Comput 20(1):27–62CrossRefGoogle Scholar
  40. 40.
    Basak A, Das S, Tan KC (2013) Multimodal optimization using a biobjective differential evolution algorithm enhanced with mean distance-based selection. IEEE Trans Evol Comput 17(5):666–685CrossRefGoogle Scholar
  41. 41.
    Wang Y, Li HX, Yen GG, Song W (2015) MOMMOP: multiobjective optimization for locating multiple optimal solutions of multimodal optimization problems. IEEE Trans Cybern 45(4):830–843CrossRefGoogle Scholar
  42. 42.
    Wang Yong, Li Han-Xiong, Yen GG, Wu Song MOMMOP (2015) Multiobjective optimization for locating multiple optimal solutions of multimodal optimization problems. IEEE Trans Cybern 45(4):830–843CrossRefGoogle Scholar
  43. 43.
    De Castro L, Von Zuben F (2000) The clonal selection algorithm with engineering applications. In: Proceedings GECCO, no July, pp 36–37Google Scholar
  44. 44.
    de Castro LN, Timmis J (2002) An artificial immune network for multimodal function optimization. In: Proceedings of the 2002 congress on evolutionary computation. CEC’02 (Cat. No.02TH8600), vol 1, pp 699–704Google Scholar
  45. 45.
    Cuevas E, González M. (2013) An optimization algorithm for multimodal functions inspired by collective animal behavior. Soft Comput 17(3):489–502CrossRefGoogle Scholar
  46. 46.
    Couzin ID, Krause J, James R, Ruxton GD, Franks NR (2002) Collective memory and spatial sorting in animal groups. J Theor Biol 218(1):1–11MathSciNetCrossRefGoogle Scholar
  47. 47.
    Ballerini M, Cabibbo N, Candelier R, Cavagna A, Cisbani E, Giardina I, Lecomte V, Orlandi A, Parisi G, Procaccini A, Viale M, Zdravkovic V (2008) Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study. Proc Natl Acad Sci USA 105(4): 1232–7CrossRefGoogle Scholar
  48. 48.
    Cuevas E, González M, Zaldivar D, Pérez-Cisneros M, García G (2012) An algorithm for global optimization inspired by collective animal behavior. Discret Dyn Nat Soc 2012:1–24MathSciNetCrossRefGoogle Scholar
  49. 49.
    Bouchekara HREH (2013) Electromagnetic device optimization based on electromagnetism-like mechanism. Appl Comput Electromagn Soc J 28(3):241–248Google Scholar
  50. 50.
    Birbil Şİ, Fang S-C (2003) An electromagnetism-like mechanism for global optimization. J Glob Optim 25(3):263–282MathSciNetCrossRefzbMATHGoogle Scholar
  51. 51.
    Hsu Y, Earley RL, Wolf LL (2005) Modulation of aggressive behaviour by fighting experience: mechanisms and contest outcomes. Biol Rev 81(1):33CrossRefGoogle Scholar
  52. 52.
    Gálvez J, Cuevas E, Avalos O (2017) Flower pollination algorithm for multimodal optimization. Int J Comput Intell Syst 10(1): 627CrossRefGoogle Scholar
  53. 53.
    Li X, Engelbrecht A, Epitropakis MG (2013) Benchmark functions for CEC’2013 special session and competition on niching methods for multimodal function optimizationGoogle Scholar
  54. 54.
    Chitsaz H, Amjady N, Zareipour H (2015) Wind power forecast using wavelet neural network trained by improved Clonal selection algorithm. Energy Convers Manag 89:588–598CrossRefGoogle Scholar
  55. 55.
    Aung TN, Khaing SS (2016) Genetic and evolutionary computing. Advances in Intelligent Systems and Computing, vol 388Google Scholar
  56. 56.
    Qu BY, Suganthan PN, Das S (2013) A distance-based locally informed particle swarm model for multimodal optimization. IEEE Trans Evol Comput 17(3):387–402CrossRefGoogle Scholar
  57. 57.
    Biswas S, Kundu S, Das S (2015) Inducing niching behavior in differential evolution through local information sharing. IEEE Trans Evol Comput 19(2):246–263CrossRefGoogle Scholar
  58. 58.
    Hui S, Suganthan PN (2016) Ensemble and arithmetic recombination-based speciation differential evolution for multimodal optimization. IEEE Trans Cybern 46(1):64–74CrossRefGoogle Scholar
  59. 59.
    Wilcoxon F (1945) Individual comparisons by ranking methods. Biometrics 1(6):80–83MathSciNetCrossRefGoogle Scholar
  60. 60.
    Vollmer DT, Soule T, Manic M (2010) A distance measure comparison to improve crowding in multi-modal optimization problems. In: Proceedings - ISRCS 2010 - 3rd international symposium on resilient control system, pp 31–36Google Scholar
  61. 61.
    De Castro L, Von Zuben F (2000) The clonal selection algorithm with engineering applications. In: Proceedings GECCO, no. July, pp 36–37Google Scholar
  62. 62.
    Kennedy J, Eberhart RC (1995) Particle swarm optimization. Proc IEEE Int Conf Neural Netw 4:1942–1948CrossRefGoogle Scholar
  63. 63.
    García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms. J Heuristics 15:617–644CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Jorge Gálvez
    • 1
  • Erik Cuevas
    • 1
  • Omar Avalos
    • 1
  • Diego Oliva
    • 1
  • Salvador Hinojosa
    • 2
  1. 1.Departamento de ElectrónicaUniversidad de Guadalajara, CUCEIGuadalajaraMexico
  2. 2.Departamento Ingeniería del Software e Inteligencia Artificial, Facultad InformáticaUniversidad Complutense de MadridMadridSpain

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