Quaternionic Flower Pollination Algorithm

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10425)


Metaheuristic-based optimization techniques offer an elegant and easy-to-follow framework to optimize different types of problems, ranging from aerodynamics to machine learning. Though such techniques are suitable for global optimization, they can still be get trapped locally under certain conditions, thus leading to reduced performance. In this work, we propose a quaternionic-based Flower Pollination Algorithm (FPA), which extends standard FPA to possibly smoother search spaces based on hypercomplex representations. We show the proposed approach is more accurate than five other metaheuristic techniques in four benchmarking functions. We also present a parallel version of the proposed approach that runs much faster.


Flower Pollination Algorithm Quaternions Metaheuristics 



The authors would like to thank FAPESP grants #2014/16250-9, #2014/12236-1, #2015/25739-4 and #2016/21243-7, as well as Capes, CNPq grant #306166/2014-3, and Capes PROCAD 2966/2014.


  1. 1.
    Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann Publishers Inc., San Francisco (2001)Google Scholar
  2. 2.
    Yang, X.-S., Gandomi, A.H.: Bat algorithm: a novel approach for global engineering optimization. Eng. Comput. 29(5), 464–483 (2012)CrossRefGoogle Scholar
  3. 3.
    Karaboga, D., Basturk, B.: A powerful and efficient algorithm for numerical function optimization: Artificial Bee Colony (ABC) algorithm. J. Global Optim. 39(3), 459–471 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Yang, S.-S., Karamanoglu, M., He, X.: Flower pollination algorithm: a novel approach for multiobjective optimization. Eng. Optim. 46(9), 1222–1237 (2014)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Fister, I., Yang, X.-S., Brest, J., Fister Jr., I.: Modified firefly algorithm using quaternion representation. Expert Syst. Appl. 40(18), 7220–7230 (2013)CrossRefGoogle Scholar
  6. 6.
    Fister, I., Brest, J., Fister Jr., I., Yang, X.-S.: Modified bat algorithm with quaternion representation. In: IEEE Congress on Evolutionary Computation, pp. 491–498 (2015)Google Scholar
  7. 7.
    Papa, J.P., Pereira, D.R., Baldassin, A., Yang, X.-S.: On the harmony search using quaternions. In: Schwenker, F., Abbas, H.M., El Gayar, N., Trentin, E. (eds.) ANNPR 2016. LNCS (LNAI), vol. 9896, pp. 126–137. Springer, Cham (2016). doi: 10.1007/978-3-319-46182-3_11 CrossRefGoogle Scholar
  8. 8.
    Wilcoxon, F.: Individual comparisons by ranking methods. Biom. Bull. 1(6), 80–83 (1945)CrossRefGoogle Scholar
  9. 9.
    Dagum, L., Menon, R.: Openmp: an industry-standard api for shared-memory programming. IEEE Comput. Sci. Eng. 5(1), 46–55 (1998)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of SciencesUNESP - São Paulo State UniversityBauruBrazil
  2. 2.Department of ComputingUFSCar - Federal University of São CarlosSão CarlosBrazil
  3. 3.Institute of Natural Sciences and TechnologyUNESP - São Paulo State UniversityRio ClaroBrazil
  4. 4.School of Science and TechnologyMiddlesex UniversityLondonUK

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