New chaotic flower pollination algorithm for unconstrained non-linear optimization functions

  • Arvinder Kaur
  • Saibal K. Pal
  • Amrit Pal SinghEmail author
Original Article


Flower pollination algorithm (FPA) is susceptible to local optimum and substandard precision of calculations. Chaotic operator (CO), which is used in local algorithms to optimize the best individuals in the population, can successfully enhance the properties of the flower pollination algorithm. A new chaotic flower pollination algorithm (CFPA) has been proposed in this work. Further FPA and its four proposed variants by using different chaotic maps are tested on nine mathematical benchmark functions of high dimensions. Proposed variants of CFPA are CFPA1, CFPA2, CFPA3 and CFPA4. The result of the experiment indicates that the proposed chaotic flower pollination variant CFPA2 could increase the precision of minimization of function value and CPU time to run an algorithm.


Chaos theory Flower pollination algorithm Function optimization Non-linear functions 


  1. Abdel-Raouf O, El-Henawy I, Abdel-Baset M (2014) A novel hybrid flower pollination algorithm with chaotic harmony search for solving sudoku puzzles. Int J Mod Educ Comput Sci 6(3):38CrossRefGoogle Scholar
  2. Aslani H, Yaghoobi M, Akbarzadeh-T MR (2015) Chaotic inertia weight in black hole algorithm for function optimization. In: 2015 international congress on technology, communication and knowledge (ICTCK). IEEE, pp 123–129Google Scholar
  3. Bansal JC, Sharma H, Arya KV, Nagar A (2013a) Memetic search in artificial bee colony algorithm. Soft Comput 17(10):1911–1928CrossRefGoogle Scholar
  4. Bansal JC, Sharma H, Nagar A, Arya KV (2013b) Balanced artificial bee colony algorithm. Int J Artif Intell Soft Comput 3(3):222–243CrossRefGoogle Scholar
  5. Bansal JC, Sharma H, Arya KV, Deep K, Pant M (2014a) Self-adaptive artificial bee colony. Optimization 63(10):1513–1532MathSciNetCrossRefzbMATHGoogle Scholar
  6. Bansal JC, Sharma H, Jadon SS, Clerc M (2014b) Spider monkey optimization algorithm for numerical optimization. Memet Comput 6(1):31–47CrossRefGoogle Scholar
  7. Barth FG, Biederman-Thorson MA (1985) Insects and flowers: the biology of a partnership. Princeton University Press, Princeton, p 111Google Scholar
  8. Dong N, Fang X, Wu AG (2016) A novel chaotic particle swarm optimization algorithm for parking space guidance. Math Probl Eng 2016:1–14, Art ID 5126808. doi: 10.1155/2016/5126808
  9. El-henawy I, Ismail M (2014) An improved chaotic flower pollination algorithm for solving large integer programming problems. Int J Digit Content Technol Appl 8(3):72Google Scholar
  10. Fister I, Perc M, Kamal SM (2015) A review of chaos-based firefly algorithms: perspectives and research challenges. Appl Math Comput 252:155–165MathSciNetzbMATHGoogle Scholar
  11. He X, Huang J, Rao Y, Gao L (2016) Chaotic teaching-learning-based optimization with Lévy flight for global numerical optimization. Comput Intell Neurosci 2016:43Google Scholar
  12. Hong YY, Beltran AA, Paglinawan AC (2016) A chaos-enhanced particle swarm optimization with adaptive parameters and its application in maximum power point tracking. Math Probl EngGoogle Scholar
  13. Hongwu L (2009) An adaptive chaotic particle swarm optimization. In: ISECS international colloquium on computing, communication, control, and management, 2009. CCCM 2009, vol 2. IEEE, pp 324–327Google Scholar
  14. Jadon SS, Bansal JC, Tiwari R, Sharma H (2014) Artificial bee colony algorithm with global and local neighborhoods. Int J Syst Assur Eng Manag 1–13. doi: 10.1007/s13198-014-0286-6
  15. Kohli M, Arora S (2017) Chaotic grey wolf optimization algorithm for constrained optimization problems. J Comput Des Eng. doi: 10.1016/j.jcde.2017.02.005 Google Scholar
  16. Liu H, Abraham A, Clerc M (2007) Chaotic dynamic characteristics in swarm intelligence. Appl Soft Comput 7(3):1019–1026CrossRefGoogle Scholar
  17. Łukasik S, Kowalski PA (2015) Study of flower pollination algorithm for continuous optimization. In: Intelligent systems’ 2014. Springer, Cham, pp 451–459Google Scholar
  18. Mantegna RN, Stanley HE (1994) Stochastic process with ultraslow convergence to a Gaussian: the truncated Lévy flight. Phys Rev Lett 73(22):2946MathSciNetCrossRefzbMATHGoogle Scholar
  19. Ouyang A, Pan G, Yue G, Du J (2014) Chaotic cuckoo search algorithm for high-dimensional functions. JCP 9(5):1282–1290CrossRefGoogle Scholar
  20. Pan G, Xu Y (2016) Chaotic glowworm swarm optimization algorithm based on Gauss mutation. In: 2016 12th international conference on natural computation, fuzzy systems and knowledge discovery (ICNC-FSKD). IEEE, pp 205–210Google Scholar
  21. Sharma H, Bansal, JC, Arya KV (2013) Opposition based lévy flight artificial bee colony. Memetic Comp 5(3):213–227CrossRefGoogle Scholar
  22. Sharma P, Sharma N, Sharma H (2017) Locally informed shuffled frog leaping algorithm. In: Proceedings of 6th international conference on soft computing for problem solving. Springer, Singapore, pp 141–152Google Scholar
  23. Song Y, Chen Z, Yuan Z (2007) New chaotic PSO-based neural network predictive control for nonlinear process. IEEE Trans Neural Netw 18(2):595–601CrossRefGoogle Scholar
  24. Talatahari S, Azar BF, Sheikholeslami R, Gandomi AH (2012) Imperialist competitive algorithm combined with chaos for global optimization. Commun Nonlinear Sci Numer Simul 17(3):1312–1319MathSciNetCrossRefzbMATHGoogle Scholar
  25. Vedula VSSS, Paladuga SR, Prithvi MR (2015) Synthesis of circular array antenna for sidelobe level and aperture size control using flower pollination algorithm. Int J Antennas Propag 2015:1–9, Art ID 819712. doi: 10.1155/2015/819712
  26. Waser NM (1986) Flower constancy: definition, cause, and measurement. Am Nat 127(5):593–603CrossRefGoogle Scholar
  27. Xiang-Tao L, Ming-Hao Y (2012) Parameter estimation for chaotic systems using the cuckoo search algorithm with an orthogonal learning method. Chin Phys B 21(5):050507CrossRefGoogle Scholar
  28. Yang XS (2010) Nature-inspired metaheuristic algorithms. Luniver press, BeckingtonGoogle Scholar
  29. Yang XS (2012) Chaos-enhanced firefly algorithm with automatic parameter tuning. Int J Swarm Intell Res 2(4):125–136Google Scholar
  30. Yang XS, Karamanoglu M, He X (2013) Multi-objective flower algorithm for optimization. Procedia Comput Sci 18:861–868CrossRefGoogle Scholar

Copyright information

© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2017

Authors and Affiliations

  • Arvinder Kaur
    • 1
  • Saibal K. Pal
    • 2
  • Amrit Pal Singh
    • 1
    Email author
  1. 1.USICT, GGSIPUNew DelhiIndia
  2. 2.SAG, DRDONew DelhiIndia

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