A new and efficient firefly algorithm for numerical optimization problems

  • Xiuqin Pan
  • Limiao Xue
  • Ruixiang Li
S.I. : Emerging Intelligent Algorithms for Edge-of-Things Computing


Firefly algorithm (FA) is an excellent global optimizer based on swarm intelligence. Some recent studies show that FA was used to optimize various engineering problems. However, there are some drawbacks for FA, such as slow convergence rate and low precision solutions. To tackles these issues, a new and efficient FA (namely NEFA) is proposed. In NEFA, three modified strategies are employed. First, a new attraction model is used to determine the number of attracted fireflies. Second, a new search operator is designed for some better fireflies. Third, the step factor is dynamically updated during the iterations. Experiment verification is carried out on ten famous benchmark functions. Experimental results demonstrate that our new approach NEFA is superior to three other different versions of FA.


Firefly algorithm Convergence speed Attraction Adaptive parameter 



This work is supported by the project of the First-Class University and the First-Class Discipline (No. 10301-017004011501), and the National Natural Science Foundation of China.

Compliance with ethical standards

Conflict of interest

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.


  1. 1.
    Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, pp 1942–1948Google Scholar
  2. 2.
    Wang H, Sun H, Li C, Rahnamayan S, Pan JS (2013) Diversity enhanced particle swarm optimization with neighborhood search. Inf Sci 223:119–135MathSciNetCrossRefGoogle Scholar
  3. 3.
    Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern Part B (Cybern) 26(1):29–41CrossRefGoogle Scholar
  4. 4.
    Yang XS (2010) Firefly algorithm, stochastic test functions and design optimization. Int J Bio-Inspired Comput 2(2):78–84CrossRefGoogle Scholar
  5. 5.
    Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical Report-TR06, Erciyes University, engineering Faculty, Computer Engineering DepartmentGoogle Scholar
  6. 6.
    Wang H, Wu ZJ, Rahnamayan S, Sun H, Liu Y, Pan JS (2014) Multi-strategy ensemble artificial bee colony algorithm. Inf Sci 279:587–603MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Yang XS, Deb S (2010) Engineering optimisation by cuckoo search. Int J Math Model Numer Optim 1(4):330–343zbMATHGoogle Scholar
  8. 8.
    Zhang MQ, Wang H, Cui ZH, Chen JJ (2017) Hybrid multi-objective cuckoo search with dynamical local search. Memet Comput. Google Scholar
  9. 9.
    Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: González JR, Pelta DA, Cruz C, Terrazas G, Krasnogor N (eds) Nature inspired cooperative strategies for optimization (NICSO 2010). Studies in computational intelligence, vol 284. Springer, BerlinGoogle Scholar
  10. 10.
    Cai XJ, Wang H, Cui ZH, Cai JH, Xue Y, Wang L (2017) Bat algorithm with triangle-flipping strategy for numerical optimization. Int J Mach Learn Cybern. Google Scholar
  11. 11.
    Fister JI, Fister I, Yang XS, Brest J (2013) A comprehensive review of firefly algorithms. Swarm Evol Comput 13:34–46CrossRefGoogle Scholar
  12. 12.
    Wang H, Wang WJ, Zhou XY, Sun H, Zhao J, Yu X, Cui ZH (2017) Firefly algorithm with neighborhood attraction. Inf Sci 382–383:374–387CrossRefGoogle Scholar
  13. 13.
    Wang H, Zhou XY, Sun H, Yu X, Zhao J, Zhang H, Cui LZ (2017) Firefly algorithm with adaptive control parameters. Soft Comput 21(17):5091–5102CrossRefGoogle Scholar
  14. 14.
    Yang XS (2008) Nature-inspired metaheuristic algorithms. Luniver Press, BeckingtonGoogle Scholar
  15. 15.
    Fister JI, Yang XS, Fister I, Brest J (2012) Memetic firefly algorithm for combinatorial optimization. In: Bioinspired optimization methods and their applications (BIOMA), pp 1–14Google Scholar
  16. 16.
    Wang H, Cui ZH, Sun H, Rahnamayan S, Yang XS (2017) Randomly attracted firefly algorithm with neighborhood search and dynamic parameter adjustment mechanism. Soft Comput 21(18):5325–5339CrossRefGoogle Scholar
  17. 17.
    Tighzert L, Fonlupt C, Mendil B (2017) A set of new compact firefly algorithms. Swarm Evol Comput. Google Scholar
  18. 18.
    Cheung NJ, Ding XM, Shen HB (2016) A non-homogeneous firefly algorithm and its convergence analysis. J Optim Theory Appl 170(2):616–628MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Yelghi A, Köse C (2018) A modified firefly algorithm for global minimum optimization. Appl Soft Comput 62:29–44CrossRefGoogle Scholar
  20. 20.
    Tilahun SL, Ngnotchouye JMT, Hamadneh NN (2017) Continuous versions of firefly algorithm: a review. Artif Intell Rev. Google Scholar
  21. 21.
    Zouache D, Nouioua F, Moussaoui A (2016) Quantum-inspired firefly algorithm with particle swarm optimization for discrete optimization problems. Soft Comput 20(7):2781–2799CrossRefGoogle Scholar
  22. 22.
    Wang H, Wang WJ, Cui LZ, Sun H, Zhao J, Wang Y, Xue Y (2017) A hybrid multi-objective firefly algorithm for big data optimization. Appl Soft Comput. Google Scholar
  23. 23.
    He L, Huang S (2017) Modified firefly algorithm based multilevel thresholding for color image segmentation. Neurocomputing 240:152–174CrossRefGoogle Scholar
  24. 24.
    Lieu QX, Doand DTT, Lee J (2018) An adaptive hybrid evolutionary firefly algorithm for shape and size optimization of truss structures with frequency constraints. Comput Struct 195:99–112CrossRefGoogle Scholar
  25. 25.
    Wang H, Wang WJ, Sun H, Rahnamayan S (2016) Firefly algorithm with random attraction. Int J Bio-Inspired Comput 8(1):33–41CrossRefGoogle Scholar
  26. 26.
    Wang H, Rahnamayan S, Sun H, Omran MGH (2013) Gaussian bare-bones differential evolution. IEEE Trans Cybern 43(2):634–647CrossRefGoogle Scholar
  27. 27.
    Zhou XY, Wang H, Wang MW, Wan JY (2017) Enhancing the modified artificial bee colony algorithm with neighborhood search. Soft Comput 21(10):2733–2743CrossRefGoogle Scholar
  28. 28.
    Wang H, Wu ZJ, Rahnamayan S, Liu Y, Ventresca M (2011) Enhancing particle swarm optimization using generalized opposition-based learning. Inf Sci 181(20):4699–4714MathSciNetCrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  1. 1.School of Information EngineeringMinzu University of ChinaBeijingChina

Personalised recommendations