Advertisement

Effect of Population Size Over Parameter-less Firefly Algorithm

  • Krishna Gopal DhalEmail author
  • Samarendu Sahoo
  • Arunita Das
  • Sanjoy Das
Chapter
Part of the Springer Tracts in Nature-Inspired Computing book series (STNIC)

Abstract

Nature-inspired optimization algorithms have proved their efficacy for solving highly nonlinear problems in science and engineering. Firefly Algorithm (FA), which is one of them, has been taken to be broadly discussed here. However, practical studies demonstrate that the proper setting of the FA’s parameters is the key difficulty. FA associates with some sensitive parameters, and proper setting of their values is extremely time-consuming. Therefore, parameter less variants of FA have been proposed in this study by incorporating the adaptive formulation of the control parameters which are free from the tuning procedure. Population size greatly influences the convergence of any nature-inspired optimization algorithm. Generally, lower population size enhances convergence speed but may trap into local optima. While larger population size maintains the diversity but slows down the convergence rate. Therefore, the crucial effect of different population size over FA’s efficiency has also been investigated here. The population size (of considered FA is varied within the size [10, 1280] where it gets doubled in each run starting with \(n = 10\). Therefore, eight instances of FA have been executed, and the best one is considered by the user over different classes of functions. Experimental results also show that the proposed parameter-less FA with a population size between 40 and 80 provides best results by considering optimization ability and consistency over any classes of functions.

Keywords

Nature-inspired optimization Swarm intelligence Firefly Algorithm Parameter-less Population size 

References

  1. 1.
    Yang XS (2010) Nature-inspired metaheuristic algorithms. Luniver pressGoogle Scholar
  2. 2.
    Yang XS (2010) Engineering optimization: an introduction to metaheuristic applications. WileyGoogle Scholar
  3. 3.
    Eberhart R, Kennedy J (1995 Oct) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, 1995. MHS’95. IEEE, New York, pp 39–43Google Scholar
  4. 4.
    Yang XS (2010) Firefly algorithm, Lévy flights, and global optimization. In: Research and development in intelligent systems XXVI. Springer, London, pp 209–218Google Scholar
  5. 5.
    Yang XS, Deb S (2009 Dec) Cuckoo search via Lévy flights. In: NaBIC 2009. world congress on nature & biologically inspired computing, 2009. IEEE, New York, pp 210–214Google Scholar
  6. 6.
    Yang XS (2010) A new metaheuristic bat-inspired algorithm. Nature inspired cooperative strategies for optimization (NICSO 2010), 65–74Google Scholar
  7. 7.
    Dhal KG, Das A, Ray S, Gálvez J, Das S (2019) Nature-inspired optimization algorithms and their application in multi-thresholding image segmentation. Arch Comput Methods Eng, 1–34.  https://doi.org/10.1007/s11831-019-09334-y
  8. 8.
    Dhal KG, Ray S, Das A, Das S (2018) A survey on nature-inspired optimization algorithms and their application in image enhancement domain. Arch Comput Methods Eng, 1–32.  https://doi.org/10.1007/s11831-018-9289-9MathSciNetCrossRefGoogle Scholar
  9. 9.
    Yang XS, He X (2016) Nature-inspired optimization algorithms in engineering: overview and applications. In: Nature-inspired computation in engineering. Springer International Publishing, pp 1–20Google Scholar
  10. 10.
    Booker L (ed) (2005) Perspectives on adaptation in natural and artificial systems (vol 8). Oxford University Press on DemandGoogle Scholar
  11. 11.
    Valdez F, Melin P, Castillo O (2014) A survey on nature-inspired optimization algorithms with fuzzy logic for dynamic parameter adaptation. Expert Syst Appl 41(14):6459–6466CrossRefGoogle Scholar
  12. 12.
    Sheikholeslami R, Kaveh A (2013) A survey of chaos embedded meta-heuristic algorithms. Int J Optim Civil Eng 3(4):617–633Google Scholar
  13. 13.
    Črepinšek M, Liu SH, Mernik M (2013) Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput Surv (CSUR) 45(3):35CrossRefGoogle Scholar
  14. 14.
    Črepinšek M, Mernik M, Liu SH (2011) Analysis of exploration and exploitation in evolutionary algorithms by ancestry trees. Int J Innov Comput Appl 3(1):11–19CrossRefGoogle Scholar
  15. 15.
    Eiben AE, Schippers CA (1998) On evolutionary exploration and exploitation. Fundam Inf 35(1–4):35–50zbMATHGoogle Scholar
  16. 16.
    Bansal JC, Singh PK, Saraswat M, Verma A, Jadon SS, Abraham A (2011 Oct) Inertia weight strategies in particle swarm optimization. In: 2011 third world congress on nature and biologically inspired computing (NaBIC). IEEE, pp 633–640Google Scholar
  17. 17.
    Yang X, Yuan J, Yuan J, Mao H (2007) A modified particle swarm optimizer with dynamic adaptation. Appl Math Comput 189(2):1205–1213MathSciNetzbMATHGoogle Scholar
  18. 18.
    Wang H, Wu Z, Rahnamayan S (2011) Particle swarm optimisation with simple and efficient neighbourhood search strategies. Int J Innov Comput Appl 3:97–104CrossRefGoogle Scholar
  19. 19.
    Wang H, Cui Z, Sun H, Rahnamayan S, Yang XS, Randomly attracted firefly algorithm with neighborhood search and dynamic parameter adjustment mechanism. Soft Comput, pp 1–15.  https://doi.org/10.1007/s00500-016-2116-zCrossRefGoogle Scholar
  20. 20.
    Baykasoğlu A, Ozsoydan FB (2015) Adaptive firefly algorithm with chaos for mechanical design optimization problems. Appl Soft Comput 36:152–164CrossRefGoogle Scholar
  21. 21.
    Baykasoğlu A, Ozsoydan FB (2014) An improved firefly algorithm for solving dynamic multidimensional knapsack problems. Expert Syst Appl 41(8):3712–3725CrossRefGoogle Scholar
  22. 22.
    Ozsoydan FB, Baykasoglu A (2015 Dec) A multi-population firefly algorithm for dynamic optimization problems. In: 2015 IEEE international conference on evolving and adaptive intelligent systems (EAIS). IEEE, pp 1–7Google Scholar
  23. 23.
    Samanta S, Mukherjee A, Ashour AS, Dey N, Tavares JMR, Abdessalem Karâa WB, … Hassanien AE (2018) Log transform based optimal image enhancement using firefly algorithm for autonomous mini unmanned aerial vehicle: an application of aerial photography. Int J Image Gr 18(04):1850019CrossRefGoogle Scholar
  24. 24.
    Dhal KG, Quraishi MI, Das S (2016) Development of firefly algorithm via chaotic sequence and population diversity to enhance the image contrast. Nat Comput 15(2):307–318MathSciNetCrossRefGoogle Scholar
  25. 25.
    Dey N, Samanta S, Chakraborty S, Das A, Chaudhuri SS, Suri JS (2014) Firefly algorithm for optimization of scaling factors during embedding of manifold medical information: an application in ophthalmology imaging. J Med Imaging Health Inf 4(3):384–394CrossRefGoogle Scholar
  26. 26.
    Dhal KG, Das S (2018) Colour retinal images enhancement using modified histogram equalisation methods and firefly algorithm. Int J Biomed Eng Technol 28(2):160–184CrossRefGoogle Scholar
  27. 27.
    Jagatheesan K, Anand B, Samanta S, Dey N, Ashour AS, Balas VE (2017) Design of a proportional-integral-derivative controller for an automatic generation control of multi-area power thermal systems using firefly algorithm. IEEE/CAA J Automat SinGoogle Scholar
  28. 28.
    Fister I Jr, Mlakar U, Yang X-S, Fister I (2016) Parameterless bat algorithm and its performance study. Nat Inspir Comput Eng Stud Comput Intell 637:267–276Google Scholar
  29. 29.
    Lobo FG, Goldberg DE (2003) An overview of the parameterless genetic algorithm. In: Proceedings of the 7th joint conference on information sciences (Invited paper), pp 20–23Google Scholar
  30. 30.
    Papa G (2013) Parameter-less algorithm for evolutionary-based optimization For continuous and combinatorial problems. Comput Optim Appl 56:209–229MathSciNetCrossRefGoogle Scholar
  31. 31.
    Teo J, Hamid MY (2005) A parameterless differential evolution optimizer. In: Proceedings of the 5th WSEAS/IASME international conference on systems theory and scientific computation, pp 330–335Google Scholar
  32. 32.
    De-Silva LA, da-Costa KAP, Ribeiro PB, Rosa G, Papa JP (2015) Parameter-setting free harmony search optimization of restricted Boltzmann machines and its applications to spam detection. In: 12th international conference applied computing, pp 143–150Google Scholar
  33. 33.
    Dhal KG, Fister I Jr, Das S (2017) Parameterless harmony search for image multi-thresholding. In: 4th student computer science research conference (StuCosRec-2017), pp 5–12Google Scholar
  34. 34.
    Dhal KG, Sen M, Das S (2018) Multi-thresholding of histopathological images using Fuzzy entropy and parameterless Cuckoo Search. In: Critical developments and application of swarm intelligence (IGI-GLOBAL), pp 339–356Google Scholar
  35. 35.
    Dhal KG, Sen M, Ray S, Das S (2018) Multi-thresholded histogram equalization based on parameterless artificial bee colony. In: Incorporating of nature-inspired paradigms in computational applications, (IGI-GLOBAL), pp 108–126Google Scholar
  36. 36.
    Liang J, Qu B, Suganthan P, Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real parameter numerical optimization. Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, SingaporeGoogle Scholar
  37. 37.
    Durbhaka GK, Selvaraj B, Nayyar A (2019) Firefly swarm: metaheuristic swarm intelligence technique for mathematical optimization. In: Data management, analytics and innovation. Springer, Singapore, pp 457–466Google Scholar
  38. 38.
    Röhler AB, Chen S (2011 Dec) An analysis of sub-swarms in multi-swarm systems. In: Australasian joint conference on artificial intelligence. Springer, Berlin, pp 271–280CrossRefGoogle Scholar
  39. 39.
    Lanzarini L, Leza V, De Giusti A (2008 June) Particle swarm optimization with variable population size. In: International conference on artificial intelligence and soft computing. Springer, Berlin, pp 438–449CrossRefGoogle Scholar
  40. 40.
    Zhu W, Tang Y, Fang JA, Zhang W (2013) Adaptive population tuning scheme for differential evolution. Inf Sci 223:164–191CrossRefGoogle Scholar
  41. 41.
    Chen D, Zhao C (2009) Particle swarm optimization with adaptive population size and its application. Appl Soft Comput 9(1):39–48CrossRefGoogle Scholar
  42. 42.
    Piotrowski AP (2017) Review of differential evolution population size. Swarm Evolut Comput 32:1–24CrossRefGoogle Scholar
  43. 43.
    Derrac J, Garcia S, Molina D, 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 1:3–18CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Krishna Gopal Dhal
    • 1
    Email author
  • Samarendu Sahoo
    • 2
  • Arunita Das
    • 3
  • Sanjoy Das
    • 4
  1. 1.Department of Computer Science and ApplicationMidnapore College (Autonomous)Paschim MedinipurIndia
  2. 2.Department of Computer ScienceVidyasagar UniversityPaschim MedinipurIndia
  3. 3.Department of Information TechnologyKalyani Government Engineering CollegeKalyaniIndia
  4. 4.Department of Engineering & Technological StudiesUniversity of KalyaniKalyaniIndia

Personalised recommendations