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Butterfly optimization algorithm: a novel approach for global optimization

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Abstract

Real-world problems are complex as they are multidimensional and multimodal in nature that encourages computer scientists to develop better and efficient problem-solving methods. Nature-inspired metaheuristics have shown better performances than that of traditional approaches. Till date, researchers have presented and experimented with various nature-inspired metaheuristic algorithms to handle various search problems. This paper introduces a new nature-inspired algorithm, namely butterfly optimization algorithm (BOA) that mimics food search and mating behavior of butterflies, to solve global optimization problems. The framework is mainly based on the foraging strategy of butterflies, which utilize their sense of smell to determine the location of nectar or mating partner. In this paper, the proposed algorithm is tested and validated on a set of 30 benchmark test functions and its performance is compared with other metaheuristic algorithms. BOA is also employed to solve three classical engineering problems (spring design, welded beam design, and gear train design). Results indicate that the proposed BOA is more efficient than other metaheuristic algorithms.

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References

  • Arora JS (2004) Introduction to optimum design. Elsevier Academic Press, England

    Book  Google Scholar 

  • Arora S, Singh S (2013a) The firefly optimization algorithm: convergence analysis and parameter selection. Int J Comput Appl 69(3):48–52

    Google Scholar 

  • Arora S, Singh S (2013b) A conceptual comparison of firefly algorithm, bat algorithm and cuckoo search. In: 2013 international conference on control computing communication and materials (ICCCCM), IEEE, pp 1–4

  • Arora S, Singh S, Singh S, Sharma B (2014) Mutated firefly algorithm. In: 2014 international conference on parallel, distributed and grid computing (PDGC), IEEE, pp 33–38

  • Back T (1996) Evolutionary algorithms in theory and practice. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Baird JC, Noma EJ (1978) Fundamentals of scaling and psychophysics. Wiley, Hoboken

    Google Scholar 

  • Belegundu AD, Arora JS (1985) A study of mathematical programming methods for structural optimization. Part I: theory. Int J Numer Methods Eng 21(9):1583–1599

    Article  MATH  Google Scholar 

  • Blair RB, Launer AE (1997) Butterfly diversity and human land use: species assemblages along an urban grandient. Biol Conserv 80(1):113–125

    Article  Google Scholar 

  • Brownlee J (2011) Clever algorithms: nature-inspired programming recipes, 1st edn. LuLu. ISBN 978-1-4467-8506-5

  • Cao Y, Wu Q (1997) Mechanical design optimization by mixed-variable evolutionary programming. In: IEEE conference on evolutionary computation, IEEE Press, p 443–446

  • Coello CAC (2000a) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41(2):113–127

    Article  Google Scholar 

  • Coello CA (2000b) Constraint-handling using an evolutionary multiobjective optimization technique. Civil Eng Syst 17(4):319–346

    Article  Google Scholar 

  • Coello CAC, Montes EM (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inform 16(3):193–203

    Article  Google Scholar 

  • Deb K (1991) Optimal design of a welded beam via genetic algorithms. AIAA J 29(11):2013–2015

    Article  Google Scholar 

  • Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2):311–338

    Article  MATH  Google Scholar 

  • Deb K, Goyal M (1996) A combined genetic adaptive search (GeneAS) for engineering design. Comput Sci Inf 26:30–45

    Google Scholar 

  • Eberhart RC, Shi Y (2001) Particle swarm optimization: developments, applications and resources. In: Proceedings of the 2001 congress on evolutionary computation, 2001, vol 1. IEEE, pp 81–86

  • Fister I Jr, Yang X-S, Fister I, Brest J, Fister D (2013) A brief review of nature-inspired algorithms for optimization. arXiv preprint arXiv:1307.4186

  • Fu J-F, Fenton RG, Cleghorn WL (1991) A mixed integer-discrete-continuous programming method and its application to engineering design optimization. Eng Optim 17(4):263–280

    Article  Google Scholar 

  • Gandomi AH, Yang X-S, Alavi AH (2013a) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35

    Article  Google Scholar 

  • Gandomi AH, Yun GJ, Yang X-S, Talatahari S (2013) Chaos-enhanced accelerated particle swarm optimization. Commun Nonlinear Sci Numer Simul 18(2):327–340

    Article  MathSciNet  MATH  Google Scholar 

  • Gazi V, Passino KM (2004) Stability analysis of social foraging swarms. Syst Man Cybern Part B: Cybern IEEE Trans 34(1):539–557

    Article  Google Scholar 

  • Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3(2):95–99

    Article  Google Scholar 

  • Gupta S, Arora S (2015) A hybrid firefly algorithm and social spider algorithm for multimodal function. Intell Syst Technol Appl 1:17

    Google Scholar 

  • He Q, Wang L (2007) An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng Appl Artif Intell 20(1):89–99

    Article  Google Scholar 

  • Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT press, Cambridge

    Book  Google Scholar 

  • Huang F-Z, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186(1):340–356

    MathSciNet  MATH  Google Scholar 

  • Kalra S, Arora S (2016) Firefly algorithm hybridized with flower pollination algorithm for multimodal functions. In: Proceedings of the international congress on information and communication technology, Springer, Singapore, pp 207–219

  • Kannan B, Kramer SN (1994) An augmented lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. J Mech Des 116(2):405–411

    Article  Google Scholar 

  • Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (abc) algorithm. J Glob Optim 39(3):459–471

    Article  MathSciNet  MATH  Google Scholar 

  • Karaboga D, Basturk B (2008) On the performance of artificial bee colony (abc) algorithm. Appl Soft Comput 8(1):687–697

    Article  Google Scholar 

  • Kennedy J (2010) Particle swarm optimization. In: Sammut C, Webb GI (eds) Encyclopedia of machine learning. Springer, Boston, MA

    Google Scholar 

  • Lee KS, Geem ZW (2005) A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194(36):3902–3933

    Article  MATH  Google Scholar 

  • Liang JJ, Qu BY, Suganthan PN, Hernández-Díaz AG (2013) Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization. Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou, China and Nanyang Technological University, Singapore, Technical Report, 201212, 3–18

  • Loh HT, Papalambros PY (1991) A sequential linearization approach for solving mixed-discrete nonlinear design optimization problems. J Mech Des 113(3):325–334

    Article  Google Scholar 

  • MacKay D (1963) Psychophysics of perceived intensity: a theoretical basis for fechner’s and stevens’ laws. Science 139(3560):1213–1216

    Article  Google Scholar 

  • Maesono Y (1987) Competitors of the wilcoxon signed rank test. Ann Inst Stat Math 39(1):363–375

    Article  MathSciNet  MATH  Google Scholar 

  • Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579

    MathSciNet  MATH  Google Scholar 

  • Mezura-Montes E, Coello CAC (2008) An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. Int J Gen Syst 37(4):443–473

    Article  MathSciNet  MATH  Google Scholar 

  • Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  • Onwubolu GC, Babu B (2004) New optimization techniques in engineering, vol 141. Springer, Berlin

    Book  MATH  Google Scholar 

  • Parsopoulos KE, Vrahatis MN (2005) Unified particle swarm optimization for solving constrained engineering optimization problems. In: Wang L, Chen K, Ong YS (eds) Advances in natural computation. Springer, Berlin, pp 582–591

    Chapter  Google Scholar 

  • Pollard E, Yates TJ (1994) Monitoring butterflies for ecology and conservation: the British butterfly monitoring scheme. Springer, Berlin

    Google Scholar 

  • Ragsdell K, Phillips D (1976) Optimal design of a class of welded structures using geometric programming. J Manuf Sci Eng 98(3):1021–1025

    Google Scholar 

  • Raguso RA (2008) Wake up and smell the roses: the ecology and evolution of floral scent. Ann Rev Ecol Evolut Syst 39:549–569

    Article  Google Scholar 

  • Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248

    Article  MATH  Google Scholar 

  • Saccheri I, Kuussaari M, Kankare M, Vikman P, Fortelius W, Hanski I (1998) Inbreeding and extinction in a butterfly metapopulation. Nature 392(6675):491–494

    Article  Google Scholar 

  • Sandgren E (1990) Nonlinear integer and discrete programming in mechanical design optimization. J Mech Des 112(2):223–229

    Article  Google Scholar 

  • Shilane D, Martikainen J, Dudoit S, Ovaska SJ (2008) A general framework for statistical performance comparison of evolutionary computation algorithms. Inf Sci 178(14):2870–2879

    Article  Google Scholar 

  • Stevens SS (1975) Psychophysics. Transaction Publishers, Routledge

    Google Scholar 

  • Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    Article  MathSciNet  MATH  Google Scholar 

  • Talbi E-G (2009) Metaheuristics: from design to implementation, vol 74. Wiley, Hoboken

    Book  MATH  Google Scholar 

  • Wang G-G, Deb S, Cui Z (2015) Monarch butterfly optimization. Neural Comput Applic. https://doi.org/10.1007/s00521-015-1923-y

  • Wang G, Guo L, Wang H, Duan H, Liu L, Li J (2014) Incorporating mutation scheme into krill herd algorithm for global numerical optimization. Neural Comput Appl 24(3–4):853–871

    Article  Google Scholar 

  • Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evolut Comput 1(1):67–82

    Article  Google Scholar 

  • Wyatt TD (2003) Pheromones and animal behaviour: communication by smell and taste. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Yang X-S, Deb S (2009) Cuckoo search via lévy flights. In: World congress on nature and biologically inspired computing, NaBIC 2009, IEEE, pp 210–214

  • Yang X-S (2009) Firefly algorithms for multimodal optimization. In: Watanabe O, Zeugmann T (eds) Stochastic algorithms: foundations and applications. SAGA 2009. Lecture Notes in Computer Science, vol 5792. Springer, Berlin, Heidelberg

  • Yang X-S (2010a) Nature-inspired metaheuristic algorithms. Luniver press, Beckington

    Google Scholar 

  • Yang X-S (2010b) Firefly algorithm, levy flights and global optimization. In: Bramer M, Ellis R, Petridis M (eds) Research and development in intelligent systems XXVI. Springer, Berlin, pp 209–218

    Chapter  Google Scholar 

  • Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. Evolut Comput IEEE Trans 3(2):82–102

    Article  Google Scholar 

  • Zhang C, Wang H (1993) Mixed-discrete nonlinear optimization with simulated annealing. Eng Optim 21:277–91

    Article  Google Scholar 

  • Zwislocki JJ (2009) Sensory neuroscience: four laws of psychophysics: four laws of psychophysics. Springer, Berlin

    Book  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the contribution of I. K. Gujral Punjab Technical University, Kapurthala, Punjab, India.

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  1. I. K. GUJRAL Punjab Technical University, Jalandhar, Punjab, India

    Sankalap Arora & Satvir Singh

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  1. Sankalap Arora
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  2. Satvir Singh
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Correspondence to Sankalap Arora.

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Communicated by A. Di Nola.

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Arora, S., Singh, S. Butterfly optimization algorithm: a novel approach for global optimization. Soft Comput 23, 715–734 (2019). https://doi.org/10.1007/s00500-018-3102-4

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