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An improved firefly algorithm for numerical optimization problems and it’s application in constrained optimization

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Abstract

Metaheuristic algorithms are successful methods of optimization. The firefly algorithm is one of the known metaheuristic algorithms used in a variety of applications. Recently, a new and efficient version of this algorithm was introduced as NEFA, which indicated a good performance in solving optimization problems. However, the introduced attraction model in this algorithm may not provide good coverage of the search space and thus trap the algorithm in a local optimum. In this paper, a new and efficient improved firefly algorithm called INEFA is proposed to improve the performance of NEFA. In INEFA, a new model of attraction is introduced in which each firefly can be attracted to brighter fireflies located in different areas of the search space, using the clustering concept to classify fireflies. To evaluate the performance of INEFA, it was used to optimize several known benchmark functions. The results were compared with the results of the firefly algorithm and some of its known improvements. The comparison of results indicated the significant power of INEFA compared to the algorithms. It was used to evaluate its application in solving a constrained optimization problem. The comparison results showed that INEFA performs better than most of the compared algorithms.

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References

  1. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95-international conference on neural networks, IEEE, vol 4, pp 1942–1948

  2. Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39

    Article  Google Scholar 

  3. Yang XS (2010) Nature-inspired metaheuristic algorithms. Luniver Press

  4. Gandomi AH, Yang XS, Alavi AH (2011) Mixed variable structural optimization using firefly algorithm. Comput Struct 89(23–24):2325–2336

    Article  Google Scholar 

  5. Marichelvam MK, Prabaharan T, Yang XS (2014) A discrete firefly algorithm for the multi-objective hybrid flowshop scheduling problems. IEEE Trans Evol Comput 18(2):301–305

    Article  Google Scholar 

  6. Yu S, Zhu S, Ma Y, Mao D (2015) A variable step size firefly algorithm for numerical optimization. Appl Math Comput 263:214–220

    MathSciNet  MATH  Google Scholar 

  7. Gandomi AH, Yang XS, Talatahari S, Alavi AH (2013) Firefly algorithm with chaos. Commun Nonlinear Sci Numer Simul 18(1):89–98

    Article  MathSciNet  Google Scholar 

  8. Wang H, Zhou X, Sun H, Yu X, Zhao J, Zhang H, Cui L (2017a) Firefly algorithm with adaptive control parameters. Soft Comput 21(17):5091–5102

    Article  Google Scholar 

  9. Wang H, Wang W, Zhou X, Sun H, Zhao J, Yu X, Cui Z (2017b) Firefly algorithm with neighborhood attraction. Inf Sci 382:374–387

    Article  Google Scholar 

  10. Wang H, Wang W, Sun H, Rahnamayan S (2016) Firefly algorithm with random attraction. Int J Bio-Inspir Comput 8(1):33–41

    Article  Google Scholar 

  11. Pan X, Xue L, Li R (2019) A new and efficient firefly algorithm for numerical optimization problems. Neural Comput Appl 31(5):1445–1453

    Article  Google Scholar 

  12. Awad NH, Ali MZ, Liang JJ, Qu BY, Suganthan PN (2016) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective bound constrained real-parameter numerical optimization. Technical Report, Nanyang Technological University, Singapore

  13. Fister I Jr, Yang XS, Fister I, Brest J (2012) Memetic firefly algorithm for combinatorial optimization. arXiv:12045165

  14. Yu S, Su S, Lu Q, Huang L (2014) A novel wise step strategy for firefly algorithm. Int J Comput Math 91(12):2507–2513

    Article  MathSciNet  Google Scholar 

  15. Zhang L, Liu L, Yang XS, Dai Y (2016) A novel hybrid firefly algorithm for global optimization. PloS one 11(9):1–17

    Google Scholar 

  16. Verma OP, Aggarwal D, Patodi T (2016) Opposition and dimensional based modified firefly algorithm. Expert Syst Appl 44:168–176

    Article  Google Scholar 

  17. Yelghi A, Köse C (2018) A modified firefly algorithm for global minimum optimization. Appl Soft Comput 62:29–44

    Article  Google Scholar 

  18. Feng Y, Wang GG, Wang L (2018) Solving randomized time-varying knapsack problems by a novel global firefly algorithm. Eng Comput 34(3):621–635

    Article  Google Scholar 

  19. Ahmed HA, Zolkipli MF, Ahmad M (2019) A novel efficient substitution-box design based on firefly algorithm and discrete chaotic map. Neural Comput Appl 31(11):7201–7210

    Article  Google Scholar 

  20. Xia X, Gui L, He G, Xie C, Wei B, Xing Y, Wu R, Tang Y (2018) A hybrid optimizer based on firefly algorithm and particle swarm optimization algorithm. J Comput Sci 26:488–500

    Article  Google Scholar 

  21. Zhou L, Ding L, Ma M, Tang W (2019) An accurate partially attracted firefly algorithm. Computing 101(5):477–493

    Article  MathSciNet  Google Scholar 

  22. Mishra S, Dash P (2019) Short-term prediction of wind power using a hybrid pseudo-inverse Legendre neural network and adaptive firefly algorithm. Neural Comput Appl 31(7):2243–2268

    Article  Google Scholar 

  23. Wang CF, Song WX (2019) A novel firefly algorithm based on gender difference and its convergence. Appl Soft Comput 80:107–124

    Article  Google Scholar 

  24. MacQueen J et al (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, Oakland, CA, USA, vol 1, pp 281–297

  25. Coello CAC, Pulido GT, Lechuga MS (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 8(3):256–279

    Article  Google Scholar 

  26. 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 

  27. 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  Google Scholar 

  28. Montemurro M, Vincenti A, Vannucci P (2013) The automatic dynamic penalisation method (ADP) for handling constraints with genetic algorithms. Comput Methods Appl Mech Eng 256:70–87

    Article  MathSciNet  Google Scholar 

  29. Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27(2):495–513

    Article  Google Scholar 

  30. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Article  Google Scholar 

  31. Gupta S, Deep K (2019) Improved sine cosine algorithm with crossover scheme for global optimization. Knowl Based Syst 165:374–406

    Article  Google Scholar 

  32. Houssein EH, Saad MR, Hashim FA, Shaban H, Hassaballah M (2020) Lévy flight distribution: a new metaheuristic algorithm for solving engineering optimization problems. Eng Appl Artif Intell 94:103731

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Faculty of Mathematics, Statistics and Computer Science, University of Sistan and Baluchestan, Zahedan, Iran

    Kamran Rezaei & Hassan Rezaei

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  1. Kamran Rezaei
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  2. Hassan Rezaei
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Correspondence to Hassan Rezaei.

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Rezaei, K., Rezaei, H. An improved firefly algorithm for numerical optimization problems and it’s application in constrained optimization. Engineering with Computers 38, 3793–3813 (2022). https://doi.org/10.1007/s00366-021-01412-9

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  • DOI: https://doi.org/10.1007/s00366-021-01412-9

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