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A novel enhanced exploration firefly algorithm for global continuous optimization problems

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Abstract

In the global optimization process of the firefly algorithm (FA), there is a need to provide a fast convergence rate and to explore the search space more effectively. Therefore, we conduct modular analysis of the FA and propose a novel enhanced exploration firefly algorithm (EE-FA), which includes an enhanced attractiveness term module and an enhanced random term module. The attractiveness term module can improve the exploration efficiency and accelerate the convergence rate by enhancing the attraction between fireflies. The random term module improves the exploration efficiency by introducing a damped vibration distribution factor. The EE-FA uses multiple parameters to balance its exploration efficiency and convergence rate. The parameters have a great influence on the performance of the EE-FA. In order to achieve the best performance of the EE-FA, each parameter of the EE-FA needs to be simulated to determine its optimal value. Compared to multiple variants of the FA, the EE-FA has better exploration efficiency and a faster convergence speed. Experimental results reveal that the EE-FA recreated consistently vanquishes the front for 24 benchmark functions and 4 real design case studies in terms of both convergence rate and exploration efficiency.

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References

  1. Horng MH (2012) Vector quantization using the firely algorithm for image compression. Expert Syst Appl 39(1):1078–1091

    Article  Google Scholar 

  2. Montiel O, Sepúlveda R, Orozco-Rosas U (2015) Optimal path planning generation for mobile robots using parallel evolutionary artificial potential field. J Intell Robot Syst 79(2):237–257

    Article  Google Scholar 

  3. Deb K (1995) Optimization for engineering design: algorithms and examples. Prentice-Hall, New Delhi

    Google Scholar 

  4. Yang X-S (2010) Firefly algorithm, stochastic test functions and design optimisation. arXiv:1003.1409

  5. Maeda K, Fukano Y, Yamamichi S, Nitta D, Kurata H (2011) An integrative and practical evolutionary optimization for a complex, dynamic model of biological networks. Bioprocess Biosyst Eng 34(4):433–446

    Article  Google Scholar 

  6. Horst R, Pardalos PM (1995) Handbook of global optimization.Spring- Science & Business Media, B.V.

  7. Kavousi-Fard A, Samet H, Marzbani F (2014) A new hybrid modified firefly algorithm and support vector regression model for accurate short term load forecasting. Expert Syst Appl 41(13):6047–6056

    Article  Google Scholar 

  8. Su CT, Lee CS (2003) Network reconfiguration of distribution systems using improved mixed-integer hybrid differential evolution. Power Deliv 18(3):1022–1027

    Article  Google Scholar 

  9. Goldfeld S M, Quandt R E, Trotter H F. (1996) Maximization by quadratic hill-climbing.Econometrica:journal of the econometric society .pp.541–551.

  10. Abbasbandy S (2003) Improving Newton-Raphson method for nonlinear equations by modified adomian decomposition method. Appl Math Comput 145(2):887–893

    MathSciNet  MATH  Google Scholar 

  11. Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7(4):308–313

    Article  MathSciNet  MATH  Google Scholar 

  12. Widrow B, Stearns D (1985) Adaptive signal processing. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  13. Liu J, Wang F, Zhao H, Han G (2017) Filtering algorithm and application of fuze echo signal based on LMS principle. J Proj Rockets Missiles Guidance 37(06):45-47+56

    Google Scholar 

  14. Yang X-S (2009) Firefly algorithms for multimodal optimization. In: International symposium on stochastic algorithm, pp 169–178

  15. Chu X, Niu B, Liang JJ et al (2016) An orthogonal-design hybrid particle swarm optimiser with application to capacitated facility location problem. Int J Bio Inspired Comput 8(5):268–285

    Article  Google Scholar 

  16. Yang X-S (2008) Nature-inspired Metaheuristic Algorithms. Luniver Press, Beckington

    Google Scholar 

  17. Yang X-S (2012) Flower pollination algorithm for global optimization. In: Durand-Lose J, Jonoska N (eds) Unconventional computation and natural computation, vol 7445. Springer, Berlin, pp 240–249

    Chapter  Google Scholar 

  18. Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47

    Article  Google Scholar 

  19. Li W, Xue M, Jian-guo L (2011) Feature selection and target recognition based on improved particle swarm optimization algorithm. Comput Eng Des 32(11)

  20. Zhen-long S, Xiao-ye L, Ying W (2015) Improved simple particle swarm optimization algorithm. Comput Sci 42(11A)

  21. Zwe-Lee G (2003) Discrete Particle swarm optimization algorithm for unit commitment. In: IEEE power engineering society general meeting, vol 1, Ontario, Canada, pp 418–424

  22. Gandomi AH, Alavi AH (2011) Multi-stage genetic programming: a new strategy to nonlinear system modelling. Inf Sci 181:5227–5239

  23. Gandomi AH, Yang XS (2011) Benchmark problems in structural optimization. In: Koziel S, Yang XS (eds) Computation optimization, methods and algorithms, Chapter 12. Spring, Berlin, pp 267–291

    Google Scholar 

  24. Lukasik S, Żak S (2009) Firefly algorithm for continuous constrained optimization tasks. In: International conference on computational collective intelligence, pp 97–106

  25. Yang X-S, Hosseini SSS, Gandomi AH (2012) Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect. Appl Soft Comput 12(3):1180–1186

    Article  Google Scholar 

  26. Jati GK et al (2011) Evolutionary discrete firefly algorithm for travelling salesman problem. In: Adaptive and intelligent systems. Springer, pp 393–403

  27. Sánchez D, Melin P, Castillo O (2017) Optimization of modular granular neural networks using a firefly algorithm for human recognition. Eng Appl Artif Intell 64:172–186

    Article  Google Scholar 

  28. Yang X-S, He X (2013) Firefly algorithm: recent advances and applications. arXiv:1308.3898

  29. Frumen O, Fevrier V, Oscar C, Claudia IG, Gabriela M, Patricia M (2017) Ant colony optimization with dynamic parameter adaptation based on interval type-2 fuzzy logic systems. Appl Soft Comput 53:74–87

    Article  Google Scholar 

  30. Daniela S, Patricia M, Oscar C (2020) Comparison of particle swarm optimization variants with fuzzy dynamic parameter adaptation for modular granular neural networks for human recognition. J Intell Fuzzy Syst 38:3229–3252

    Article  Google Scholar 

  31. Frumen O, Fevrier V, Oscar C, Patricia M (2016) Dynamic parameter adaptation in particle swarm optimization using interval type-2 fuzzy logic. Soft Comput 20:1057–1070

    Article  Google Scholar 

  32. Frumen O, Fevrier V, Patricia M, Alberto S, Oscar C (2019) Interval type-2 fuzzy logic for dynamic parameter adaptation in a modified gravitational search algorithm. Inf Sci 476:159–175

    Article  Google Scholar 

  33. Daniela S, Patricia M, Oscar C (2017) Optimization of modular granular neural networks using a firefly algorithm for human recognition. Eng Appl Artif Intell 64:172–186

    Article  Google Scholar 

  34. Lagunes ML, Castillo O, Valdez F, Soria J, Melin P (2018) Parameter optimization for membership functions of type-2 fuzzy controllers for autonomous mobile robots using the firefly algorithm. In: North American fuzzy information processing society annual conference, pp 569–579

  35. Castillo O, Soto C, Valdez F (2018) A review of fuzzy and mathematic methods for dynamic Parameter adaptation in the firefly algorithm. In: Advances in data analysis with computational Intelligence methods. Springer, pp 311–321

  36. Yang X-S (2010) Firefly algorithm, Levy flights and global optimization. In: Research and development in intelligent systems, vol xxvi. Springer, pp 209–218

  37. Shuhao Y, Xukun Z, Xianglin F, Zhengyu L, Mingjing P (2021) An improved firefly algorithm based on personalized step strategy. Computing. https://doi.org/10.1007/s00607-021-00919-9

    Article  MathSciNet  Google Scholar 

  38. Ao L, Li P, Deng X, Ren L (2021) A sigmoid attractiveness based improved firefly algorithm and its applications in IIR filter design. Connect Sci 33(1):1–25. https://doi.org/10.1080/09540091.2020.1742660

    Article  Google Scholar 

  39. Navid K, Abidhan B, Pijush S, Majidreza N, Annan Z, Danial JA (2021) A novel technique based on the improved firefly algorithm coupled with extreme learning machine (ELM-IFF) for predicting the thermal conductivity of soil. Eng Comput. https://doi.org/10.1007/s00366-021-01329-3

    Article  Google Scholar 

  40. Jinran W, Wang Y-G, Burrage K, Tian Y-C, Lawson B, Ding Z (2020) An improved firefly algorithm for global continuous optimization problems. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2020.113340

    Article  Google Scholar 

  41. Huang J, Cui X, Li D, Feng Y, Lu D (2004) Observation and data analysis in phase space for Pohl pendulum. Acta Sci Natur Univ Sunyatseni 43(Suppl):39–41

    Google Scholar 

  42. Surjanovic S, Bingham D (2018) Virtual library of simulation experiments: test functions and datasets. http://www.sfu.ca/~ssurjano. Accessed 3 Dec

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

    Article  Google Scholar 

  44. Fleury C, Braibant V (1986) Structural optimization: a new dual method using mixed variables. Int J Methods Eng 23(3):409–428

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  46. Dhiman G, Kumar V (2017) Spotted hyena optimizer: a novel bio-inspired based metaheuristic technique for engineering applications. Adv Eng Softw 114:48–70

Download references

Acknowledgements

This work utilizes the resources and services provided by Southeast University. The platform for calculating data is supported by the laboratory of Nanjing Institute of Technology. This work was supported by National Natural Science Foundation of China (Grant No. 51705238)

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JL conceptualization, investigation, methodology, validation, software, writing, revision, review and editing, visualization; JS supervision, project administration, funding acquisition; FH methodology, formal analysis; writing, revision; formal analysis; MD software, revision, review, conceptualization, formal analysis; XZ revision, review, analysis.

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Correspondence to Jianxun Liu or Jinfei Shi.

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Liu, J., Shi, J., Hao, F. et al. A novel enhanced exploration firefly algorithm for global continuous optimization problems. Engineering with Computers 38 (Suppl 5), 4479–4500 (2022). https://doi.org/10.1007/s00366-021-01477-6

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  • DOI: https://doi.org/10.1007/s00366-021-01477-6

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