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Enhanced Butterfly Optimization Algorithm for Large-Scale Optimization Problems

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Abstract

To solve large-scale optimization problems, Fragrance coefficient and variant Particle Swarm local search Butterfly Optimization Algorithm (FPSBOA) is proposed. In the position update stage of Butterfly Optimization Algorithm (BOA), the fragrance coefficient is designed to balance the exploration and exploitation of BOA. The variant particle swarm local search strategy is proposed to improve the local search ability of the current optimal butterfly and prevent the algorithm from falling into local optimality. 19 2000-dimensional functions and 20 1000-dimensional CEC 2010 large-scale functions are used to verify FPSBOA for complex large-scale optimization problems. The experimental results are statistically analyzed by Friedman test and Wilcoxon rank-sum test. All attained results demonstrated that FPSBOA can better solve more challenging scientific and industrial real-world problems with thousands of variables. Finally, four mechanical engineering problems and one ten-dimensional process synthesis and design problem are applied to FPSBOA, which shows FPSBOA has the feasibility and effectiveness in real-world application problems.

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References

  1. Fan, X. M., Yao, Q. H., Cai, Y. P., Miao, F., Sun, F. M., & Li, Y. (2018). Multiscaled fusion of deep convolutional neural networks for screening atrial fibrillation from single lead short ECG recordings. IEEE Journal of Biomedical and Health Informatics, 22, 1744–1753.

    Article  Google Scholar 

  2. Reddy, K. S., Panwar, L. K., Panigrahi, B. K., & Kumar, R. (2018). A new binary variant of sine–cosine algorithm: Development and application to solve profit-based unit commitment problem. Arabian Journal for Science and Engineering, 43, 4041–4056.

    Article  Google Scholar 

  3. Chen, S., Montgomery, J., & Bolufé-Röhler, A. (2015). Measuring the curse of dimensionality and its effects on particle swarm optimization and differential evolution. Applied Intelligence, 42, 514–526.

    Article  Google Scholar 

  4. Li, Y., Zhao, Y. R., & Liu, J. S. (2021). Dynamic sine cosine algorithm for large-scale global optimization problems. Expert Systems with Applications, 177, 114950.

    Article  Google Scholar 

  5. Salih, S. Q., & Alsewari, A. A. (2020). A new algorithm for normal and large-scale optimization problems: Nomadic people optimizer. Neural Computing and Applications, 32, 10359–10386.

    Article  Google Scholar 

  6. Anita, Yadav, A., & Kumar, N. (2020). Artificial electric field algorithm for engineering optimization problems. Expert Systems with Applications, 149, 113308.

    Article  Google Scholar 

  7. Dhiman, G., & Kumar, V. (2017). Spotted hyena optimizer: A novel bio-inspired based metaheuristic technique for engineering applications. Advances in Engineering Software, 114, 48–70.

    Article  Google Scholar 

  8. Dhiman, G., & Kaur, A. (2019). STOA: A bio-inspired based optimization algorithm for industrial engineering problems. Engineering Applications of Artificial Intelligence, 82, 148–174.

    Article  Google Scholar 

  9. Arora, S., & Singh, S. (2019). Butterfly optimization algorithm: A novel approach for global optimization. Soft Computing, 23, 715–734.

    Article  Google Scholar 

  10. Tan, L. S., Zainuddin, Z., & Ong, P. (2020). Wavelet neural networks based solutions for elliptic partial differential equations with improved butterfly optimization algorithm training. Applied Soft Computing, 95, 106518.

    Article  Google Scholar 

  11. Yıldız, B. S., Yıldız, A. R., Albak, E. İ, Abderazek, H., Sait, S. M., & Bureerat, S. (2020). Butterfly optimization algorithm for optimum shape design of automobile suspension components. Materials Testing, 62, 365–370.

    Article  Google Scholar 

  12. Long, W., Wu, T. B., Xu, M., Tang, M. Z., & Cai, S. H. (2021). Parameters identification of photovoltaic models by using an enhanced adaptive butterfly optimization algorithm. Energy, 229, 120750.

    Article  Google Scholar 

  13. Sharma, T. K. (2021). Enhanced butterfly optimization algorithm for reliability optimization problems. Journal of Ambient Intelligence and Humanized Computing, 12, 7595–7619.

    Article  Google Scholar 

  14. Maheshwari, P., Sharma, A. K., & Verma, K. (2021). Energy efficient cluster based routing protocol for WSN using butterfly optimization algorithm and ant colony optimization. Ad Hoc Networks, 110, 102317.

    Article  Google Scholar 

  15. Sharma, S., & Saha, A. K. (2021). BOSCA—a hybrid butterfly optimization algorithm modified with sine cosine algorithm. Progress in Advanced Computing and Intelligent Engineering, 1198, 360–372.

    Article  Google Scholar 

  16. Fan, Y. Q., Shao, J. P., Sun, G. T., & Shao, X. (2020). A self-adaption butterfly optimization algorithm for numerical optimization problems. IEEE Access, 8, 88026–88041.

    Article  Google Scholar 

  17. Sharma, S., & Saha, A. K. (2020). m-MBOA: A novel butterfly optimization algorithm enhanced with mutualism scheme. Soft Computing, 24, 4809–4827.

    Article  Google Scholar 

  18. Mortazavi, A., & Moloodpoor, M. (2021). Enhanced butterfly optimization algorithm with a new fuzzy regulator strategy and virtual butterfly concept. Knowledge-based Systems, 228, 107291.

    Article  Google Scholar 

  19. Long, W., Wu, T. B., Tang, M. Z., Xu, M., & Cai, S. H. (2020). Grey wolf optimizer algorithm based on lens imaging learning strategy. Acta Automatica Sinica, 46, 2148–2164. in Chinese.

    MATH  Google Scholar 

  20. Yi J. Improvements of harmony search algorithm with its applications in optimization. PhD thesis, Huazhong University of Science and Technology, Wuhan, China, 2017. (in Chinese)

  21. Poli, R., Kennedy, J., & Blackwell, T. (2007). Particle swarm optimization. Swarm Intelligence, 1, 33–57.

    Article  Google Scholar 

  22. Jamil, M., & Yang, X. S. (2013). A literature survey of benchmark functions for global optimisation problems. International Journal of Mathematical Modelling and Numerical Optimisation, 4, 150–194.

    Article  MATH  Google Scholar 

  23. Sun, Y. J., Wang, X. L., Chen, Y. H., & Liu, Z. J. (2018). A modified whale optimization algorithm for large-scale global optimization problems. Expert Systems with Applications, 114, 563–577.

    Article  Google Scholar 

  24. Hadi, A. A., Mohamed, A. W., & Jambi, K. M. (2019). LSHADE-SPA memetic framework for solving large-scale optimization problems. Complex & Intelligent Systems, 5, 25–40.

    Article  Google Scholar 

  25. Dhiman, G., & Kumar, V. (2019). Seagull optimization algorithm: Theory and its applications for large-scale industrial engineering problems. Knowledge-based Systems, 165, 169–196.

    Article  Google Scholar 

  26. Mirjalili, S. (2016). SCA: A sine cosine algorithm for solving optimization problems. Knowledge-based systems, 96, 120–133.

    Article  Google Scholar 

  27. Kaur, S., Awasthi, L. K., Sangal, A. L., & Dhiman, G. (2020). Tunicate swarm algorithm: a new bio-inspired based metaheuristic paradigm for global optimization. Engineering Applications of Artificial Intelligence, 90, 103541.

    Article  Google Scholar 

  28. Mirjalili, S., & Lewis, A. (2016). The whale optimization algorithm. Advances in Engineering Software, 95, 51–67.

    Article  Google Scholar 

  29. Heidari, A. A., Mirjalili, S., Faris, H., Aljarah, I., Mafarja, M., & Chen, H. L. (2019). Harris hawks optimization: Algorithm and applications. Future Generation Computer Systems, 97, 849–872.

    Article  Google Scholar 

  30. Faramarzi, A., Heidarinejad, M., Mirjalili, S., & Gandomi, A. H. (2020). Marine predators algorithm: a nature-inspired metaheuristic. Expert Systems with Applications, 152, 113377.

    Article  Google Scholar 

  31. Meddis, R. (1980). Unified analysis of variance by ranks. British Journal of Mathematical and Statistical Psychology, 33, 84–98.

    Article  MathSciNet  MATH  Google Scholar 

  32. Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1, 80–83.

    Article  Google Scholar 

  33. Hu, K., Jiang, H., Ji, C. G., & Pan, Z. (2021). A modified butterfly optimization algorithm: an adaptive algorithm for global optimization and the support vector machine. Expert Systems, 38, e12642.

    Article  Google Scholar 

  34. Wu, J., Nan, R. J., & Chen, L. (2019). Improved salp swarm algorithm based on weight factor and adaptive mutation. Journal of Experimental & Theoretical Artificial Intelligence, 31, 493–515.

    Article  Google Scholar 

  35. Yang, X. S., & He, X. S. (2013). Bat algorithm: Literature review and applications. International Journal of Bio-inspired computation, 5, 141–149.

    Article  Google Scholar 

  36. Mirjalili, S. (2016). Dragonfly algorithm: A new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Computing and Applications, 27, 1053–1073.

    Article  Google Scholar 

  37. Gandomi, A. H., Yang, X. S., & Alavi, A. H. (2013). Cuckoo search algorithm: A metaheuristic approach to solve structural optimization problems. Engineering with Computers, 29, 17–35.

    Article  Google Scholar 

  38. Ray, T., & Saini, P. (2001). Engineering design optimization using a swarm with an intelligent information sharing among individuals. Engineering Optimization, 33, 735–748.

    Article  Google Scholar 

  39. Lee, K. S., & Geem, Z. W. (2005). A new meta-heuristic algorithm for continuous engineering optimization: Harmony search theory and practice. Computer Methods in Applied Mechanics and Engineering, 194, 3902–3933.

    Article  MATH  Google Scholar 

  40. Liu, J. L. (2005). Novel orthogonal simulated annealing with fractional factorial analysis to solve global optimization problems. Engineering Optimization, 37, 499–519.

    Article  MathSciNet  Google Scholar 

  41. Atiqullah, M. M., & Rao, S. S. (2000). Simulated annealing and parallel processing: An implementation for constrained global design optimization. Engineering Optimization, 32, 659–685.

    Article  Google Scholar 

  42. Babalik, A., Cinar, A. C., & Kiran, M. S. (2018). A modification of tree-seed algorithm using Deb’s rules for constrained optimization. Applied Soft Computing, 63, 289–305.

    Article  Google Scholar 

  43. Gandomi, A. H. (2014). Interior search algorithm (ISA): A novel approach for global optimization. ISA Transactions, 53, 1168–1183.

    Article  Google Scholar 

  44. He, S., Prempain, E., & Wu, Q. H. (2004). An improved particle swarm optimizer for mechanical design optimization problems. Engineering Optimization, 36, 585–605.

    Article  MathSciNet  Google Scholar 

  45. Deb, K. (1991). Optimal design of a welded beam via genetic algorithms. AIAA Journal, 29, 2013–2015.

    Article  Google Scholar 

  46. Akhtar, S., Tai, K., & Ray, T. (2002). A socio-behavioural simulation model for engineering design optimization. Engineering Optimization, 34, 341–354.

    Article  Google Scholar 

  47. Dinkar, S. K., & Deep, K. (2018). An efficient opposition based Lévy flight antlion optimizer for optimization problems. Journal of Computational Science, 29, 119–141.

    Article  Google Scholar 

  48. Zhang, J. L., Liang, C. Y., Huang, Y. Q., Wu, J., & Yang, S. L. (2009). An effective multiagent evolutionary algorithm integrating a novel roulette inversion operator for engineering optimization. Applied Mathematics and Computation, 211, 392–416.

    Article  MathSciNet  MATH  Google Scholar 

  49. Hedar, A. R., & Fukushima, M. (2006). Derivative-free filter simulated annealing method for constrained continuous global optimization. Journal of Global Optimization, 35, 521–549.

    Article  MathSciNet  MATH  Google Scholar 

  50. Mirjalili, S., Mirjalili, S. M., & Hatamlou, A. (2016). Multi-verse optimizer: A nature-inspired algorithm for global optimization. Neural Computing and Applications, 27, 495–513.

    Article  Google Scholar 

  51. Coello, C. A. C., & Montes, E. M. (2002). Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Advanced Engineering Informatics, 16, 193–203.

    Article  Google Scholar 

  52. Arora, J. S. (2004). Introduction to Optimum Design (p. 728). Elsevier Academic Presss.

    Google Scholar 

  53. Belegundu, A. D., & Arora, J. S. (1985). A study of mathematical programming methods for structural optimization. Part I: theory. International Journal for Numerical Methods in Engineering, 21, 1583–1599.

    Article  MathSciNet  MATH  Google Scholar 

  54. Mirjalili, S. (2015). The ant lion optimizer. Advances in Engineering Software, 83, 80–98.

    Article  Google Scholar 

  55. Saremi, S., Mirjalili, S., & Lewis, A. (2017). Grasshopper optimisation algorithm: Theory and application. Advances in Engineering Software, 105, 30–47.

    Article  Google Scholar 

  56. Zhou, Y. Q., Ling, Y., & Luo, Q. F. (2018). Lévy flight trajectory-based whale optimization algorithm for engineering optimization. Engineering Computations, 35, 2406–2428.

    Article  Google Scholar 

  57. Coello, C. A. C. (2000). Use of a self-adaptive penalty approach for engineering optimization problems. Computers in Industry, 41, 113–127.

    Article  Google Scholar 

  58. Kumar, A., Wu, G. H., Ali, M. Z., Mallipeddi, R., Suganthan, P. N., & Das, S. (2020). A test-suite of non-convex constrained optimization problems from the real-world and some baseline results. Swarm and Evolutionary Computation, 56, 100693.

    Article  Google Scholar 

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Funding

This study was funded by the National Natural Science Foundation of China (No. 72104069), the Science and Technology Department of Henan Province, China (No. 182102310886 and 162102110109), and the Postgraduate Meritocracy Scheme, China (No. SYL19060145).

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Authors and Affiliations

  1. Institute of Management Science and Engineering, and School of Business, Henan University, Kaifeng, 475004, China

    Yu Li

  2. School of Business, Henan University, Kaifeng, 475004, China

    Xiaomei Yu

  3. Institute of Intelligent Network Systems, and Software School, Henan University, Kaifeng, 475004, China

    Jingsen Liu

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  1. Yu Li
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Correspondence to Jingsen Liu.

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Li, Y., Yu, X. & Liu, J. Enhanced Butterfly Optimization Algorithm for Large-Scale Optimization Problems. J Bionic Eng 19, 554–570 (2022). https://doi.org/10.1007/s42235-021-00143-3

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