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Black eagle optimizer: a metaheuristic optimization method for solving engineering optimization problems

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Abstract

This paper proposes a new intelligent optimization algorithm named Black Eagle Optimizer (BEO) based on the biological behaviour of the black eagle. The BEO algorithm combines the biological laws of the black eagle and mathematical transformations to guide the search behaviour of the particles. The highly adaptive BEO algorithm has strong optimisation capabilities due to its unique algorithmic structure and novel iterative approach. In the performance testing experiments of the BEO algorithm, this paper firstly conducts the parametric analysis experiments of the BEO algorithm, then analyses the complexity of the BEO algorithm, and finally conducts a comprehensive testing of the performance of the BEO algorithm on 30 CEC2017 test functions with the widest variety of functions and 12 newest CEC2022 test functions, and its performance is compared with the seven state-of-the-art optimization algorithms. The test results show that the convergence accuracy of the BEO algorithm reaches the theoretical value in 100% of unimodal functions, the convergence accuracy is higher than the comparison algorithm in 78.95% of complex functions, and the standard deviation ranks in the top three in 90.48% of functions, which demonstrates the outstanding local optimisation ability, global optimisation ability and stability of BEO algorithm. Meanwhile, the BEO algorithm also maintains a fast convergence speed. However, the complexity analysis shows that the BEO algorithm has the disadvantage of slightly higher complexity. In order to verify the optimisation ability of the BEO algorithm in real engineering problems, we used the BEO algorithm to deal with four complex engineering design problems. The experimental results show that the BEO algorithm has excellent convergence accuracy and stability when dealing with real engineering problems, but the real-time performance is slightly below average. Therefore, the BEO algorithm is optimal for handling non-real-time engineering optimisation problems. The source code of the BEO algorithm is available at https://github.com/haobinzhang123/A-metaheuristic-algorithm.

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References

  1. Gao, G., Zhang, S., Na, J., Liu, F.: Industrial robot trajectory error compensation based on calibration and joint space interpolation. J. Mech. Eng. 57(21), 55–67 (2021)

    Google Scholar 

  2. Grebner, T., Janoudi, V., Schoeder, P., Waldschmidt, C.: Self-calibration of a network of radar sensors for autonomous robots. IEEE Trans. Aerosp. Electron. Syst. (2023). https://doi.org/10.1109/TAES.2023.3277427

    Article  Google Scholar 

  3. Yang, Z., Chen, C., Huang, G.: A hybrid global optimization algorithm for GA-nonuniform kriging-gradient projection for optimal design of robots. J. Mech. Eng. 55(11), 61–68 (2019)

    Google Scholar 

  4. Koike, R., Ariizumi, R., Matsuno, F.: Simultaneous optimization of discrete and continuous parameters defining a robot morphology and controller. IEEE Trans. Neural Netw. Learn. Syst. (2023). https://doi.org/10.1109/TNNLS.2023.3272068

    Article  Google Scholar 

  5. Kumar, R., Dhiman, G.: A comparative study of fuzzy optimization through fuzzy number. Int. J. Mod. Res. 1(1), 1–14 (2021)

    Google Scholar 

  6. Chatterjee, I.: Artificial intelligence and patentability: review and discussions. Int. J. Mod. Res. 1(1), 15–21 (2021)

    Google Scholar 

  7. Fan, J., Guo, Y., Wu, X., Chen, X., Lin, Y.: Planetary gearbox fault diagnosis based on LSTM neural network and fault feature enhancement. J. Vib. Shock 40(20), 271–277 (2021)

    Google Scholar 

  8. Hasan, A., Tahavori, M., Midtiby, H.S.: Model-based fault diagnosis algorithms for robotic systems. IEEE Access 11, 2250–2258 (2023)

    Google Scholar 

  9. Chen, Y., Chen, L.: An inverse optimization approach to vehicle path planning problems. J. Shanghai Jiaotong Univ. (Chin. Ed.) 56(1), 81 (2022)

    Google Scholar 

  10. Dogru, S., Marques, L.: Path and trajectory planning for UV-C disinfection robots. IEEE Robot. Autom. Lett. (2023). https://doi.org/10.1109/LRA.2023.3280800

    Article  Google Scholar 

  11. Alrashed, F.A., Alsubiheen, A.M., Alshammari, H., Mazi, S.I., Al-Saud, S.A., Alayoubi, S., Kachanathu, S.J., Albarrati, A., Aldaihan, M.M., Ahmad, T., et al.: Stress, anxiety, and depression in pre-clinical medical students: prevalence and association with sleep disorders. Sustainability 14(18), 11320 (2022)

    Google Scholar 

  12. Vaishnav, P.K., Sharma, S., Sharma, P.: Analytical review analysis for screening COVID-19 disease. Int. J. Mod. Res. 1(1), 22–29 (2021)

    Google Scholar 

  13. Gupta, V.K., Shukla, S.K., Rawat, R.S., et al.: Crime tracking system and people’s safety in India using machine learning approaches. Int. J. Mod. Res. 2(1), 1–7 (2022)

    Google Scholar 

  14. Sharma, T., Nair, R., Gomathi, S.: Breast cancer image classification using transfer learning and convolutional neural network. Int. J. Mod. Res. 2(1), 8–16 (2022)

    Google Scholar 

  15. Ahmad, F., Shahid, M., Alam, M., Ashraf, Z., Sajid, M., Kotecha, K., Dhiman, G.: Levelized multiple workflow allocation strategy under precedence constraints with task merging in IAAS cloud environment. IEEE Access 10, 92809–92827 (2022)

    Google Scholar 

  16. Singamaneni, K.K., Dhiman, G., Juneja, S., Muhammad, G., AlQahtani, S.A., Zaki, J.: A novel QKD approach to enhance IIOT privacy and computational knacks. Sensors 22(18), 6741 (2022)

    Google Scholar 

  17. Shukla, S.K., Gupta, V.K., Joshi, K., Gupta, A., Singh, M.K.: Self-aware execution environment model (SAE2) for the performance improvement of multicore systems. Int. J. Mod. Res. 2(1), 17–27 (2022)

    Google Scholar 

  18. Li, J., Shen, Y., Yang, S.: A study of variable order fractional order gradient descent method. J. Vib. Shock 40, 43–47 (2021)

    Google Scholar 

  19. Pho, K.-H.: Improvements of the Newton-Raphson method. J. Comput. Appl. Math. 408, 114106 (2022)

    MathSciNet  Google Scholar 

  20. Bortoletti, A., Di Fiore, C., Fanelli, S., Zellini, P.: A new class of quasi-Newtonian methods for optimal learning in MLP-networks. IEEE Trans. Neural Netw. 14(2), 263–273 (2003)

    Google Scholar 

  21. Li, W., Wang, G.-G., Gandomi, A.H.: A survey of learning-based intelligent optimization algorithms. Arch. Comput. Methods Eng. 28, 3781–3799 (2021)

    MathSciNet  Google Scholar 

  22. Holland, J.H.: Genetic algorithms. Sci. Am. 267(1), 66–73 (1992)

    Google Scholar 

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

    Google Scholar 

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

  25. Eglese, R.W.: Simulated annealing: a tool for operational research. Eur. J. Oper. Res. 46(3), 271–281 (1990)

    MathSciNet  Google Scholar 

  26. Neshat, M., Sepidnam, G., Sargolzaei, M., Toosi, A.N.: Artificial fish swarm algorithm: a survey of the state-of-the-art, hybridization, combinatorial and indicative applications. Artif. Intell. Rev. 42(4), 965–997 (2014)

    Google Scholar 

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

    MathSciNet  Google Scholar 

  28. Dasgupta, D.: Artificial immune systems and their applications. Springer, Berlin (2012)

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

    Google Scholar 

  30. Mirjalili, S.: SCA: a sine cosine algorithm for solving optimization problems. Knowl.-Based Syst. 96, 120–133 (2016)

    Google Scholar 

  31. Mirjalili, S.: Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl.-Based Syst. 89, 228–249 (2015)

    Google Scholar 

  32. Xue, J., Shen, B.: A novel swarm intelligence optimization approach: sparrow search algorithm. Syst. Sci. Control Eng. 8(1), 22–34 (2020)

    Google Scholar 

  33. Heidari, A.A., Mirjalili, S., Faris, H., Aljarah, I., Mafarja, M., Chen, H.: Harris Hawks optimization: algorithm applications. Futur. Gener. Comput. Syst. 97, 849–872 (2019)

    Google Scholar 

  34. Dehghani, M., Hubálovskỳ, Š, Trojovskỳ, P.: Northern goshawk optimization: a new swarm-based algorithm for solving optimization problems. IEEE Access 9, 162059–162080 (2021)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  37. Dhiman, G., Kumar, V.: Emperor penguin optimizer: a bio-inspired algorithm for engineering problems. Knowl.-Based Syst. 159, 20–50 (2018)

    Google Scholar 

  38. Kaur, S., Awasthi, L.K., Sangal, A.L., Dhiman, G.: Tunicate swarm algorithm: a new bio-inspired based metaheuristic paradigm for global optimization. Eng. Appl. Artif. Intell. 90, 103541 (2020)

    Google Scholar 

  39. Dhiman, G., Kaur, A.: STOA: a bio-inspired based optimization algorithm for industrial engineering problems. Eng. Appl. Artif. Intell. 82, 148–174 (2019)

    Google Scholar 

  40. Dhiman, G., Kumar, V.: Seagull optimization algorithm: theory and its applications for large-scale industrial engineering problems. Knowl.-Based Syst. 165, 169–196 (2019)

    Google Scholar 

  41. Dehghani, M., Montazeri, Z., Malik, O.P., Dhiman, G., Kumar, V., et al.: BOSA: binary orientation search algorithm. Int. J. Innov. Technol. Explor. Eng. 9(1), 5306–5310 (2019)

    Google Scholar 

  42. Dhiman, G., Garg, M., Nagar, A., Kumar, V., Dehghani, M.: A novel algorithm for global optimization: rat swarm optimizer. J. Ambient. Intell. Humaniz. Comput. 12, 8457–8482 (2021)

    Google Scholar 

  43. Dehghani, M., Montazeri, Z., Dehghani, A., Ramirez-Mendoza, R.A., Samet, H., Guerrero, J.M., Dhiman, G.: MLO: Multi leader optimizer. Int. J. Intell. Eng. Syst. 13(6) (2020)

  44. Dehghani, M., Montazeri, Z., Givi, H., Guerrero, J.M., Dhiman, G.: Darts game optimizer: a new optimization technique based on darts game. Int. J. Intell. Eng. Syst. 13(5), 286–294 (2020)

    Google Scholar 

  45. Dehghani, M., Montazeri, Z., Dhiman, G., Malik, O., Morales-Menendez, R., Ramirez-Mendoza, R.A., Dehghani, A., Guerrero, J.M., Parra-Arroyo, L.: A spring search algorithm applied to engineering optimization problems. Appl. Sci. 10(18), 6173 (2020)

    Google Scholar 

  46. Dhiman, G., Oliva, D., Kaur, A., Singh, K.K., Vimal, S., Sharma, A., Cengiz, K.: BEPO: a novel binary emperor penguin optimizer for automatic feature selection. Knowl.-Based Syst. 211, 106560 (2021)

    Google Scholar 

  47. Dhiman, G.: ESA: a hybrid bio-inspired metaheuristic optimization approach for engineering problems. Eng. Comput. 37, 323–353 (2021)

    Google Scholar 

  48. Salgotra, R., Singh, U.: The naked mole-rat algorithm. Neural Comput. Appl. 31, 8837–8857 (2019)

    Google Scholar 

  49. Abdel-Basset, M., Mohamed, R., Jameel, M., Abouhawwash, M.: Spider wasp optimizer: a novel meta-heuristic optimization algorithm. Artif. Intell. Rev. 56, 1–64 (2023)

  50. Trojovská, E., Dehghani, M., Trojovskỳ, P.: Zebra optimization algorithm: a new bio-inspired optimization algorithm for solving optimization algorithm. IEEE Access 10, 49445–49473 (2022)

    Google Scholar 

  51. Azizi, M., Aickelin, U., A. Khorshidi, H., Shishehgarkhaneh, M.B.: Energy valley optimizer: a novel metaheuristic algorithm for global and engineering optimization. Sci. Rep. 13(1), 226 ( 2023)

  52. Abdel-Basset, M., Mohamed, R., Azeem, S.A.A., Jameel, M., Abouhawwash, M.: Kepler optimization algorithm: a new metaheuristic algorithm inspired by kepler’s laws of planetary motion. Knowl.-Based Syst. 268, 110454 (2023)

    Google Scholar 

  53. Zolf, K.: Gold rush optimizer: a new population-based metaheuristic algorithm. Oper. Res. Decis. 33(1) (2023)

  54. Abdel-Basset, M., Mohamed, R., Sallam, K.M., Chakrabortty, R.K.: Light spectrum optimizer: a novel physics-inspired metaheuristic optimization algorithm. Mathematics 10(19), 3466 (2022)

    Google Scholar 

  55. Su, H., Zhao, D., Heidari, A.A., Liu, L., Zhang, X., Mafarja, M., Chen, H.: RIME: a physics-based optimization. Neurocomputing 532, 183–214 (2023)

    Google Scholar 

  56. Abdel-Basset, M., Mohamed, R., Jameel, M., Abouhawwash, M.: Nutcracker optimizer: a novel nature-inspired metaheuristic algorithm for global optimization and engineering design problems. Knowl.-Based Syst. 262, 110248 (2023)

    Google Scholar 

  57. Zhang, Q., Gao, H., Zhan, Z.-H., Li, J., Zhang, H.: Growth optimizer: a powerful metaheuristic algorithm for solving continuous and discrete global optimization problems. Knowl.-Based Syst. 261, 110206 (2023)

    Google Scholar 

  58. Shehadeh, H.A.: Chernobyl disaster optimizer (CDO): a novel meta-heuristic method for global optimization. Neural Comput. Appl. 35(15), 10733–10749 (2023)

    Google Scholar 

  59. Trojovskỳ, P., Dehghani, M.: Subtraction-average-based optimizer: a new swarm-inspired metaheuristic algorithm for solving optimization problems. Biomimetics 8(2), 149 (2023)

    Google Scholar 

  60. Mirrashid, M., Naderpour, H.: Incomprehensible but intelligible-in-time logics: theory and optimization algorithm. Knowl.-Based Syst. 264, 110305 (2023)

    Google Scholar 

  61. Adegboye, O.R., Feda, A.K., Ojekemi, O.S., Agyekum, E.B., Hussien, A.G., Kamel, S.: Chaotic opposition learning with mirror reflection and worst individual disturbance grey wolf optimizer for continuous global numerical optimization. Sci. Rep. 14(1), 4660 (2024)

    Google Scholar 

  62. Feda, A.K., Adegboye, M., Adegboye, O.R., Agyekum, E.B., Mbasso, W.F., Kamel, S.: S-shaped grey wolf optimizer-based fox algorithm for feature selection. Heliyon 10(2) (2024)

  63. Adegboye, O.R., Deniz Ülker, E.: Gaussian mutation specular reflection learning with local escaping operator based artificial electric field algorithm and its engineering application. Appl. Sci. 13(7), 4157 (2023)

    Google Scholar 

  64. Zhang, H., San, H., Sun, H., Ding, L., Wu, X.: A novel optimization method: wave search algorithm. J. Supercomput. 1–36 (2024)

  65. Akpinar, S.: Hybrid large neighbourhood search algorithm for capacitated vehicle routing problem. Expert Syst. Appl. 61, 28–38 (2016)

    Google Scholar 

  66. Wang, J., Wang, W., Hu, X., Qiu, L., Zang, H.: Black-winged kite algorithm: a nature-inspired meta-heuristic for solving benchmark functions and engineering problems. Artif. Intell. Rev. 57(4), 1–53 (2024)

    Google Scholar 

  67. Droste, S., Jansen, T., Wegener, I.: Optimization with randomized search heuristics-the (a) NFL theorem, realistic scenarios, and difficult functions. Theoret. Comput. Sci. 287(1), 131–144 (2002)

    MathSciNet  Google Scholar 

  68. Gürses, D., Mehta, P., Sait, S.M., Yildiz, A.R.: African vultures optimization algorithm for optimization of shell and tube heat exchangers. Mater. Test. 64(8), 1234–1241 (2022)

    Google Scholar 

  69. Mohammadi-Balani, A., Nayeri, M.D., Azar, A., Taghizadeh-Yazdi, M.: Golden eagle optimizer: a nature-inspired metaheuristic algorithm. Comput. Ind. Eng. 152, 107050 (2021)

    Google Scholar 

  70. Azizi, M., Talatahari, S., Gandomi, A.H.: Fire hawk optimizer: a novel metaheuristic algorithm. Artif. Intell. Rev. 56(1), 287–363 (2023)

    Google Scholar 

  71. Alsattar, H.A., Zaidan, A., Zaidan, B.: Novel meta-heuristic bald eagle search optimisation algorithm. Artif. Intell. Rev. 53, 2237–2264 (2020)

    Google Scholar 

  72. Lei, Z., Xiao-Nong, Y., Guang, H., Qin, H., Tian-Tian, L., ZI-YUE, D., Qian, W.: A review of the distribution of black eagle ictinaetus malaiensis in mainland china. Forktail 30, 45–49 (2014)

    Google Scholar 

  73. Lin, W.-H., Hong, S.-Y., Lin, S.-M.: Home range and movement pattern of a tailless black eagle in taiwan: a special case of noninvasive study by community science. J. Raptor Res. 55(4), 644–648 (2021)

    Google Scholar 

  74. Mahdavi, S., Rahnamayan, S., Deb, K.: Opposition based learning: a literature review. Swarm Evol. Comput. 39, 1–23 (2018)

    Google Scholar 

  75. Wu, G., Mallipeddi, R., Suganthan, P.: Problem definitions and evaluation criteria for the CEC 2017 competition and special session on constrained single objective real-parameter optimization. Nanyang Technol. Univ., Singapore, Tech. Rep. 1–18 (2016)

  76. Yazdani, D., Branke, J., Omidvar, M.N., Li, X., Li, C., Mavrovouniotis, M., Nguyen, T.T., Yang, S., Yao, X.: IEEE CEC 2022 competition on dynamic optimization problems generated by generalized moving peaks benchmark. arXiv:2106.06174 (2021)

  77. Montazeri, Z., Niknam, T., Aghaei, J., Malik, O.P., Dehghani, M., Dhiman, G.: Golf optimization algorithm: a new game-based metaheuristic algorithm and its application to energy commitment problem considering resilience. Biomimetics 8(5), 386 (2023)

    Google Scholar 

  78. Wilcoxon, N.L., Kotz, S.F.: Individual Comparisons by Ranking Methods Breakthroughs in Statistics. Springer, New York (1992)

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

    Google Scholar 

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Acknowledgements

The authors would like to acknowledge the financial support from the Yunnan Province Basic Research Program Project 202301AU070059 and the Kunming University of Science and Technology college level personnel training project KKZ3202301041.

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  1. Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming, 650500, China

    Haobin Zhang, Hongjun San, Jiupeng Chen, Haijie Sun, Lin Ding & Xingmei Wu

  2. Key Laboratory of Advanced Equipment Intelligent Manufacturing Technology of Yunnan Province, Kunming, 650500, China

    Haobin Zhang, Hongjun San, Jiupeng Chen, Haijie Sun, Lin Ding & Xingmei Wu

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Zhang, H., San, H., Chen, J. et al. Black eagle optimizer: a metaheuristic optimization method for solving engineering optimization problems. Cluster Comput 27, 12361–12393 (2024). https://doi.org/10.1007/s10586-024-04586-1

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