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Multi-strategy boosted Aquila optimizer for function optimization and engineering design problems

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Abstract

As the complexity of optimization problems continues to rise, the demand for high-performance algorithms becomes increasingly urgent. This paper addresses the challenges faced by the Aquila Optimizer (AO), a novel swarm-based intelligent optimizer simulating the predatory behaviors of Aquila in North America. While AO has shown good performance in prior studies, it grapples with issues such as poor convergence accuracy and a tendency to fall into local optima when tackling complex optimization tasks. To overcome these challenges, this paper proposes a multi-strategy boosted AO algorithm (PGAO) aimed at providing enhanced reliability for global optimization. The proposed algorithm incorporates several key strategies. Initially, a chaotic map is employed to initialize the positions of all search agents, enriching population diversity and laying a solid foundation for global exploration. Subsequently, the pinhole imaging learning strategy is introduced to identify superior candidate solutions in the opposite direction of the search domain during each iteration, accelerating convergence and increasing the probability of obtaining the global optimal solution. To achieve a more effective balance between the exploration and development phases in AO, a nonlinear switching factor is designed to replace the original fixed switching mechanism. Finally, the golden sine operator is utilized to enhance the algorithm’s local exploitation trends. Through these four improvement strategies, the optimization performance of AO is significantly enhanced. The proposed PGAO algorithm’s effectiveness is validated across 23 classical, 29 IEEE CEC2017, and 10 IEEE CEC2019 benchmark functions. Additionally, six real-world engineering design problems are employed to assess the practicability of PGAO. Results demonstrate that PGAO exhibits better competitiveness and application prospects compared to the basic method and various advanced algorithms. In conclusion, this study contributes to addressing the challenges of complex optimization problems, significantly improving the performance of global optimization algorithms, and holds both theoretical and practical significance.

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References

  1. Jia, H., Zhang, W., Zheng, R., Wang, S., Leng, X., Cao, N.: Ensemble mutation slime mould algorithm with restart mechanism for feature selection. Int. J. Intell. Syst. 37, 2335–2370 (2021)

    Google Scholar 

  2. Xiao, Y., Sun, X., Guo, Y., Cui, H., Wang, Y., Li, J., Li, S.: An enhanced honey badger algorithm based on Lévy flight and refraction opposition-based learning for engineering design problems. J. Intell. Fuzzy Syst. 43, 4517–4540 (2022)

    Google Scholar 

  3. Zhang, X., Zhao, K., Niu, Y.: Improved Harris hawks optimization based on adaptive cooperative foraging and dispersed foraging strategies. IEEE Access 8, 160297–160314 (2020)

    Google Scholar 

  4. Mahajan, S., Mittal, N., Pandit, A.K.: Image segmentation using multilevel thresholding based on type II fuzzy entropy and marine predators algorithm. Multimedia Tools Appl. 80, 19335–19359 (2021)

    Google Scholar 

  5. Pang, J., Zhou, H., Tsai, Y.-C., Chou, F.-D.: A scatter simulated annealing algorithm for the bi-objective scheduling problem for the wet station of semiconductor manufacturing. Comput. Ind. Eng. 123, 54–66 (2018)

    Google Scholar 

  6. Guo, W., Xu, P., Dai, F., Hou, Z.: Harris hawks optimization algorithm based on elite fractional mutation for data clustering. Appl. Intell. 52, 11407–11433 (2022)

    Google Scholar 

  7. Shi, K., Liu, C., Sun, Z., Yue, X.: Coupled orbit-attitude dynamics and trajectory tracking control for spacecraft electromagnetic docking. Appl. Math. Model. 101, 553–572 (2022)

    MathSciNet  Google Scholar 

  8. Liu, C., Yue, X., Zhang, J., Shi, K.: Active disturbance rejection control for delayed electromagnetic docking of spacecraft in elliptical orbits. IEEE Trans. Aerosp. Electron. Syst. 58, 2257–2268 (2022)

    Google Scholar 

  9. Fan, Q., Huang, H., Yang, K., Zhang, S., Yao, L., Xiong, Q.: A modified equilibrium optimizer using opposition-based learning and novel update rules. Expert Syst. Appl. 170, 114575 (2021)

    Google Scholar 

  10. Jia, H., Li, Y., Sun, K., Cao, N., Zhou, H.-M.: Hybrid sooty tern optimization and differential evolution for feature selection. Comput. Syst. Sci. Eng. 39, 321–335 (2021)

    Google Scholar 

  11. Hu, G., Zhong, J., Du, B., Wei, G.: An enhanced hybrid arithmetic optimization algorithm for engineering applications. Comput. Meth. Appl. Mech. Eng. 394, 114901 (2022)

    MathSciNet  Google Scholar 

  12. Hussain, K., Mohd Salleh, M.N., Cheng, S., Shi, Y.: Metaheuristic research: a comprehensive survey. Artif. Intell. Rev. 52, 2191–2233 (2019)

    Google Scholar 

  13. Yang, J., Liu, Z., Zhang, X., Hu, G.: Elite chaotic manta ray algorithm integrated with chaotic initialization and opposition-based learning. Mathematics 10, 2960 (2022)

    Google Scholar 

  14. Xiao, Y., Guo, Y., Cui, H., Wang, Y., Li, J., Zhang, Y.: IHAOAVOA: an improved hybrid Aquila optimizer and African vultures optimization algorithm for global optimization problems. Math. Biosci. Eng. 19, 10963–11017 (2022)

    Google Scholar 

  15. Zheng, R., Jia, H., Wang, S., Liu, Q.: Enhanced slime mould algorithm with multiple mutation strategy and restart mechanism for global optimization. J. Intell. Fuzzy Syst. 42, 5069–5083 (2022)

    Google Scholar 

  16. Wang, Y., Xiao, Y., Guo, Y., Li, J.: Dynamic chaotic opposition-based learning-driven hybrid Aquila optimizer and artificial Rabbits optimization algorithm: framework and applications. Processes 10, 2703 (2022)

    Google Scholar 

  17. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983)

    MathSciNet  Google Scholar 

  18. Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24, 1097–1100 (1997)

    MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  20. Holland, J.H.: Genetic algorithms. Sci. Am. 267, 66–72 (1992)

    Google Scholar 

  21. Nguyen, T.-T., Wang, H.-J., Dao, T.-K., Pan, J.-S., Liu, J.-H., Weng, S.: An improved slime mold algorithm and its application for optimal operation of cascade hydropower stations. IEEE Access 8, 226754–226772 (2020)

    Google Scholar 

  22. Wen, C., Jia, H., Wu, D., Rao, H., Li, S., Liu, Q., Abualigah, L.: Modified remora optimization algorithm with multistrategies for global optimization problem. Mathematics 10, 3604 (2022)

    Google Scholar 

  23. Simon, D.: Biogeography-based optimization. IEEE Trans. Evol. Comput. 12, 702–713 (2008)

    Google Scholar 

  24. Abualigah, L., Diabat, A., Mirjalili, S., AbdElaziz, M., Gandomi, A.H.: The arithmetic optimization algorithm. Comput. Meth. Appl. Mech. Eng. 376, 113609 (2021)

    MathSciNet  Google Scholar 

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

    Google Scholar 

  26. Li, S., Chen, H., Wang, M., Heidari, A.A., Mirjalili, S.: Slime mould algorithm: a new method for stochastic optimization. Future Gener. Comp. Syst. 111, 300–323 (2020)

    Google Scholar 

  27. Heidari, A.A., Mirjalili, S., Faris, H., Aljarah, I., Mafarja, M., Chen, H.: Harris hawks optimization: algorithm and applications. Future Gener. Comp. Syst. 97, 849–872 (2019)

    Google Scholar 

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

    Google Scholar 

  29. Rao, R.V., Savsani, V.J., Vakharia, D.P.: Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput. Aided Des. 43, 303–315 (2011)

    Google Scholar 

  30. Manjarres, D., Landa-Torres, I., Gil-Lopez, S., Del Ser, J., Bilbao, M.N., Salcedo-Sanz, S., Geem, Z.W.: A survey on applications of the harmony search algorithm. Eng. Appl. Artif. Intell. 26, 1818–1831 (2013)

    Google Scholar 

  31. Askari, Q., Younas, I., Saeed, M.: Political optimizer: a novel socio-inspired meta-heuristic for global optimization. Knowl. Based Syst. 195, 105709 (2020)

    Google Scholar 

  32. Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1, 67–82 (1997)

    Google Scholar 

  33. Xiao, Y., Sun, X., Zhang, Y., Guo, Y., Wang, Y., Li, J.: An improved slime mould algorithm based on tent chaotic mapping and nonlinear inertia weight. Int. J. Innov. Comp. Inform. Control. 17, 2151–2176 (2021)

    Google Scholar 

  34. Rezaei, F., Safavi, H.R., AbdElaziz, M., Abualigah, L., Mirjalili, S., Gandomi, A.H.: Diversity-based evolutionary population dynamics: a new operator for grey wolf optimizer. Processes 10, 2615 (2022)

    Google Scholar 

  35. Ziyu, T., Dingxue, Z.: A modified particle swarm optimization with an adaptive acceleration coefficients. Inform. Process. Asia-Pacific Conf. 2009(2), 330–332 (2009)

    Google Scholar 

  36. Mousavi, Y., Alfi, A., Kucukdemiral, I.: Enhanced fractional chaotic whale optimization algorithm for parameter identification of isolated wind-diesel power systems. IEEE Access 8, 140862–140875 (2020)

    Google Scholar 

  37. Khishe, M., Mosavi, M.R.: Improved whale trainer for sonar datasets classification using neural network. Appl. Acoust. 154, 176–192 (2019)

    Google Scholar 

  38. Zhang, Y.J., Yan, Y.X., Zhao, J., Gao, Z.M.: CSCAHHO: chaotic hybridization algorithm of the sine cosine with Harris hawk optimization algorithms for solving global optimization problems. PLoS ONE 17, 32 (2022)

    Google Scholar 

  39. Hosseinzadeh, M., Masdari, M., Rahmani, A.M., Mohammadi, M., Aldalwie, A.H.M., Majeed, M.K., Karim, S.H.T.: Improved butterfly optimization algorithm for data placement and scheduling in edge computing environments. J. Grid Comput. 19, 14 (2021)

    Google Scholar 

  40. Abualigah, L., Yousri, D., Elsayed Abd Elaziz, M., Ewees, A., Al-qaness, M.A.A., Gandomi, A.: Aquila optimizer: a novel meta-heuristic optimization algorithm. Comput. Ind. Eng. 157, 107250 (2021)

    Google Scholar 

  41. Guo, Z., Yang, B., Han, Y., He, T., He, P., Meng, X., He, X.: Optimal PID tuning of PLL for PV inverter based on Aquila optimizer. Front. Energy Res. 9, 812467 (2022)

    Google Scholar 

  42. Hussien, A., Yu, H., Jia, H., Zhou, J.: Enhanced Aquila optimizer algorithm for global optimization and constrained engineering problems. Math. Biosci. Eng.: MBE. 19, 14173–14211 (2022)

    Google Scholar 

  43. Ma, C., Huang, H., Fan, Q., Wei, J., Du, Y., Gao, W.: Grey wolf optimizer based on Aquila exploration method. Expert Syst. Appl. 205, 117629 (2022)

    Google Scholar 

  44. Mahajan, S., Abualigah, L., Pandit, A.K., Altalhi, M.: Hybrid Aquila optimizer with arithmetic optimization algorithm for global optimization tasks. Soft. Comput. 26, 4863–4881 (2022)

    Google Scholar 

  45. Wang, S., Jia, H., Liu, Q., Zheng, R.: An improved hybrid Aquila optimizer and Harris hawks optimization for global optimization. Math. Biosci. Eng. 18, 7076–7109 (2021)

    MathSciNet  Google Scholar 

  46. Zhao, J., Gao, Z.M., Chen, H.F.: The simplified Aquila optimization algorithm. IEEE Access 10, 22487–22515 (2022)

    Google Scholar 

  47. Long, W., Jiao, J., Liang, X., Wu, T., Xu, M., Cai, S.: Pinhole-imaging-based learning butterfly optimization algorithm for global optimization and feature selection. Appl. Soft Comput. 103, 107146 (2021)

    Google Scholar 

  48. Xie, W., Wang, J.S., Tao, Y.: Improved black hole algorithm based on golden sine operator and levy flight operator. IEEE Access 7, 161459–161486 (2019)

    Google Scholar 

  49. Tizhoosh, H.R.: Opposition-based learning: a new scheme for machine intelligence. Int. Conf. Comput. Intel. Modell. 1, 695–701 (2005)

    Google Scholar 

  50. Wang, L., Cao, Q., Zhang, Z., Mirjalili, S., Zhao, W.: Artificial rabbits optimization: a new bio-inspired meta-heuristic algorithm for solving engineering optimization problems. Eng. Appl. Artif. Intell. 114, 105082 (2022)

    Google Scholar 

  51. Tanyildizi, E., Demir, G.: Golden sine algorithm: a novel math-inspired algorithm. Adv. Electr. Comput. Eng. 17, 71–78 (2017)

    Google Scholar 

  52. Xiao, Y., Sun, X., Guo, Y., Li, S., Zhang, Y., Wang, Y.: An improved gorilla troops optimizer based on lens opposition-based learning and adaptive β-Hill climbing for global optimization, CMES-Comp. Model Eng. Sci. 131, 815–850 (2022)

    Google Scholar 

  53. Houssein, E.H., Saad, M.R., Hashim, F.A., Shaban, H., Hassaballah, M.: Lévy flight distribution: a new metaheuristic algorithm for solving engineering optimization problems. Eng. Appl. Artif. Intell. 94, 103731 (2020)

    Google Scholar 

  54. 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 

  55. Chopra, N., Mohsin Ansari, M.: Golden jackal optimization: a novel nature-inspired optimizer for engineering applications. Expert Syst. Appl. 198, 116924 (2022)

    Google Scholar 

  56. 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 

  57. Khishe, M., Mosavi, M.R.: Chimp optimization algorithm. Expert Syst. Appl. 149, 113338 (2020)

    Google Scholar 

  58. Zhao, S., Wu, Y., Tan, S., Cui, Z., Wang, Y.: QQLMPA: a quasi-opposition learning and Q-learning based marine predators algorithm. Expert Syst. Appl. 213, 119246 (2022)

    Google Scholar 

  59. Naik, M.K., Swain, M., Panda, R., Abraham, A.: An evolutionary dynamic control cuckoo search algorithm for solving the constrained engineering design problems. Int. J. Swarm Intell. Res. 13, 1–25 (2022)

    Google Scholar 

  60. Zhao, J., Gao, Z.M.: The heterogeneous Aquila optimization algorithm. Math. Biosci. Eng. 19, 5867–5904 (2022)

    Google Scholar 

  61. Theodorsson-Norheim, E.: Friedman and Quade tests: basic computer program to perform nonparametric two-way analysis of variance and multiple comparisons on ranks of several related samples. Comput. Biol. Med. 17, 85–99 (1987)

    Google Scholar 

  62. Al-qaness, M.A.A., Ewees, A.A., Fan, H., AlRassas, A.M., Elaziz, M.A.: Modified Aquila optimizer for forecasting oil production. Geo-Spatial Inform. Sci. 25, 519–535 (2022)

    Google Scholar 

  63. Hashim, F.A., Houssein, E.H., Hussain, K., Mabrouk, M.S., Al-Atabany, W.: Honey badger algorithm: new metaheuristic algorithm for solving optimization problems. Math. Comput. Simul. 192, 84–110 (2022)

    MathSciNet  Google Scholar 

  64. Abdollahzadeh, B., Gharehchopogh, F.S., Mirjalili, S.: African vultures optimization algorithm: a new nature-inspired metaheuristic algorithm for global optimization problems. Comput. Ind. Eng. 158, 107408 (2021)

    Google Scholar 

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

    Google Scholar 

  66. Abualigah, L., Elaziz, M.A., Sumari, P., Geem, Z.W., Gandomi, A.H.: Reptile search algorithm (RSA): a nature-inspired meta-heuristic optimizer. Expert Syst. Appl. 191, 116158 (2022)

    Google Scholar 

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

    Google Scholar 

  68. Mirjalili, S., Gandomi, A.H., Mirjalili, S.Z., Saremi, S., Faris, H., Mirjalili, S.M.: Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv. Eng. Softw. 114, 163–191 (2017)

    Google Scholar 

  69. Faramarzi, A., Heidarinejad, M., Mirjalili, S., Gandomi, A.H.: Marine predators algorithm: a nature-inspired metaheuristic. Expert Syst. Appl. 152, 113377 (2020)

    Google Scholar 

  70. Nadimi-Shahraki, M.H., Taghian, S., Mirjalili, S., Faris, H.: MTDE: an effective multi-trial vector-based differential evolution algorithm and its applications for engineering design problems. Appl. Soft Comput. 97, 106761 (2020)

    Google Scholar 

  71. Ahmadianfar, I., Heidari, A.A., Gandomi, A.H., Chu, X., Chen, H.: RUN beyond the metaphor: an efficient optimization algorithm based on Runge Kutta method. Expert Syst. Appl. 181, 115079 (2021)

    Google Scholar 

  72. Mohammadi-Balani, A., Nayeri, M., Azar, A., Taghizadeh-Yazdi, M.: Golden eagle optimizer: a nature-inspired metaheuristic algorithm. Comput. Ind. Eng. 152, 107050 (2020)

    Google Scholar 

  73. Pan, J.-S., Zhang, L.-G., Wang, R.-B., Snášel, V., Chu, S.-C.: Gannet optimization algorithm: a new metaheuristic algorithm for solving engineering optimization problems. Math. Comput. Simul. 202, 343–373 (2022)

    MathSciNet  Google Scholar 

  74. Rushdi, H., Al-Naima, F.: Coot optimization algorithm for paramete estimation of photovoltaic model. MEST J. 10, 177–185 (2022)

    Google Scholar 

  75. Chen, Y., Wang, N.: Cuckoo search algorithm with explosion operator for modeling proton exchange membrane fuel cells. Int. J. Hydrogen Energy 44, 3075–3087 (2019)

    Google Scholar 

  76. Yang, X.S., Hossein Gandomi, A.: Bat algorithm: a novel approach for global engineering optimization. Eng. Comput. 29, 464–483 (2012)

    Google Scholar 

  77. Yildiz, B.S., Pholdee, N., Bureerat, S., Yildiz, A.R., Sait, S.M.: Enhanced grasshopper optimization algorithm using elite opposition-based learning for solving real-world engineering problems. Eng. Comput. 38, 4207–4219 (2022)

    Google Scholar 

  78. Zhang, Y.-J., Wang, Y.-F., Tao, L.-W., Yan, Y.-X., Zhao, J., Gao, Z.-M.: Self-adaptive classification learning hybrid JAYA and Rao-1 algorithm for large-scale numerical and engineering problems. Eng. Appl. Artif. Intell. 114, 105069 (2022)

    Google Scholar 

  79. Yin, S., Luo, Q., Zhou, Y.: EOSMA: an equilibrium optimizer slime mould algorithm for engineering design problems. Arab. J. Sci. Eng. 47, 10115–10146 (2022)

    Google Scholar 

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Funding

This work was financially supported by the National Natural Science Foundation of China under Grant 52075090, Key Research and Development Program Projects of Heilongjiang Province under Grant GA21A403.

Author information

Authors and Affiliations

  1. College of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin, 150040, China

    Hao Cui & Yanling Guo

  2. Center for Control Science and Technology, Southern University of Science and Technology, Shenzhen, 518055, China

    Yaning Xiao

  3. Department of Computer and Information Science, Linköping University, 58183, Linköping, Sweden

    Abdelazim G. Hussien

  4. Faculty of Science, Fayoum University, Faiyum, 63514, Egypt

    Abdelazim G. Hussien

  5. MEU Research Unit, Middle East University, Amman, 11831, Jordan

    Abdelazim G. Hussien

  6. Applied Science Research Center, Applied Science Private University, Amman, 11931, Jordan

    Abdelazim G. Hussien

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  1. Hao Cui
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  2. Yaning Xiao
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  3. Abdelazim G. Hussien
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  4. Yanling Guo
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Contributions

HC: Conceptualization, Methodology, Investigation, Writing-original draft. YX: Conceptualization, Formal analysis, Validation. AGH: Data curation, Visualization, Writing-review & editing. YG: Conceptualization, Validation.

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Correspondence to Abdelazim G. Hussien.

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Appendix

Appendix

See Tables 17, 18, 19, 20, 21, 22.

Table 17 Details of 10 chaotic mappings
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Table 18 Unimodal benchmark functions
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Table 19 Multimodal benchmark functions
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Table 20 Fix-dimension multimodal benchmark functions
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Table 21 IEEE CEC2017 benchmark functions
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Table 22 IEEE CEC2019 benchmark functions
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Cui, H., Xiao, Y., Hussien, A.G. et al. Multi-strategy boosted Aquila optimizer for function optimization and engineering design problems. Cluster Comput 27, 7147–7198 (2024). https://doi.org/10.1007/s10586-024-04319-4

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