The aquila optimization algorithm (AO) is an efficient swarm intelligence algorithm proposed recently. However, considering that AO has better performance and slower late convergence speed in the optimization process. For solving this effect of AO and improving its performance, this paper proposes an enhanced aquila optimization algorithm with a velocity-aided global search mechanism and adaptive opposition-based learning (VAIAO) which is based on AO and simplified Aquila optimization algorithm (IAO). In VAIAO, the velocity and acceleration terms are set and included in the update formula. Furthermore, an adaptive opposition-based learning strategy is introduced to improve local optima. To verify the performance of the proposed VAIAO, 27 classical benchmark functions, the Wilcoxon statistical sign-rank experiment, the Friedman test and five engineering optimization problems are tested. The results of the experiment show that the proposed VAIAO has better performance than AO, IAO and other comparison algorithms. This also means the introduction of these two strategies enhances the global exploration ability and convergence speed of the algorithm.
Citation: Yufei Wang, Yujun Zhang, Yuxin Yan, Juan Zhao, Zhengming Gao. An enhanced aquila optimization algorithm with velocity-aided global search mechanism and adaptive opposition-based learning[J]. Mathematical Biosciences and Engineering, 2023, 20(4): 6422-6467. doi: 10.3934/mbe.2023278
The aquila optimization algorithm (AO) is an efficient swarm intelligence algorithm proposed recently. However, considering that AO has better performance and slower late convergence speed in the optimization process. For solving this effect of AO and improving its performance, this paper proposes an enhanced aquila optimization algorithm with a velocity-aided global search mechanism and adaptive opposition-based learning (VAIAO) which is based on AO and simplified Aquila optimization algorithm (IAO). In VAIAO, the velocity and acceleration terms are set and included in the update formula. Furthermore, an adaptive opposition-based learning strategy is introduced to improve local optima. To verify the performance of the proposed VAIAO, 27 classical benchmark functions, the Wilcoxon statistical sign-rank experiment, the Friedman test and five engineering optimization problems are tested. The results of the experiment show that the proposed VAIAO has better performance than AO, IAO and other comparison algorithms. This also means the introduction of these two strategies enhances the global exploration ability and convergence speed of the algorithm.
| [1] |
S. Mirjalili, A. Lewis, The whale optimization algorithm, Adv. Eng. Software, 95 (2016), 51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008 doi: 10.1016/j.advengsoft.2016.01.008
|
| [2] |
M. Mernik, S. H. Liu, D. Karaboga, M. Črepinšek, On clarifying misconceptions when comparing variants of the artificial bee colony algorithm by offering a new implementation, Inf. Sci., 291 (2016), 115–127. https://doi.org/10.1016/j.ins.2014.08.040. doi: 10.1016/j.ins.2014.08.040
|
| [3] |
R. V. Rao, V. J. Savsani, D. P. Vakharia, Teaching–learning-based optimization: an optimization method for continuous non-linear large scale problems, Inf. Sci., 183 (2012), 1–15. https://doi.org/10.1016/j.ins.2011.08.006 doi: 10.1016/j.ins.2011.08.006
|
| [4] | Y. Tan, Y. Zhu, Fireworks algorithm for optimization, in International conference in swarm intelligence, (2010), 355–364. https://doi.org/10.1007/978-3-642-13495-1_44 |
| [5] |
C. Armin, H. K. Mostafa, P. M. Mahdi, Tree Growth Algorithm (TGA), Eng. Appl. Artif. Intell., 72 (2018), 393–414. https://doi.org/10.1016/j.engappai.2018.04.021 doi: 10.1016/j.engappai.2018.04.021
|
| [6] |
L. Abualigah, A. Diabatb, S. Mirjalilid, M. A. Elazizf, A. H. Gandomih, The arithmetic optimization algorithm, Comput. Methods Appl. Mech. Eng., 376 (2021), 113609. https://doi.org/10.1016/j.cma.2020.113609 doi: 10.1016/j.cma.2020.113609
|
| [7] |
J. F. Frenzel, Genetic algorithms, IEEE Potentials, 12 (1993), 21–24. https://doi.org/10.1109/45.282292 doi: 10.1109/45.282292
|
| [8] |
R. A. Sarker, S. M. Elsayed, R. Tapabrata, Differential evolution with dynamic parameters selection for optimization problems, IEEE Trans. Evol. Comput., 18 (2014), 689–707. https://doi.org/10.1109/TEVC.2013.2281528 doi: 10.1109/TEVC.2013.2281528
|
| [9] | J. R. Koza, J. P. Rice, Automatic programming of robots using genetic programming, in Proceedings of the Tenth 20 Computational Intelligence and Neuroscience National Conference on Artificial Intelligence, (1992). |
| [10] |
H. G. Beyer, H. P. Schwefel, Evolution strategies–A comprehensive introduction, Nat. Comput., 1 (2002), 3–52. https://doi.org/10.1023/A:1015059928466 doi: 10.1023/A:1015059928466
|
| [11] |
Z. W. Geem, J. H. Kim, G. V. Loganathan, A new heuristic optimization algorithm: harmony search, Simulation, 76 (2001), 60–68. https://doi.org/10.1177/003754970107600201 doi: 10.1177/003754970107600201
|
| [12] | E. Atashpaz-Gargari, C. Lucas, Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition, in 2007 IEEE Congress on Evolutionary Computation, (2007), 4661–4667. https://doi.org/10.1109/CEC.2007.4425083 |
| [13] |
Q. Zhang, R. Wang, K. D. Juan Yang, Y. Li, J. Hu, Collective decision optimization algorithm: A new heuristic optimization method, Neurocomputing, 221 (2017), 123–137. https://doi.org/10.1016/j.neucom.2016.09.068 doi: 10.1016/j.neucom.2016.09.068
|
| [14] |
M. Kumar, A. J. Kulkarni, S. C. Satapathy, Socio evolution & learning optimization algorithm: A socio-inspired optimization methodology, Future Gener. Comput. Syst., 81 (2018), 252–272. https://doi.org/10.1016/j.future.2017.10.052 doi: 10.1016/j.future.2017.10.052
|
| [15] |
A. Qamar, Y. Irfan, S. Mehreen, Political Optimizer: A novel socio-inspired meta-heuristic for global optimization, Knowl. Based Syst., 195 (2020), 105709. https://doi.org/10.1016/j.knosys.2020.105709 doi: 10.1016/j.knosys.2020.105709
|
| [16] |
F. A. Hashim, E. H. Houssein, M. S. Mabrouk, W. Al-Atabany, S. Mirjalili, Henry gas solubility optimization: A novel physics-based algorithm, Future Gener. Comput. Syst., 101 (2019), 646–667. https://doi.org/10.1016/j.future.2019.07.015 doi: 10.1016/j.future.2019.07.015
|
| [17] |
O. K. Erol, I. Eksin, A new optimization method: big bang–big crunch, Adv. Eng. Software, 37 (2006), 106–111. https://doi.org/10.1016/j.advengsoft.2005.04.005 doi: 10.1016/j.advengsoft.2005.04.005
|
| [18] |
S. Mirjalili, S. M. Mirjalili, A. Hatamlou, Multi-verse optimizer: a nature-inspired algorithm for global optimization, Neural Comput. Appl., 27 (2016), 495–513. https://doi.org/10.1007/s00521-015-1870-7 doi: 10.1007/s00521-015-1870-7
|
| [19] |
H. Abedinpourshotorban, S. M. Shamsuddin, Z. Beheshti, D. N. A. Jawawi, Electromagnetic field optimization: A physics-inspired metaheuristic optimization algorithm, Swarm Evol. Comput., 26 (2016), 8–22. https://doi.org/10.1016/j.swevo.2015.07.002 doi: 10.1016/j.swevo.2015.07.002
|
| [20] |
E. Rashedi, H. Nezamabadi-pour, S. Saryazdi, GSA: A gravitational search algorithm, Inf. Sci., 179 (2009), 2232–2248. https://doi.org/10.1016/j.ins.2009.03.004 doi: 10.1016/j.ins.2009.03.004
|
| [21] |
A. Kaveh, A. Dadras, A novel meta-heuristic optimization algorithm: thermal exchange optimization, Adv. Eng. Software, 110 (2017), 69–84. https://doi.org/10.1016/j.advengsoft.2017.03.014 doi: 10.1016/j.advengsoft.2017.03.014
|
| [22] |
R. A. Formato, Central force optimization, Progress Electromagn. Res., 77 (2007), 425–491. https://doi.org/10.2528/PIER07082403 doi: 10.2528/PIER07082403
|
| [23] |
D. Karaboga, B. Basturk, A powerful and efficient algorithm for numerical function optimization: artificial bee colony (abc) algorithm, J. Global Optim., 39 (2007), 459–471. https://doi.org/10.1007/s10898-007-9149-x doi: 10.1007/s10898-007-9149-x
|
| [24] | R. Eberhart, J. Kennedy, A new optimizer using particle swarm theory, in MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, (1995), 39–43. |
| [25] |
S. Mirjalili, Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm, Knowl. Based Syst., 89 (2015), 228–249. https://doi.org/10.1016/j.knosys.2015.07.006 doi: 10.1016/j.knosys.2015.07.006
|
| [26] |
M. Dorigo, V. Maniezzo, A. Colorni, Ant system: optimization by a colony of cooperating agents, IEEE Trans. Syst. Man Cybern. Part B, 26 (1996), 29–41. https://doi.org/10.1109/3477.484436 doi: 10.1109/3477.484436
|
| [27] |
A. Faramarzi, M. Heidarinejad, S. Mirjalili, A. H. Gandomic, Marine predators algorithm: A nature-inspired metaheuristic, Expert Syst. Appl., 152 (2020), 113377. https://doi.org/10.1016/j.eswa.2020.113377 doi: 10.1016/j.eswa.2020.113377
|
| [28] |
D. Gaurav, K. Vijay, Seagull optimization algorithm: Theory and its applications for large-scale industrial engineering problems, Knowl. Based Syst., 165 (2019), 169–196. https://doi.org/10.1016/j.knosys.2018.11.024 doi: 10.1016/j.knosys.2018.11.024
|
| [29] |
D. Gaurav, K. Amandeep, STOA: A bio-inspired based optimization algorithm for industrial engineering problems, Eng. Appl. Artif. Intell., 82 (2019), 148–174. https://doi.org/10.1016/j.engappai.2019.03.021 doi: 10.1016/j.engappai.2019.03.021
|
| [30] |
L. Abualigah, D. Yousri, M. A. Elaziz, A. A.Ewees, M. A. A. Al-qaness, A. H. Gandomi, Aquila Optimizer: a novel meta-heuristic optimization algorithm, Comput. Ind. Eng., 157 (2021), 107250. https://doi.org/10.1016/j.cie.2021.107250 doi: 10.1016/j.cie.2021.107250
|
| [31] |
S. Mirjalili, S. M. Mirjalili, A. Lewis, Grey wolf optimizer, Adv. Eng. Software, 69 (2014), 46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007 doi: 10.1016/j.advengsoft.2013.12.007
|
| [32] |
S. Mirjalili, A. H. Gandomi, S. Z. Mirjalili, S. Saremi, H. Faris, S. M. Mirjalili, Salp swarm algorithm: A bio-inspired optimizer for engineering design problems, Adv. Eng. Software, 114 (2017), 163–191. https://doi.org/10.1016/j.advengsoft.2017.07.002 doi: 10.1016/j.advengsoft.2017.07.002
|
| [33] |
A. A. Heidari, H. Faris, I. Aljarah, M. Mafarja, H. Chen, Harris hawks optimization: Algorithm and applications, Future Gener. Comput. Syst., 97 (2019), 849–872. https://doi.org/10.1016/j.future.2019.02.028 doi: 10.1016/j.future.2019.02.028
|
| [34] |
Y. Feng, S. Deb, G. G. Wang, A. H. Alavi, Monarch butterfly optimization: a comprehensive review, Expert Syst. Appl., 168 (2020), 114418. https://doi.org/10.1016/j.eswa.2020.114418 doi: 10.1016/j.eswa.2020.114418
|
| [35] |
S. Li, H. Chen, M. Wang, A. A. Heidari, S. Mirjalili, Slime mould algorithm: A new method for stochastic optimization, Future Gener. Comput. Syst., 111 (2020), 300–323. https://doi.org/10.1016/j.future.2020.03.055 doi: 10.1016/j.future.2020.03.055
|
| [36] |
A. Luque-Chang, E. Cuevas, M. Pérez-Cisneros, F. Fausto, R. Sarkar, Moth swarm algorithm for image contrast enhancement, Knowl. Based Syst., 212 (2021), 106607. https://doi.org/10.1016/j.knosys.2020.106607 doi: 10.1016/j.knosys.2020.106607
|
| [37] | Y. Yang, H. Chen, A. A. Heidari, A. H. Gandomi, Open source MATLAB software of hunger games search (HGS) optimization algorithm, 2021. http://dx.doi.org/10.13140/RG.2.2.10702.18241 |
| [38] |
D. Aniszewska, Multiplicative Runge–Kutta methods, Nonlinear Dyn., 50 (2007), 265–272. https://doi.org/10.1007/s11071-006-9156-3 doi: 10.1007/s11071-006-9156-3
|
| [39] |
R. S. Parpinelli, H. S. Lopes, A. A. Freitas, Data mining with an ant colony optimization algorithm, Evol. Comput. IEEE Trans., 6 (2002), 321–332. https://doi.org/10.1109/TEVC.2002.802452 doi: 10.1109/TEVC.2002.802452
|
| [40] |
I. Ahmadianfar, A. A. Heidari, S. Noshadian, H. Chen, A. H. Gandomi, INFO: An efficient optimization algorithm based on weighted mean of vectors, Expert Syst. Appl., 195 (2022). https://doi.org/10.1016/j.eswa.2022.116516 doi: 10.1016/j.eswa.2022.116516
|
| [41] |
F. A. Hashim, R. R. Mostafa, A. G. Hussien, S. Mirjalili, K. M. Sallam, Fick's Law Algorithm: A physical law-based algorithm for numerical optimization, Knowl. Based Syst., 260 (2023) 110146. https://doi.org/10.1016/j.knosys.2022.110146 doi: 10.1016/j.knosys.2022.110146
|
| [42] |
A. S. Assiri, A. G. Hussien, M. Amin, Ant lion optimization: Variants, hybrids, and applications, IEEE Access, 8 (2020), 77746–77764. https://doi.org/10.1109/ACCESS.2020.2990338 doi: 10.1109/ACCESS.2020.2990338
|
| [43] |
Z. M. Gao, J. Zhao, Y. R. Hu, H. F. Chen, The challenge for the nature-inspired global optimization algorithms: Non-symmetric benchmark functions, IEEE Access, 9 (2021), 106317–106339. https://doi.org/10.1109/ACCESS.2021.3100365 doi: 10.1109/ACCESS.2021.3100365
|
| [44] |
S. Wang, H. Jia, L. Abualigah, Q. Liu, R. Zheng, An improved hybrid aquila optimizer and harris hawks algorithm for solving industrial engineering optimization problems, Processes, 9 (2021), 1551. https://doi.org/10.3390/pr9091551 doi: 10.3390/pr9091551
|
| [45] |
M. Ahmadein, Boosting COVID-19 image classification using MobileNetV3 and aquila optimizer algorithm, Entropy, 23 (2021), https://doi.org/10.3390/e23111383 doi: 10.3390/e23111383
|
| [46] |
Y. J. Zhang, Y. X. Yan, J. Zhao, Z. M. Gao, AOAAO: The hybrid algorithm of arithmetic optimization algorithm with aquila optimizer, IEEE Access, 10 (2022), 10907–10933. https://doi.org/10.1109/ACCESS.2022.3144431 doi: 10.1109/ACCESS.2022.3144431
|
| [47] |
J. Zhao, Y. Zhang, S. Li, Y. Wang, Y. Yan, Z. Gao, A chaotic self-adaptive JAYA algorithm for parameter extraction of photovoltaic models, Math. Biosci. Eng., 19 (2022), 5638–5670. https://doi.org/10.3934/mbe.2022264 doi: 10.3934/mbe.2022264
|
| [48] |
Y. Zhang, Y. Wang, S. Li, F. Yao, L. Tao, Y. Yan, An enhanced adaptive comprehensive learning hybrid algorithm of Rao-1 and JAYA algorithm for parameter extraction of photovoltaic models, Math. Biosci. Eng., 19 (2022), 5610–5637. https://doi.org/10.3934/mbe.2022263 doi: 10.3934/mbe.2022263
|
| [49] |
W. Zhou, P. Wang, A. A. Heidari, X. Zhao, H. Turabieh, M. Mafarja, Metaphor-free dynamic spherical evolution for parameter estimation of photovoltaic modules, Energy Rep., 7 (2021), 5175–5202. https://doi.org/10.1016/j.egyr.2021.07.041 doi: 10.1016/j.egyr.2021.07.041
|
| [50] |
S. Singh, H. Singh, N. Mittal, H. Singh, A. G. Hussien, F. Sroubek, A feature level image fusion for Night-Vision context enhancement using Arithmetic optimization algorithm based image segmentation, Expert Syst. Appl., 209 (2022), 118272. https://doi.org/10.1016/j.eswa.2022.118272. doi: 10.1016/j.eswa.2022.118272
|
| [51] |
A. G. Hussien, L. Abualigah, R. A. Zitar, F. A. Hashim, M. Amin, A. Saber, et al., Recent advances in harris hawks optimization: A comparative study and applications, Electronics, 11 (2022), 1919. https://doi.org/10.3390/electronics11121919 doi: 10.3390/electronics11121919
|
| [52] |
S. Wang, A. G. Hussien, H. Jia, L. Abualigah, R. Zheng, Enhanced remora optimization algorithm for solving constrained engineering optimization problems, Mathematics, 10 (2022), 1696. https://doi.org/10.3390/math10101696 doi: 10.3390/math10101696
|
| [53] |
F. A. Hashim, A. G. Hussien, Snake optimizer: A novel meta-heuristic optimization algorithm, Knowl. Based Syst., 242 (2022), 108320. https://doi.org/10.1016/j.knosys.2022.108320 doi: 10.1016/j.knosys.2022.108320
|
| [54] |
R. Zheng, A. G. Hussien, H. M. Jia, L. Abualigah, S. Wang, D. Wu, An improved wild horse optimizer for solving optimization problems, Mathematics, 10 (2022), 8. https://doi.org/10.3390/math10081311 doi: 10.3390/math10081311
|
| [55] | A. Hussien, R. Mostafa, M. Khan, S. Kadry, F. A. Hashim, Enhanced COOT optimization algorithm for dimensionality reduction, in 2022 Fifth International Conference of Women in Data Science at Prince Sultan University (WiDS PSU), (2022). https://doi.org/10.1109/WiDS-PSU54548.2022.00020 |
| [56] |
H. Yu, H. Jia, J. Zhou, A. G. Hussien, Enhanced Aquila optimizer algorithm for global optimization and constrained engineering problems, Math. Biosci. Eng., 19 (2022), 14173–14211. https://doi.org/10.3934/mbe.2022660 doi: 10.3934/mbe.2022660
|
| [57] |
Y. Yang, C. Qian, H. Li, Y. Gao, J. Wu, C. Liu, et al., An efficient DBSCAN optimized by arithmetic optimization algorithm with opposition-based learning, J. Supercomput., 78 (2022), 19566–19604. https://doi.org/10.1007/s11227-022-04634-w doi: 10.1007/s11227-022-04634-w
|
| [58] | Z. Cui, X. Hou, H. Zhou, W. Lian, J. Wu, Modified slime mould algorithm via levy flight, in 13th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI), (2020). |
| [59] |
Y. Yang, Y. Gao, S. Tan, S. Zhao, J. Wu, S. Gao, et al., An opposition learning and spiral modelling based arithmetic optimization algorithm for global continuous optimization problems, Eng. Appl. Artif. Intell., 113 (2022), 104981. https://doi.org/10.1016/j.engappai.2022.104981 doi: 10.1016/j.engappai.2022.104981
|
| [60] |
M. Abd Elaziz, D. Oliva, Parameter estimation of solar cells diode models by an improved opposition-based whale optimization algorithm, Energy Convers. Manage., 171 (2018), 1843–1859. https://doi.org/10.1016/j.enconman.2018.05.062 doi: 10.1016/j.enconman.2018.05.062
|
| [61] |
A. G. Hussien, M. Amin, M. Abd El Aziz, A comprehensive review of moth-flame optimisation: variants, hybrids, and applications, J. Exp. Theor. Artif. Intell., 32 (2020), 705–725. https://doi.org/10.1080/0952813X.2020.1737246 doi: 10.1080/0952813X.2020.1737246
|
| [62] |
H. Yu, S. Qiao, A. A. Heidari, A. A. El-Saleh, C. Bi, M. Mafarja, et al., Laplace crossover and random replacement strategy boosted Harris hawks optimization: performance optimization and analysis, J. Comput. Design Eng., 9 (2022), 1879–1916. https://doi.org/10.1093/jcde/qwac085 doi: 10.1093/jcde/qwac085
|
| [63] |
A. Qi, D. Zhao, F. Yu, A. A. Heidari, H. Chen, L. Xiao, Directional mutation and crossover for immature performance of whale algorithm with application to engineering optimization, J. Comput. Design Eng., 9 (2022), 519–563. https://doi.org/10.1093/jcde/qwac014 doi: 10.1093/jcde/qwac014
|
| [64] |
D. Zhao, L. Liu, F. Yu, A. A. Heidari, M. Wang, H. Chen, et al., Opposition-based ant colony optimization with all-dimension neighborhood search for engineering design, J. Comput. Design Eng., 9 (2022), 1007–1044. https://doi.org/10.1093/jcde/qwac038 doi: 10.1093/jcde/qwac038
|
| [65] |
X. Zhou, W. Gui, A. A. Heidari, Z. Cai, H. Elmannai, M. Hamdi, et al., Advanced orthogonal learning and Gaussian barebone hunger games for engineering design, J. Comput. Design Eng., 9 (2022), 1699–1736. https://doi.org/10.1093/jcde/qwac075 doi: 10.1093/jcde/qwac075
|
| [66] |
F. Rezaei, H. R. Safavi, M. Abd Elaziz, S. H. A. El-Sappagh, M. A. Al-Betar, T. Abuhmed, An enhanced grey wolf optimizer with a velocity-aided global search mechanism, Mathematics, 10 (2022), 351. https://doi.org/10.3390/math10030351 doi: 10.3390/math10030351
|
| [67] |
J. Zhao, Z. M. Gao, H. F. Chen, The simplified aquila optimization algorithm, IEEE Access, 10 (2022), 22487–22515. https://doi.org/10.1109/ACCESS.2022.3153727 doi: 10.1109/ACCESS.2022.3153727
|
| [68] |
M. Khishe, M. R. Mosavi, Chimp optimization algorithm, Expert Syst. Appl., 149 (2020), 113338. https://doi.org/10.1016/j.eswa.2020.113338 doi: 10.1016/j.eswa.2020.113338
|
| [69] |
L. Abualigah, D. Yousri, M. Abd Elaziz, A. A. Ewees, M. A. A. Al-qaness, A. H. Gandomi, Aquila Optimizer: A novel meta-heuristic optimization algorithm, Comput. Ind. Eng., 157 (2021), 107250. https://doi.org/10.1016/j.cie.2021.107250 doi: 10.1016/j.cie.2021.107250
|
| [70] |
A. G. Hussien, M. Amin, A self-adaptive Harris Hawks optimization algorithm with opposition-based learning and chaotic local search strategy for global optimization and feature selection, Int. J. Mach. Learn. Cybern., 13 (2022), 309–336. https://doi.org/10.1007/s13042-021-01326-4 doi: 10.1007/s13042-021-01326-4
|
| [71] |
A. G. Hussien, An enhanced opposition-based Salp Swarm Algorithm for global optimization and engineering problems, J. Ambient Intell. Humanized Comput., 13 (2022), 129–150. https://doi.org/10.1007/s12652-021-02892-9 doi: 10.1007/s12652-021-02892-9
|
| [72] |
H. Bayzidi, S. Talatahari, M. Saraee, C. P. Lamarche, Social network search for solving engineering optimization problems, Comput. Intell. Neurosci., 2021 (2021), 8548639. https://doi.org/10.1155/2021/8548639 doi: 10.1155/2021/8548639
|
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Yufei Wang, Yujun Zhang, Yuxin Yan, Juan Zhao, Zhengming Gao. An enhanced aquila optimization algorithm with velocity-aided global search mechanism and adaptive opposition-based learning[J]. Mathematical Biosciences and Engineering, 2023, 20(4): 6422-6467. doi: 10.3934/mbe.2023278
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