{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T13:13:32Z","timestamp":1783689212019,"version":"3.55.0"},"reference-count":49,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T00:00:00Z","timestamp":1783641600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>Metaheuristic algorithms remain a widely used class of solvers for solving complex, non-convex optimization problems where gradient information is unavailable, yet two failure modes continue to limit their practical reach: premature convergence caused by inadequate exploration diversity in late iterations and population stagnation that persists even when individual agents are nominally assigned to the exploration phase. This paper proposes the Stagnation-Aware Aquila Optimizer (SAAO), a hybrid algorithm that addresses both failure modes by embedding three targeted mechanisms into the Aquila Optimizer (AO) framework: (i) an adaptive exploration probability that responds to global fitness-improvement history; (ii) individual-level stagnation counters that force exploration re-entry for any agent that fails to improve for more than 30 consecutive iterations, regardless of the global phase schedule; and (iii) a diversity-maintenance module that reinitializes completely stagnant agents via random sampling or opposition-based learning. The biological repertoire of search operators is simultaneously enriched by incorporating four physics-grounded operators from the Animated Oat Optimization (AOO) algorithm centroid-guided dispersal, elite-guided dispersal, hygroscopic rolling, and spring ejection, alongside the original AO operators, yielding six complementary update rules partitioned equally between exploration and exploitation. The SAAO was evaluated against nine state-of-the-art algorithms on the CEC2015 benchmark and CEC2022 under identical experimental settings. The SAAO achieved the best Friedman mean rank on both suites and delivered competitive or superior performance against the nine baselines, with Wilcoxon rank-sum tests confirming statistically significant advantages over most competitors. On three classical engineering design problems, the SAAO achieved competitive outcomes. In a real-world equipment anomaly prediction task, an SAAO-optimized ensemble classifier attained 98.23% accuracy, surpassing the compared baseline models. These results establish SAAO as a robust and computationally tractable optimizer for both benchmark and applied settings.<\/jats:p>","DOI":"10.3390\/biomimetics11070483","type":"journal-article","created":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T11:43:34Z","timestamp":1783683814000},"page":"483","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-Strategy Improved Aquila Optimizer with Adaptive Exploration and Individual-Level Stagnation Control: A Bio-Inspired Hybrid Metaheuristic and Its Engineering Applications"],"prefix":"10.3390","volume":"11","author":[{"given":"Oluwatayomi Rereloluwa","family":"Adegboye","sequence":"first","affiliation":[{"name":"Department of Management Information Systems, University of Mediterranean Karpasia, Northern Cyprus, TR-10 Mersin, Lefkosa 99010, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5762-6678","authenticated-orcid":false,"given":"Huseyin","family":"Kusetogullari","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Blekinge Institute of Technology, 37141 Karlskrona, Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Afi Kekeli","family":"Feda","sequence":"additional","affiliation":[{"name":"Advanced Research Centre, European University of Lefke, Northern Cyprus, TR-10 Mersin, Lefke 99010, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1002\/suco.70292","article-title":"Intelligent structural design of composite concrete-encased steel columns based on hybrid machine learning and multiobjective optimization","volume":"27","author":"Zhang","year":"2026","journal-title":"Struct. Concr."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"125953","DOI":"10.1016\/j.envpol.2025.125953","article-title":"PM2.5 concentration prediction using a whale optimization algorithm based hybrid deep learning model in Beijing, China","volume":"371","author":"Wei","year":"2025","journal-title":"Environ. Pollut."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Yang, X.-S. (2021). Nature-Inspired Optimization Algorithms, Academic Press. Available online: https:\/\/www.sciencedirect.com\/book\/monograph\/9780128219867\/nature-inspired-optimization-algorithms.","DOI":"10.1016\/B978-0-12-821986-7.00018-4"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1942","DOI":"10.1109\/ICNN.1995.488968","article-title":"Particle Swarm Optimization","volume":"Volume 4","author":"Kennedy","year":"1995","journal-title":"Proceedings of ICNN\u201995\u2014International Conference on Neural Networks"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1109\/4235.585892","article-title":"Ant colony system: A cooperative learning approach to the traveling salesman problem","volume":"1","author":"Dorigo","year":"1997","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Holland, J.H. (1992). Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, The MIT Press.","DOI":"10.7551\/mitpress\/1090.001.0001"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","article-title":"Differential Evolution\u2014A Simple and Efficient Heuristic for global Optimization over Continuous Spaces","volume":"11","author":"Storn","year":"1997","journal-title":"J. Glob. Optim."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2232","DOI":"10.1016\/j.ins.2009.03.004","article-title":"GSA: A Gravitational Search Algorithm","volume":"179","author":"Rashedi","year":"2009","journal-title":"Inf. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"105190","DOI":"10.1016\/j.knosys.2019.105190","article-title":"Equilibrium optimizer: A novel optimization algorithm","volume":"191","author":"Faramarzi","year":"2020","journal-title":"Knowl.-Based Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.advengsoft.2016.01.008","article-title":"The Whale Optimization Algorithm","volume":"95","author":"Mirjalili","year":"2016","journal-title":"Adv. Eng. Softw."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1016\/j.future.2019.02.028","article-title":"Harris hawks optimization: Algorithm and applications","volume":"97","author":"Heidari","year":"2019","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"20983","DOI":"10.1007\/s00521-024-10346-4","article-title":"Polar fox optimization algorithm: A novel meta-heuristic algorithm","volume":"36","author":"Ghiaskar","year":"2024","journal-title":"Neural Comput. Applic"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/4235.585893","article-title":"No free lunch theorems for optimization","volume":"1","author":"Wolpert","year":"1997","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2501654.2501658","article-title":"Exploration and exploitation in evolutionary algorithms: A survey","volume":"45","author":"Liu","year":"2013","journal-title":"ACM Comput. Surv."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1111\/itor.12001","article-title":"Metaheuristics\u2014The metaphor exposed","volume":"22","year":"2015","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"107250","DOI":"10.1016\/j.cie.2021.107250","article-title":"Aquila Optimizer: A novel meta-heuristic optimization algorithm","volume":"157","author":"Abualigah","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"131489","DOI":"10.1016\/j.eswa.2026.131489","article-title":"Robot path planning based on multi-strategy enhanced aquila optimizer algorithm in complex environments","volume":"312","author":"Zhou","year":"2026","journal-title":"Expert Syst. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"117629","DOI":"10.1016\/j.eswa.2022.117629","article-title":"Grey wolf optimizer based on Aquila exploration method","volume":"205","author":"Ma","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Ewees, A.A., Algamal, Z.Y., Abualigah, L., Al-qaness, M.A.A., Yousri, D., Ghoniem, R.M., and Abd Elaziz, M. (2022). A Cox Proportional-Hazards Model Based on an Improved Aquila Optimizer with Whale Optimization Algorithm Operators. Mathematics, 10.","DOI":"10.3390\/math10081273"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"113589","DOI":"10.1016\/j.knosys.2025.113589","article-title":"The Animated Oat Optimization Algorithm: A nature-inspired metaheuristic for engineering optimization and a case study on Wireless Sensor Networks","volume":"318","author":"Wang","year":"2025","journal-title":"Knowl.-Based Syst."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Gao, B., Shi, Y., Xu, F., and Xu, X. (2022). An Improved Aquila Optimizer Based on Search Control Factor and Mutations. Processes, 10.","DOI":"10.3390\/pr10081451"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Varshney, M., Kumar, P., Ali, M., and Gulzar, Y. (2024). Dynamic Random Walk and Dynamic Opposition Learning for Improving Aquila Optimizer: Solving Constrained Engineering Design Problems. Biomimetics, 9.","DOI":"10.3390\/biomimetics9040215"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"13079","DOI":"10.1038\/s41598-025-95888-w","article-title":"Enhanced aquila optimizer for global optimization and data clustering","volume":"15","author":"Abualigah","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"89153","DOI":"10.1109\/ACCESS.2022.3200386","article-title":"Chaotic Mapping Based Advanced Aquila Optimizer With Single Stage Evolutionary Algorithm","volume":"10","author":"Verma","year":"2022","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"14173","DOI":"10.3934\/mbe.2022660","article-title":"Enhanced Aquila optimizer algorithm for global optimization and constrained engineering problems","volume":"19","author":"Yu","year":"2022","journal-title":"MBE"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"22487","DOI":"10.1109\/ACCESS.2022.3153727","article-title":"The Simplified Aquila Optimization Algorithm","volume":"10","author":"Zhao","year":"2022","journal-title":"IEEE Access"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Kan, H., Xiao, Y., Gao, Z., and Zhang, X. (2025). Improved Multi-Strategy Aquila Optimizer for Engineering Optimization Problems. Biomimetics, 10.","DOI":"10.3390\/biomimetics10090620"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s10586-024-04929-y","article-title":"Improved Aquila optimizer and its applications","volume":"28","author":"Guo","year":"2025","journal-title":"Clust. Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"7076","DOI":"10.3934\/mbe.2021352","article-title":"An improved hybrid Aquila Optimizer and Harris Hawks Optimization for global optimization","volume":"18","author":"Wang","year":"2021","journal-title":"MBE"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"10963","DOI":"10.3934\/mbe.2022512","article-title":"IHAOAVOA: An improved hybrid aquila optimizer and African vultures optimization algorithm for global optimization problems","volume":"19","author":"Xiao","year":"2022","journal-title":"MBE"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Bousmaha, R. (2022, January 12\u201313). A novel hybrid Aquila optimizer with Whale optimziation algorithm for global optimization, feature selection and optimizing SVM parameters. Proceedings of the 2022 4th International Conference on Pattern Analysis and Intelligent Systems (PAIS), Oum El Bouaghi, Algeria.","DOI":"10.1109\/PAIS56586.2022.9946891"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Chu, F., Wang, J., and Tian, F. (2023). A hybrid Aquila Optimizer sine cosine Algorithm for Numerical Optimization. Proceedings of the 2023 2nd Asia Conference on Algorithms, Computing and Machine Learning, Association for Computing Machinery.","DOI":"10.1145\/3590003.3590048"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"8045","DOI":"10.1007\/s12652-022-04347-1","article-title":"A new hybrid method based on Aquila optimizer and tangent search algorithm for global optimization","volume":"14","author":"Akyol","year":"2023","journal-title":"J. Ambient Intell. Humaniz. Comput."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Chen, D., Du, X., Wang, H., Xian, Q., Sha, J., and Yao, C. (2024, January 6\u20138). An Improved Hybrid Aquila Optimizer and Pigeon-Inspired Optimization Algorithm with Its Application in PID Parameter Optimization. Proceedings of the 2024 8th International Symposium on Computer Science and Intelligent Control (ISCSIC), Zhengzhou, China.","DOI":"10.1109\/ISCSIC64297.2024.00082"},{"key":"ref_36","unstructured":"Liang, J.J., Qu, B.Y., Suganthan, P.N., and Chen, Q. (2014). Problem Definitions and Evaluation Criteria for the CEC 2015 Competition on Learning-Based Real-Parameter Single Objective Optimization, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University. Technical Report201411A."},{"key":"ref_37","unstructured":"Kumar, A., Price, K.V., Mohamed, A.W., Hadi, A.A., and Suganthan, P.N. (2021). Problem definitions and evaluation criteria for the 2022 special session and competition on single objective bound constrained numerical optimization. Technical Report, Nanyang Technological University."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"8","DOI":"10.5334\/jors.508","article-title":"Opfunu: An Open-source Python Library for Optimization Benchmark Functions","volume":"12","year":"2024","journal-title":"J. Open Res. Softw."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1007\/s10462-024-10723-4","article-title":"Black-winged kite algorithm: A nature-inspired meta-heuristic for solving benchmark functions and engineering problems","volume":"57","author":"Wang","year":"2024","journal-title":"Artif. Intell. Rev."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1919","DOI":"10.1007\/s10462-023-10567-4","article-title":"Crayfish optimization algorithm","volume":"56","author":"Jia","year":"2023","journal-title":"Artif. Intell. Rev."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"7305","DOI":"10.1007\/s11227-022-04959-6","article-title":"Dung beetle optimizer: A new meta-heuristic algorithm for global optimization","volume":"79","author":"Xue","year":"2023","journal-title":"J. Supercomput."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"108064","DOI":"10.1016\/j.compbiomed.2024.108064","article-title":"Parrot optimizer: Algorithm and applications to medical problems","volume":"172","author":"Lian","year":"2024","journal-title":"Comput. Biol. Med."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Trojovsk\u00fd, P., and Dehghani, M. (2022). Pelican Optimization Algorithm: A Novel Nature-Inspired Algorithm for Engineering Applications. Sensors, 22.","DOI":"10.3390\/s22030855"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"19599","DOI":"10.1109\/ACCESS.2022.3151641","article-title":"Tasmanian Devil Optimization: A New Bio-Inspired Optimization Algorithm for Solving Optimization Algorithm","volume":"10","author":"Dehghani","year":"2022","journal-title":"IEEE Access"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"3926","DOI":"10.1007\/s10489-020-01727-y","article-title":"Transient search optimization: A new meta-heuristic optimization algorithm","volume":"50","author":"Qais","year":"2020","journal-title":"Appl. Intell."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"20017","DOI":"10.1007\/s00521-022-07530-9","article-title":"Prairie Dog Optimization Algorithm","volume":"34","author":"Ezugwu","year":"2022","journal-title":"Neural Comput. Appl."},{"key":"ref_47","unstructured":"Van Thieu, N. (2023). ENOPPY: A Python Library for Engineering Optimization Problems. Zenodo, Available online: https:\/\/zenodo.org\/records\/7953529."},{"key":"ref_48","unstructured":"(2026, May 20). Industrial Equipment Monitoring Dataset. Available online: https:\/\/www.kaggle.com\/datasets\/dnkumars\/industrial-equipment-monitoring-dataset."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1007\/s10586-025-05366-1","article-title":"Dynamic fitness-distance balance competitive swarm optimizer: Performance investigation, engineering Simulation, and application in superconductor critical temperature prediction","volume":"28","author":"Cao","year":"2025","journal-title":"Clust. Comput."}],"container-title":["Biomimetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/7\/483\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T12:17:52Z","timestamp":1783685872000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/7\/483"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,10]]},"references-count":49,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2026,7]]}},"alternative-id":["biomimetics11070483"],"URL":"https:\/\/doi.org\/10.3390\/biomimetics11070483","relation":{},"ISSN":["2313-7673"],"issn-type":[{"value":"2313-7673","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,10]]}}}