{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T05:03:38Z","timestamp":1780549418541,"version":"3.54.1"},"reference-count":50,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T00:00:00Z","timestamp":1779408000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ningxia Higher Education Institution Project","award":["NYG2024093)"],"award-info":[{"award-number":["NYG2024093)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>Inspired by the hovering, diving, and cooperative hunting behaviors of the pied kingfisher, the Pied Kingfisher Optimizer (PKO) has demonstrated competitive performance in optimization tasks. However, it exhibits several phase-specific limitations, including uneven population distribution caused by random initialization, insufficient use of historical information during exploration, over-reliance on the global best during exploitation, and weakly guided perturbation in the symbiosis phase. To address these issues, this study proposes an Improved Pied Kingfisher Optimizer (IPKO), which incorporates biologically inspired adaptive strategies. Drawing inspiration from the kingfisher\u2019s diverse perching, gaze adjustment during hovering, evasive diving after failed strikes, and territory shifting based on flock position, four mechanisms are developed. Specifically, sine chaotic opposition-based initialization enhances population diversity; adaptive directional search regulates the exploration\u2013exploitation balance; stochastic perturbation-based information fusion improves the ability to escape local optima; and centroid-based adaptive boundary handling strengthens constraint adaptability. The performance of IPKO is evaluated on the CEC2017 benchmark suite (10, 30, 50, and 100 dimensions) and two real-world engineering problems. Experimental results show that IPKO achieves superior overall performance compared with eleven state-of-the-art algorithms, with statistical significance confirmed by the Friedman test and Holm\u2019s post-hoc procedure. Ablation studies further verify the contribution of each strategy. In engineering applications such as cold chain logistics and dynamic multi-UAV cooperative path planning, the IPKO algorithm demonstrates superior solution quality, robustness, and constraint-handling capability compared with competing algorithms. These results demonstrate that IPKO is a robust and effective bio-inspired optimization approach for solving complex, high-dimensional constrained engineering problems.<\/jats:p>","DOI":"10.3390\/biomimetics11060361","type":"journal-article","created":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T13:12:08Z","timestamp":1779455528000},"page":"361","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Hybrid Metaheuristic for High-Dimensional Constrained Optimization: Applications to Logistics and UAV Path Planning"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-6150-1427","authenticated-orcid":false,"given":"Yarong","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chuandong","family":"Qin","sequence":"additional","affiliation":[{"name":"Ningxia Key Laboratory of Intelligent Information and Big Data Processing, North Minzu University, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"111047","DOI":"10.1016\/j.asoc.2023.111047","article-title":"A systematic review of metaheuristic algorithms in electric power systems optimization","volume":"150","author":"Amaya","year":"2024","journal-title":"Appl. Soft Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"105858","DOI":"10.1016\/j.compbiomed.2022.105858","article-title":"Enhanced whale optimization algorithm for medical feature selection: A COVID-19 case study","volume":"148","author":"Zamani","year":"2022","journal-title":"Comput. Biol. Med."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Li, X.D., Tian, B., Hou, S.D., Li, X.X., Li, Y., Liu, C., and Li, J.M. (2023). Path Planning for Mount Robot Based on Improved Particle Swarm Optimization Algorithm. Electronics, 12.","DOI":"10.3390\/electronics12153289"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.eswa.2017.04.029","article-title":"Multilevel thresholding using grey wolf optimizer for image segmentation","volume":"86","author":"Khairuzzaman","year":"2017","journal-title":"Expert Syst. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1007\/s10462-024-10982-1","article-title":"Artificial intelligence-based optimization techniques for optimal reactive power dispatch problem: A contemporary survey, experiments, and analysis","volume":"58","author":"Mohamed","year":"2024","journal-title":"Artif. Intell. Rev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"104054","DOI":"10.1016\/j.asej.2026.104054","article-title":"Hybrid metaheuristic optimization-based solution for reactive power dispatch in dynamic power systems","volume":"17","author":"Ullah","year":"2026","journal-title":"Ain Shams Eng. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1016\/j.renene.2023.04.012","article-title":"Development and validation of a concise and anisotropic irradiance model for bifacial photovoltaic modules","volume":"209","author":"Sun","year":"2023","journal-title":"Renew. Energy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1109\/TSG.2024.3454050","article-title":"Enabling High-Efficiency Economic Dispatch of Hybrid AC\/DC Networked Microgrids: Steady-State Convex Bi-Directional Converter Models","volume":"16","author":"Liang","year":"2025","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Das, A., Rai, R., Sasmal, B., Dhal, K.G., Khurma, R.A., and Saha, R. (2025). Metaheuristic Algorithms Since 2020: Development, Taxonomy, Analysis, and Applications. Arch. Comput. Methods Eng.","DOI":"10.1007\/s11831-025-10408-3"},{"key":"ref_10","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_11","doi-asserted-by":"crossref","first-page":"113377","DOI":"10.1016\/j.eswa.2020.113377","article-title":"Marine Predators Algorithm: A Nature-inspired Metaheuristic","volume":"152","author":"Faramarzi","year":"2020","journal-title":"Expert Syst. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"116924","DOI":"10.1016\/j.eswa.2022.116924","article-title":"Golden jackal optimization: A novel nature-inspired optimizer for engineering applications","volume":"198","author":"Chopra","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_13","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the ICNN\u201995-International Conference on Neural Networks, Perth, WA, Australia."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","article-title":"Grey Wolf Optimizer","volume":"69","author":"Mirjalili","year":"2014","journal-title":"Adv. Eng. Softw."},{"key":"ref_15","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_16","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1137\/0202009","article-title":"Genetic algorithms and the optimal allocation of trials","volume":"2","author":"Holland","year":"1973","journal-title":"SIAM J. Comput."},{"key":"ref_17","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_18","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_19","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1126\/science.220.4598.671","article-title":"Optimization by Simulated Annealing","volume":"220","author":"Kirkpatrick","year":"1983","journal-title":"Science"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.cad.2010.12.015","article-title":"Teaching-Learning-Based Optimization: A Novel Method for Constrained Mechanical Design Optimization Problems","volume":"43","author":"Rao","year":"2011","journal-title":"Comput.-Aided Des."},{"key":"ref_21","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_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.swevo.2012.05.001","article-title":"Evolutionary dynamic optimization: A survey of the state of the art","volume":"6","author":"Nguyen","year":"2012","journal-title":"Swarm Evol. Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"101336","DOI":"10.1016\/j.swevo.2023.101336","article-title":"A novel adaptive algorithm of particle swarm optimization based on the human social learning intelligence","volume":"80","author":"E","year":"2023","journal-title":"Swarm Evol. Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"101737","DOI":"10.1016\/j.swevo.2024.101737","article-title":"Multi-strategy particle swarm optimization with adaptive forgetting for base station layout","volume":"91","author":"Zhu","year":"2024","journal-title":"Swarm Evol. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"101746","DOI":"10.1016\/j.swevo.2024.101746","article-title":"An adaptive co-evolutionary competitive particle swarm optimizer for constrained multi-objective optimization problems","volume":"91","author":"Meng","year":"2024","journal-title":"Swarm Evol. Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"108320","DOI":"10.1016\/j.knosys.2022.108320","article-title":"Snake Optimizer: A novel meta-heuristic optimization algorithm","volume":"242","author":"Hashim","year":"2022","journal-title":"Knowl. Based Syst."},{"key":"ref_27","first-page":"15455","article-title":"Pied kingfisher optimizer: A new bio-inspired algorithm for solving numerical optimization and industrial engineering problems","volume":"36","author":"Bouaouda","year":"2024","journal-title":"Neural Comput. Appl."},{"key":"ref_28","first-page":"186","article-title":"Nonlinear Grey Wolf Optimization Algorithm with Chaotic Mapping and Elite Gaussian Perturbation","volume":"43","author":"Cai","year":"2022","journal-title":"Comput. Eng. Des."},{"key":"ref_29","unstructured":"Tizhoosh, H.R. (2005, January 28\u201330). Opposition-based learning: A new scheme for machine intelligence. Proceedings of the International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC\u201906), Vienna, Austria."},{"key":"ref_30","first-page":"3","article-title":"Improved Beluga Whale Optimization Algorithm Based on Chaotic Opposition-based Learning and Water Wave Algorithm","volume":"41","author":"Wang","year":"2024","journal-title":"Appl. Res. Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10462-024-10738-x","article-title":"Modified crayfish optimization algorithm for solving multiple engineering application problems","volume":"57","author":"Jia","year":"2024","journal-title":"Artif. Intell. Rev."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"115878","DOI":"10.1016\/j.cma.2023.115878","article-title":"DTCSMO: An efficient hybrid starling murmuration optimizer for engineering applications","volume":"405","author":"Hu","year":"2023","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"111257","DOI":"10.1016\/j.knosys.2023.111257","article-title":"Crested Porcupine Optimizer: A new nature-inspired metaheuristic","volume":"284","author":"Mohamed","year":"2024","journal-title":"Knowl.-Based Syst."},{"key":"ref_34","first-page":"44","article-title":"Improved Frost Ice Optimization Algorithm for UAV Three-Dimensional Path Planning","volume":"48","author":"Wang","year":"2025","journal-title":"Electron. Meas. Technol."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Tanabe, R., and Fukunaga, A. (2013, January 20\u201323). Success-History Based Parameter Adaptation for Differential Evolution. Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC), Cancun, Mexico.","DOI":"10.1109\/CEC.2013.6557555"},{"key":"ref_36","unstructured":"Hansen, N. (2016). The CMA Evolution Strategy: A Tutorial. arXiv."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"14895","DOI":"10.1007\/s00521-022-07297-z","article-title":"Assessing cloud QoS predictions using OWA in neural network methods","volume":"34","author":"Hussain","year":"2022","journal-title":"Neural Comput. Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"121413","DOI":"10.1016\/j.eswa.2023.121413","article-title":"A nonlinear African vulture optimization algorithm combining Henon chaotic mapping theory and reverse learning competition strategy","volume":"236","author":"Wang","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"107532","DOI":"10.1016\/j.engappai.2023.107532","article-title":"Newton-Raphson-based optimizer: A new population-based metaheuristic algorithm for continuous optimization problems","volume":"128","author":"Sowmya","year":"2024","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"109189","DOI":"10.1016\/j.knosys.2022.109189","article-title":"A new metaheuristic optimization based on K-means clustering algorithm and its application to structural damage identification","volume":"251","author":"Minh","year":"2022","journal-title":"Knowl. Based Syst."},{"key":"ref_41","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_42","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.matcom.2021.08.013","article-title":"New metaheuristic algorithm for solving optimization problems","volume":"192","author":"Hashim","year":"2022","journal-title":"Math. Comput. Simul."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.ins.2020.06.037","article-title":"Gradient-based optimizer: A new metaheuristic optimization algorithm","volume":"540","author":"Ahmadianfar","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_44","unstructured":"Zhu, Y. (2026, May 18). Research on the Optimization of Green Cold Chain Logistics Distribution Routes of Fresh Products Based on Ant Colony Algorithm. Available online: https:\/\/www.doc88.com\/p-98739013599678.html."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Rahman, M., Sarkar, N.I., and Lutui, R. (2025). A Survey on Multi-UAV Path Planning: Classification, Algorithms, Open Research Problems, and Future Directions. Drones, 9.","DOI":"10.3390\/drones9040263"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Wang, Z., Gong, H., Nie, M., and Liu, X. (2024). Research on Multi-UAV Cooperative Dynamic Path Planning Algorithm Based on Conflict Search. Drones, 8.","DOI":"10.3390\/drones8060274"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Qiao, Y., Han, Z., Fu, H., and Gao, Y. (2025). An Improved Red-Billed Blue Magpie Algorithm and Its Application to Constrained Optimization Problems. Biomimetics, 10.","DOI":"10.3390\/biomimetics10110788"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"3955","DOI":"10.1109\/TIE.2022.3177758","article-title":"A Gaussian mixture model based fast motion planning method through online environmental feature learning","volume":"70","author":"Yuan","year":"2022","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"111850","DOI":"10.1016\/j.knosys.2024.111850","article-title":"Optimization based on the smart behavior of plants with its engineering applications: Ivy algorithm","volume":"295","author":"Ghasemi","year":"2024","journal-title":"Knowl.-Based Syst."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"5032","DOI":"10.1038\/s41598-024-54910-3","article-title":"Hippopotamus optimization algorithm: A novel nature-inspired optimization algorithm","volume":"14","author":"Amiri","year":"2024","journal-title":"Sci. Rep."}],"container-title":["Biomimetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/6\/361\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T04:13:24Z","timestamp":1780546404000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/6\/361"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,22]]},"references-count":50,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["biomimetics11060361"],"URL":"https:\/\/doi.org\/10.3390\/biomimetics11060361","relation":{},"ISSN":["2313-7673"],"issn-type":[{"value":"2313-7673","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,22]]}}}