{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T15:23:36Z","timestamp":1787498616790,"version":"build-2736575974"},"reference-count":97,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T00:00:00Z","timestamp":1779408000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"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-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"DOI":"10.1038\/s41598-026-44516-2","type":"journal-article","created":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T03:36:16Z","timestamp":1779420976000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Heart rate optimizer: a novel bio-inspired metaheuristic algorithm"],"prefix":"10.1038","volume":"16","author":[{"given":"Mosa E.","family":"Hosney","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marwa M.","family":"Emam","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammed R.","family":"Saad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nagwan Abdel","family":"Samee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Essam H.","family":"Houssein","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,22]]},"reference":[{"key":"44516_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2024.117718","volume":"436","author":"Y Lang","year":"2025","unstructured":"Lang, Y. & Gao, Y. Dream optimization algorithm (DOA): A novel metaheuristic optimization algorithm inspired by human dreams and its applications to real-world engineering problems. Comput. Methods Appl. Mech. Eng. 436, 117718 (2025).","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1","key":"44516_CR2","doi-asserted-by":"publisher","DOI":"10.1186\/s40537-025-01129-2","volume":"12","author":"MM Emam","year":"2025","unstructured":"Emam, M. M., Saad, M. R., Younan, M. & Houssein, E. H. An efficient enhanced exponential distribution optimizer: Applications in global, engineering, and combinatorial optimization problems. J. Big Data 12(1), 90 (2025).","journal-title":"J. Big Data"},{"issue":"2","key":"44516_CR3","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1016\/j.ejor.2013.10.060","volume":"234","author":"PN Kolm","year":"2014","unstructured":"Kolm, P. N., T\u00fct\u00fcnc\u00fc, R. & Fabozzi, F. J. 60 years of portfolio optimization: Practical challenges and current trends. Eur. J. Oper. Res. 234(2), 356\u2013371 (2014).","journal-title":"Eur. J. Oper. Res."},{"key":"44516_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2024.124581","volume":"255","author":"MM Emam","year":"2024","unstructured":"Emam, M. M., Houssein, E. H., Samee, N. A., Alohali, M. A. & Hosney, M. E. Breast cancer diagnosis using optimized deep convolutional neural network based on transfer learning technique and improved coati optimization algorithm. Expert Syst. Appl. 255, 124581 (2024).","journal-title":"Expert Syst. Appl."},{"key":"44516_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2023.110454","volume":"268","author":"M Abdel-Basset","year":"2023","unstructured":"Abdel-Basset, M., Mohamed, R., Azeem, S. A. A., Jameel, M. & Abouhawwash, M. Kepler optimization algorithm: A new metaheuristic algorithm inspired by Kepler\u2019s laws of planetary motion. Knowl. Based Syst. 268, 110454 (2023).","journal-title":"Knowl. Based Syst."},{"key":"44516_CR6","doi-asserted-by":"publisher","DOI":"10.1016\/j.compbiomed.2023.107389","volume":"165","author":"EH Houssein","year":"2023","unstructured":"Houssein, E. H., Oliva, D., Samee, N. A., Mahmoud, N. F. & Emam, M. M. Liver cancer algorithm: A novel bio-inspired optimizer. Comput. Biol. Med. 165, 107389 (2023).","journal-title":"Comput. Biol. Med."},{"key":"44516_CR7","doi-asserted-by":"crossref","unstructured":"D.\u00a0Chauhan, A.\u00a0Yadav, A comprehensive survey on artificial electric field algorithm: Theories and applications: D. chauhan, a. yadav, Archives of Computational Methods in Engineering 31\u00a0(5),\u00a02663\u20132715 (2024).","DOI":"10.1007\/s11831-023-10058-3"},{"key":"44516_CR8","doi-asserted-by":"publisher","DOI":"10.32604\/cmes.2023.026019","author":"H Cui","year":"2023","unstructured":"Cui, H. et al. Enhanced Harris Hawks Optimization integrated with Coot Bird Optimization for solving continuous numerical optimization problems.. Comput. Model. Eng. Sci. https:\/\/doi.org\/10.32604\/cmes.2023.026019 (2023).","journal-title":"Comput. Model. Eng. Sci."},{"key":"44516_CR9","doi-asserted-by":"crossref","unstructured":"M.\u00a0Cavazzuti, Deterministic optimization, in: Optimization methods: From theory to design scientific and technological aspects in mechanics, 77\u2013102 (Springer, 2012).\u00a0","DOI":"10.1007\/978-3-642-31187-1_4"},{"key":"44516_CR10","doi-asserted-by":"crossref","unstructured":"V.\u00a0Rajinikanth, N.\u00a0Razmjooy, A comprehensive survey of meta-heuristic algorithms, Metaheuristics and Optimization in Computer and Electrical Engineering: Volume 2: Hybrid and Improved Algorithms 1\u201339 (2023).","DOI":"10.1007\/978-3-031-42685-8_1"},{"issue":"1","key":"44516_CR11","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1186\/s40537-024-00931-8","volume":"11","author":"RA Khurma","year":"2024","unstructured":"Khurma, R. A. et al. Advanced Rime Architecture for global optimization and feature selection. J. Big Data 11(1), 89. (2024).","journal-title":"J. Big Data"},{"key":"44516_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2023.107458","volume":"128","author":"F Yu","year":"2024","unstructured":"Yu, F., Lu, C., Zhou, J., Yin, L. & Wang, K. A knowledge-guided bi-population evolutionary algorithm for energy-efficient scheduling of distributed flexible job shop problem. Eng. Appl. Artif. Intell. 128, 107458 (2024).","journal-title":"Eng. Appl. Artif. Intell."},{"key":"44516_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2025.128017","volume":"285","author":"MM Emam","year":"2025","unstructured":"Emam, M. M., Mostafa, R. R. & Houssein, E. H. Computer-aided diagnosis system for predicting liver cancer disease using modified Genghis Khan shark optimizer algorithm. Expert Syst. Appl. 285, 128017 (2025).","journal-title":"Expert Syst. Appl."},{"key":"44516_CR14","doi-asserted-by":"crossref","unstructured":"E.-G. Talbi, Metaheuristics: from design to implementation, (John Wiley & Sons, 2009).","DOI":"10.1002\/9780470496916"},{"issue":"4598","key":"44516_CR15","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1126\/science.220.4598.671","volume":"220","author":"S Kirkpatrick","year":"1983","unstructured":"Kirkpatrick, S., Gelatt, C. D. Jr. & Vecchi, M. P. Optimization by simulated annealing. Science 220(4598), 671\u2013680 (1983).","journal-title":"Science"},{"issue":"8","key":"44516_CR16","doi-asserted-by":"publisher","first-page":"1288","DOI":"10.1109\/9.940936","volume":"46","author":"KA Sullivan","year":"2001","unstructured":"Sullivan, K. A. & Jacobson, S. H. A convergence analysis of generalized hill climbing algorithms. IEEE Trans. Autom. Control. 46(8), 1288\u20131293 (2001).","journal-title":"IEEE Trans. Autom. Control."},{"issue":"11","key":"44516_CR17","doi-asserted-by":"publisher","first-page":"1097","DOI":"10.1016\/S0305-0548(97)00031-2","volume":"24","author":"N Mladenovi\u0107","year":"1997","unstructured":"Mladenovi\u0107, N. & Hansen, P. Variable neighborhood search. Comput. Oper. Res. 24(11), 1097\u20131100 (1997).","journal-title":"Comput. Oper. Res."},{"issue":"1","key":"44516_CR18","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1038\/scientificamerican0792-66","volume":"267","author":"JH Holland","year":"1992","unstructured":"Holland, J. H. Genetic algorithms. Sci. Am. 267(1), 66\u201373 (1992).","journal-title":"Sci. Am."},{"issue":"2","key":"44516_CR19","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1007\/s00500-016-2474-6","volume":"22","author":"D Wang","year":"2018","unstructured":"Wang, D., Tan, D. & Liu, L. Particle swarm optimization algorithm: An overview. Soft Comput. 22(2), 387\u2013408 (2018).","journal-title":"Soft Comput."},{"issue":"4","key":"44516_CR20","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1109\/MCI.2006.329691","volume":"1","author":"M Dorigo","year":"2007","unstructured":"Dorigo, M., Birattari, M. & Stutzle, T. Ant colony optimization. IEEE Comput. Intell. Mag. 1(4), 28\u201339 (2007).","journal-title":"IEEE Comput. Intell. Mag."},{"key":"44516_CR21","unstructured":"X.-S. Yang, Nature-inspired metaheuristic algorithms, (Luniver press, 2010)."},{"issue":"1\u20134","key":"44516_CR22","doi-asserted-by":"publisher","first-page":"35","DOI":"10.3233\/FI-1998-35123403","volume":"35","author":"AE Eiben","year":"1998","unstructured":"Eiben, A. E. & Schippers, C. A. On evolutionary exploration and exploitation. Fundam. Inform. 35(1\u20134), 35\u201350 (1998).","journal-title":"Fundam. Inform."},{"key":"44516_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jocs.2020.101104","volume":"46","author":"X-S Yang","year":"2020","unstructured":"Yang, X.-S. Nature-inspired optimization algorithms: Challenges and open problems. J. Comput. Sci. 46, 101104 (2020).","journal-title":"J. Comput. Sci."},{"issue":"1","key":"44516_CR24","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1109\/4235.585893","volume":"1","author":"DH Wolpert","year":"1997","unstructured":"Wolpert, D. H. & Macready, W. G. No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1(1), 67\u201382 (1997).","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"4","key":"44516_CR25","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1023\/A:1008202821328","volume":"11","author":"R Storn","year":"1997","unstructured":"Storn, R. & Price, K. Differential evolution-A simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341\u2013359 (1997).","journal-title":"J. Glob. Optim."},{"key":"44516_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2019.105190","volume":"191","author":"A Faramarzi","year":"2020","unstructured":"Faramarzi, A., Heidarinejad, M., Stephens, B. & Mirjalili, S. Equilibrium optimizer: A novel optimization algorithm. Knowl. Based Syst. 191, 105190 (2020).","journal-title":"Knowl. Based Syst."},{"issue":"13","key":"44516_CR27","doi-asserted-by":"publisher","first-page":"2232","DOI":"10.1016\/j.ins.2009.03.004","volume":"179","author":"E Rashedi","year":"2009","unstructured":"Rashedi, E., Nezamabadi-Pour, H. & Saryazdi, S. Gsa: A gravitational search algorithm. Inf. Sci. 179(13), 2232\u20132248 (2009).","journal-title":"Inf. Sci."},{"key":"44516_CR28","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/j.compstruc.2012.07.010","volume":"110","author":"H Eskandar","year":"2012","unstructured":"Eskandar, H., Sadollah, A., Bahreininejad, A. & Hamdi, M. Water cycle algorithm-A novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput. Struct. 110, 151\u2013166 (2012).","journal-title":"Comput. Struct."},{"key":"44516_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2023.107532","volume":"128","author":"R Sowmya","year":"2024","unstructured":"Sowmya, R., Premkumar, M. & Jangir, P. Newton-Raphson-based optimizer: A new population-based metaheuristic algorithm for continuous optimization problems. Eng. Appl. Artif. Intell. 128, 107532 (2024).","journal-title":"Eng. Appl. Artif. Intell."},{"key":"44516_CR30","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2022.116516","volume":"195","author":"I Ahmadianfar","year":"2022","unstructured":"Ahmadianfar, I., Heidari, A. A., Noshadian, S., Chen, H. & Gandomi, A. H. Info: An efficient optimization algorithm based on weighted mean of vectors. Expert Syst. Appl. 195, 116516 (2022).","journal-title":"Expert Syst. Appl."},{"key":"44516_CR31","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/ade378","author":"X Wang","year":"2025","unstructured":"Wang, X. Bighorn Sheep Optimization Algorithm: A novel and efficient approach for wireless sensor network coverage optimization. Phys. Scr. https:\/\/doi.org\/10.1088\/1402-4896\/ade378 (2025).","journal-title":"Phys. Scr."},{"issue":"3","key":"44516_CR32","doi-asserted-by":"publisher","first-page":"1531","DOI":"10.1007\/s10489-020-01893-z","volume":"51","author":"FA Hashim","year":"2021","unstructured":"Hashim, F. A., Hussain, K., Houssein, E. H., Mabrouk, M. S. & Al-Atabany, W. Archimedes optimization algorithm: A new metaheuristic algorithm for solving optimization problems. Appl. Intell. 51(3), 1531\u20131551 (2021).","journal-title":"Appl. Intell."},{"key":"44516_CR33","doi-asserted-by":"publisher","DOI":"10.1016\/j.measurement.2025.118361","author":"X Wang","year":"2025","unstructured":"Wang, X. & Yao, L. Cape lynx optimizer: A novel metaheuristic algorithm for enhancing wireless sensor network coverage. Measurement https:\/\/doi.org\/10.1016\/j.measurement.2025.118361 (2025).","journal-title":"Measurement"},{"issue":"2","key":"44516_CR34","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1177\/003754970107600201","volume":"76","author":"ZW Geem","year":"2001","unstructured":"Geem, Z. W., Kim, J. H. & Loganathan, G. V. A new heuristic optimization algorithm: Harmony search. simulation 76(2), 60\u201368 (2001).","journal-title":"simulation"},{"issue":"3","key":"44516_CR35","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/j.cad.2010.12.015","volume":"43","author":"RV Rao","year":"2011","unstructured":"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(3), 303\u2013315 (2011).","journal-title":"Comput. Aided Des."},{"key":"44516_CR36","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2024.111880","volume":"296","author":"SO Oladejo","year":"2024","unstructured":"Oladejo, S. O., Ekwe, S. O. & Mirjalili, S. The hiking optimization algorithm: A novel human-based metaheuristic approach. Knowl. Based Syst. 296, 111880 (2024).","journal-title":"Knowl. Based Syst."},{"key":"44516_CR37","doi-asserted-by":"publisher","first-page":"83639","DOI":"10.1109\/ACCESS.2023.3298105","volume":"11","author":"SO Oladejo","year":"2023","unstructured":"Oladejo, S. O., Ekwe, S. O., Akinyemi, L. A. & Mirjalili, S. A. The deep sleep optimizer: A human-based metaheuristic approach. IEEE Access 11, 83639\u201383665 (2023).","journal-title":"IEEE Access"},{"key":"44516_CR38","doi-asserted-by":"publisher","first-page":"849","DOI":"10.1016\/j.future.2019.02.028","volume":"97","author":"AA Heidari","year":"2019","unstructured":"Heidari, A. A. et al. Harris Hawks optimization: Algorithm and applications. Future Gener. Comput. Syst. 97, 849\u2013872 (2019).","journal-title":"Future Gener. Comput. Syst."},{"key":"44516_CR39","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1016\/j.future.2020.03.055","volume":"111","author":"S Li","year":"2020","unstructured":"Li, S., Chen, H., Wang, M., Heidari, A. A. & Mirjalili, S. Slime mould algorithm: A new method for stochastic optimization. Future Gener. Comput. Syst. 111, 300\u2013323. https:\/\/doi.org\/10.1016\/j.future.2020.03.055 (2020).","journal-title":"Future Gener. Comput. Syst."},{"key":"44516_CR40","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2024.103694","volume":"195","author":"W-C Wang","year":"2024","unstructured":"Wang, W.-C., Tian, W.-C., Xu, D.-M. & Zang, H.-F. Arctic puffin optimization: A bio-inspired metaheuristic algorithm for solving engineering design optimization. Adv. Eng. Softw. 195, 103694 (2024).","journal-title":"Adv. Eng. Softw."},{"issue":"3","key":"44516_CR41","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/s10462-023-10653-7","volume":"57","author":"H Peraza-V\u00e1zquez","year":"2024","unstructured":"Peraza-V\u00e1zquez, H., Pe\u00f1a-Delgado, A., Merino-Trevi\u00f1o, M., Morales-Cepeda, A. B. & Sinha, N. A novel metaheuristic inspired by horned lizard defense tactics. Artif. Intell. Rev. 57(3), 59 (2024).","journal-title":"Artif. Intell. Rev."},{"issue":"9","key":"44516_CR42","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1007\/s10462-025-11269-9","volume":"58","author":"L Wang","year":"2025","unstructured":"Wang, L. et al. Tianji\u2019s horse racing optimization (thro): A new metaheuristic inspired by ancient wisdom and its engineering optimization applications. Artif. Intell. Rev. 58(9), 282 (2025).","journal-title":"Artif. Intell. Rev."},{"issue":"5","key":"44516_CR43","doi-asserted-by":"publisher","first-page":"3641","DOI":"10.1007\/s00521-024-10694-1","volume":"37","author":"C Zhong","year":"2025","unstructured":"Zhong, C. et al. Starfish optimization algorithm (sfoa): A bio-inspired metaheuristic algorithm for global optimization compared with 100 optimizers. Neural Comput. Appl. 37(5), 3641\u20133683 (2025).","journal-title":"Neural Comput. Appl."},{"issue":"6","key":"44516_CR44","doi-asserted-by":"publisher","first-page":"362","DOI":"10.1007\/s10586-024-04976-5","volume":"28","author":"A Rodan","year":"2025","unstructured":"Rodan, A., Al-Tamimi, A.-K., Al-Alnemer, L. & Mirjalili, S. Stellar oscillation optimizer: A nature-inspired metaheuristic optimization algorithm. Cluster Comput. 28(6), 362 (2025).","journal-title":"Cluster Comput."},{"issue":"1","key":"44516_CR45","doi-asserted-by":"publisher","first-page":"1391","DOI":"10.1109\/TTE.2025.3628607","volume":"12","author":"H Yang","year":"2025","unstructured":"Yang, H. et al. An electrified railway catenary component anomaly detection frame based on invariant normal region prototype with segment anything model. IEEE Transactions on Transportation Electrification 12(1), 1391\u20131402 (2025).","journal-title":"IEEE Transactions on Transportation Electrification"},{"key":"44516_CR46","doi-asserted-by":"crossref","unstructured":"J.\u00a0Yan, et al., Research on multimodal techniques for arc detection in railway systems with limited data, Structural Health Monitoring 14759217251336797 (2025).","DOI":"10.1177\/14759217251336797"},{"issue":"9","key":"44516_CR47","doi-asserted-by":"publisher","first-page":"3792","DOI":"10.1016\/j.asoc.2013.05.010","volume":"13","author":"S-H Liu","year":"2013","unstructured":"Liu, S.-H., Mernik, M., Hrn\u010di\u010d, D. & \u010crepin\u0161ek, M. A parameter control method of evolutionary algorithms using exploration and exploitation measures with a practical application for fitting Sovova\u2019s mass transfer model. Appl. Soft Comput. 13(9), 3792\u20133805 (2013).","journal-title":"Appl. Soft Comput."},{"issue":"1","key":"44516_CR48","doi-asserted-by":"publisher","first-page":"1171","DOI":"10.1103\/PhysRevE.56.1171","volume":"56","author":"T Asselmeyer","year":"1997","unstructured":"Asselmeyer, T., Ebeling, W. & Ros\u00e9, H. Evolutionary strategies of optimization. Phys. Rev. E 56(1), 1171 (1997).","journal-title":"Phys. Rev. E"},{"issue":"2","key":"44516_CR49","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1007\/s00521-015-1870-7","volume":"27","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili, S., Mirjalili, S. M. & Hatamlou, A. Multi-verse optimizer: A nature-inspired algorithm for global optimization. Neural Comput. Appl. 27(2), 495\u2013513 (2016).","journal-title":"Neural Comput. Appl."},{"key":"44516_CR50","doi-asserted-by":"publisher","first-page":"66084","DOI":"10.1109\/ACCESS.2019.2918406","volume":"7","author":"Z Wei","year":"2019","unstructured":"Wei, Z., Huang, C., Wang, X., Han, T. & Li, Y. Nuclear reaction optimization: A novel and powerful physics-based algorithm for global optimization. IEEE Access 7, 66084\u201366109 (2019).","journal-title":"IEEE Access"},{"key":"44516_CR51","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.120069","volume":"225","author":"L Deng","year":"2023","unstructured":"Deng, L. & Liu, S. Snow ablation optimizer: A novel metaheuristic technique for numerical optimization and engineering design. Expert Syst. Appl. 225, 120069 (2023).","journal-title":"Expert Syst. Appl."},{"key":"44516_CR52","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/j.neucom.2023.02.010","volume":"532","author":"H Su","year":"2023","unstructured":"Su, H. et al. Rime: A physics-based optimization. Neurocomputing 532, 183\u2013214 (2023).","journal-title":"Neurocomputing"},{"key":"44516_CR53","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1016\/j.future.2017.10.052","volume":"81","author":"M Kumar","year":"2018","unstructured":"Kumar, M., Kulkarni, A. J. & Satapathy, S. C. Socio evolution & learning optimization algorithm: A socio-inspired optimization methodology. Future Gener. Comput. Syst. 81, 252\u2013272 (2018).","journal-title":"Future Gener. Comput. Syst."},{"key":"44516_CR54","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.swevo.2014.02.002","volume":"17","author":"N Moosavian","year":"2014","unstructured":"Moosavian, N. & Roodsari, B. K. Soccer league competition algorithm: A novel meta-heuristic algorithm for optimal design of water distribution networks. Swarm Evol. Comput. 17, 14\u201324 (2014).","journal-title":"Swarm Evol. Comput."},{"key":"44516_CR55","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","volume":"69","author":"S Mirjalili","year":"2014","unstructured":"Mirjalili, S., Mirjalili, S. M. & Lewis, A. Grey wolf optimizer. Adv. Eng. Softw. 69, 46\u201361 (2014).","journal-title":"Adv. Eng. Softw."},{"key":"44516_CR56","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2021.107408","volume":"158","author":"B Abdollahzadeh","year":"2021","unstructured":"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).","journal-title":"Comput. Ind. Eng."},{"issue":"1","key":"44516_CR57","doi-asserted-by":"publisher","first-page":"1030","DOI":"10.1007\/s10489-022-03533-0","volume":"53","author":"H Mohammed","year":"2023","unstructured":"Mohammed, H. & Rashid, T. Fox: A fox-inspired optimization algorithm. Appl. Intell. 53(1), 1030\u20131050 (2023).","journal-title":"Appl. Intell."},{"key":"44516_CR58","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2021.114685","volume":"174","author":"MS Braik","year":"2021","unstructured":"Braik, M. S. Chameleon swarm algorithm: A bio-inspired optimizer for solving engineering design problems. Expert Syst. Appl. 174, 114685 (2021).","journal-title":"Expert Syst. Appl."},{"key":"44516_CR59","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.advengsoft.2016.01.008","volume":"95","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili, S. & Lewis, A. The whale optimization algorithm. Adv. Eng. Softw. 95, 51\u201367 (2016a).","journal-title":"Adv. Eng. Softw."},{"key":"44516_CR60","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2020.113338","volume":"149","author":"M Khishe","year":"2020","unstructured":"Khishe, M. & Mosavi, M. R. Chimp optimization algorithm. Expert Syst. Appl. 149, 113338 (2020).","journal-title":"Expert Syst. Appl."},{"key":"44516_CR61","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2022.116924","volume":"198","author":"N Chopra","year":"2022","unstructured":"Chopra, N. & Ansari, M. M. Golden jackal optimization: A novel nature-inspired optimizer for engineering applications. Expert Syst. Appl. 198, 116924 (2022).","journal-title":"Expert Syst. Appl."},{"key":"44516_CR62","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2020.113377","volume":"152","author":"A Faramarzi","year":"2020","unstructured":"Faramarzi, A., Heidarinejad, M., Mirjalili, S. & Gandomi, A. H. Marine predators algorithm: A nature-inspired metaheuristic. Expert Syst. Appl. 152, 113377 (2020).","journal-title":"Expert Syst. Appl."},{"issue":"8","key":"44516_CR63","doi-asserted-by":"publisher","first-page":"8457","DOI":"10.1007\/s12652-020-02580-0","volume":"12","author":"G Dhiman","year":"2021","unstructured":"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(8), 8457\u20138482 (2021).","journal-title":"J. Ambient Intell. Humaniz. Comput."},{"key":"44516_CR64","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2020.103541","volume":"90","author":"S Kaur","year":"2020","unstructured":"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).","journal-title":"Eng. Appl. Artif. Intell."},{"key":"44516_CR65","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2022.108457","volume":"243","author":"M Braik","year":"2022","unstructured":"Braik, M., Hammouri, A., Atwan, J., Al-Betar, M. A. & Awadallah, M. A. White shark optimizer: A novel bio-inspired meta-heuristic algorithm for global optimization problems. Knowl. Based Syst. 243, 108457. https:\/\/doi.org\/10.1016\/j.knosys.2022.108457 (2022).","journal-title":"Knowl. Based Syst."},{"key":"44516_CR66","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.matcom.2021.08.013","volume":"192","author":"FA Hashim","year":"2022","unstructured":"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\u2013110. https:\/\/doi.org\/10.1016\/j.matcom.2021.08.013 (2022).","journal-title":"Math. Comput. Simul."},{"key":"44516_CR67","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/j.advengsoft.2017.07.002","volume":"114","author":"S Mirjalili","year":"2017","unstructured":"Mirjalili, S. et al. Salp swarm algorithm: A bio-inspired optimizer for engineering design problems. Adv. Eng. Softw. 114, 163\u2013191. https:\/\/doi.org\/10.1016\/j.advengsoft.2017.07.002 (2017).","journal-title":"Adv. Eng. Softw."},{"key":"44516_CR68","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2022.108320","volume":"242","author":"FA Hashim","year":"2022","unstructured":"Hashim, F. A. & Hussien, A. G. Snake optimizer: A novel meta-heuristic optimization algorithm. Knowl. Based Syst. 242, 108320. https:\/\/doi.org\/10.1016\/j.knosys.2022.108320 (2022).","journal-title":"Knowl. Based Syst."},{"key":"44516_CR69","doi-asserted-by":"publisher","DOI":"10.1016\/j.compbiomed.2024.108064","volume":"172","author":"J Lian","year":"2024","unstructured":"Lian, J. et al. Parrot optimizer: Algorithm and applications to medical problems. Comput. Biol. Med. 172, 108064 (2024).","journal-title":"Comput. Biol. Med."},{"key":"44516_CR70","doi-asserted-by":"crossref","unstructured":"Rai, P. Heart rate. In Encyclopedia of Evolutionary Psychological Science 1\u20137 (Springer, 2020).","DOI":"10.1007\/978-3-319-16999-6_2995-1"},{"issue":"8","key":"44516_CR71","doi-asserted-by":"publisher","first-page":"716","DOI":"10.1093\/eurheartj\/ehab892","volume":"43","author":"A Timmis","year":"2022","unstructured":"Timmis, A. et al. European society of cardiology: cardiovascular disease statistics 2021. European heart journal 43(8), 716\u2013799 (2022).","journal-title":"European heart journal"},{"issue":"1","key":"44516_CR72","doi-asserted-by":"publisher","DOI":"10.3390\/ijerph20010199","volume":"20","author":"C Goncalves","year":"2022","unstructured":"Goncalves, C. et al. Influence of two exercise programs on heart rate variability, body temperature, central nervous system fatigue, and cortical arousal after a heart attack. Int. J. Environ. Res. Public Health 20(1), 199 (2022).","journal-title":"Int. J. Environ. Res. Public Health"},{"key":"44516_CR73","doi-asserted-by":"crossref","unstructured":"M.\u00a0Jahani, M.\u00a0K. Moridani & M.\u00a0Anisi, Mathematical model presenting to assess variations in heart rate of different age groups., Bratislava Medical Journal\/Bratislavsk\u00e9 Lek\u00e1rske Listy 124\u00a0(6).","DOI":"10.4149\/BLL_2023_070"},{"issue":"3","key":"44516_CR74","doi-asserted-by":"publisher","first-page":"594","DOI":"10.1007\/s10664-013-9249-9","volume":"18","author":"A Arcuri","year":"2013","unstructured":"Arcuri, A. & Fraser, G. Parameter tuning or default values? An empirical investigation in search-based software engineering. Empir. Softw. Eng. 18(3), 594\u2013623 (2013).","journal-title":"Empir. Softw. Eng."},{"issue":"2","key":"44516_CR75","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/s13042-017-0711-7","volume":"10","author":"AW Mohamed","year":"2019","unstructured":"Mohamed, A. W. & Mohamed, A. K. Adaptive guided differential evolution algorithm with novel mutation for numerical optimization. Int. J. Mach. Learn. Cybern. 10(2), 253\u2013277 (2019).","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"44516_CR76","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.advengsoft.2016.01.008","volume":"95","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili, S. & Lewis, A. The whale optimization algorithm. Adv. Eng. Softw. 95, 51\u201367 (2016b).","journal-title":"Adv. Eng. Softw."},{"key":"44516_CR77","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2021.115079","volume":"181","author":"I Ahmadianfar","year":"2021","unstructured":"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).","journal-title":"Expert Syst. Appl."},{"issue":"5","key":"44516_CR78","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/s10462-024-10729-y","volume":"57","author":"Y Fu","year":"2024","unstructured":"Fu, Y., Liu, D., Chen, J. & He, L. Secretary bird optimization algorithm: A new metaheuristic for solving global optimization problems. Artif. Intell. Rev. 57(5), 123 (2024).","journal-title":"Artif. Intell. Rev."},{"key":"44516_CR79","unstructured":"W.\u00a0Luo, X.\u00a0Lin, C.\u00a0Li, S.\u00a0Yang & Y.\u00a0Shi, Benchmark functions for cec 2022 competition on seeking multiple optima in dynamic environments, arXiv preprint arXiv:2201.00523."},{"key":"44516_CR80","unstructured":"G.\u00a0Ausiello, P.\u00a0Crescenzi, G.\u00a0Gambosi, V.\u00a0Kann, A.\u00a0Marchetti-Spaccamela & M.\u00a0Protasi, Complexity and approximation: Combinatorial optimization problems and their approximability properties, (Springer Science & Business Media, 2012)."},{"key":"44516_CR81","unstructured":"M.\u00a0R. Gary & D.\u00a0S. Johnson, Computers and intractability: A guide to the theory of np-completeness (1979)."},{"key":"44516_CR82","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2021.114689","volume":"174","author":"EH Houssein","year":"2021","unstructured":"Houssein, E. H., Mahdy, M. A., Blondin, M. J., Shebl, D. & Mohamed, W. M. Hybrid slime mould algorithm with adaptive guided differential evolution algorithm for combinatorial and global optimization problems. Expert Syst. Appl. 174, 114689 (2021).","journal-title":"Expert Syst. Appl."},{"key":"44516_CR83","unstructured":"A.\u00a0Scholl & R.\u00a0Klein, Bin packing, On line document at http:\/\/wwwwiwi.uni-jena.deEntscheidung\/binpp\/, last visited on October."},{"issue":"2","key":"44516_CR84","doi-asserted-by":"publisher","DOI":"10.5815\/ijieeb.2012.02.02","volume":"4","author":"A Layeb","year":"2012","unstructured":"Layeb, A. & Chenche, S. A novel GRASP algorithm for solving the bin packing problem. International Journal of Information Engineering and Electronic. Business 4(2), 8 (2012).","journal-title":"International Journal of Information Engineering and Electronic. Business"},{"key":"44516_CR85","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jocs.2017.03.004","volume":"20","author":"R Ligeiro","year":"2017","unstructured":"Ligeiro, R. Linked Markovian quantum tunnels: An approximation technique for solving the bin packing problem. J. Comput. Sci. 20, 1\u20137 (2017).","journal-title":"J. Comput. Sci."},{"issue":"4","key":"44516_CR86","first-page":"5368","volume":"5","author":"K Chandra","year":"2014","unstructured":"Chandra, K. & Singh, S. Firefly algorithm to solve two dimensional bin packing problem. Int. J. Comput. Sci. Inf. Technol. 5(4), 5368\u20135373 (2014).","journal-title":"Int. J. Comput. Sci. Inf. Technol."},{"key":"44516_CR87","doi-asserted-by":"crossref","unstructured":"Zendaoui, Z. & Layeb, A. Adaptive cuckoo search algorithm for the bin packing problem. In Modelling and Implementation of Complex Systems 107\u2013120 (Springer, 2016).","DOI":"10.1007\/978-3-319-33410-3_8"},{"key":"44516_CR88","doi-asserted-by":"publisher","DOI":"10.2307\/1907742","author":"TC Koopmans","year":"1957","unstructured":"Koopmans, T. C. & Beckmann, M. Assignment problems and the location of economic activities. Econometrica https:\/\/doi.org\/10.2307\/1907742 (1957).","journal-title":"Econometrica"},{"issue":"4","key":"44516_CR89","doi-asserted-by":"publisher","first-page":"586","DOI":"10.1287\/mnsc.9.4.586","volume":"9","author":"EL Lawler","year":"1963","unstructured":"Lawler, E. L. The quadratic assignment problem. Manag. Sci. 9(4), 586\u2013599 (1963).","journal-title":"Manag. Sci."},{"issue":"1","key":"44516_CR90","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/0377-2217(91)90197-4","volume":"55","author":"RE Burkard","year":"1991","unstructured":"Burkard, R. E., Karisch, S. & Rendl, F. Qaplib-a quadratic assignment problem library. Eur. J. Oper. Res. 55(1), 115\u2013119 (1991).","journal-title":"Eur. J. Oper. Res."},{"issue":"4\u20135","key":"44516_CR91","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1016\/S0167-8191(05)80147-4","volume":"17","author":"\u00c9 Taillard","year":"1991","unstructured":"Taillard, \u00c9. Robust taboo search for the quadratic assignment problem. Parallel Comput. 17(4\u20135), 443\u2013455 (1991).","journal-title":"Parallel Comput."},{"key":"44516_CR92","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2022.116552","volume":"195","author":"EH Houssein","year":"2022","unstructured":"Houssein, E. H., Celik, E., Mahdy, M. A. & Ghoniem, R. M. Self-adaptive equilibrium optimizer for solving global, combinatorial, engineering, and multi-objective problems. Expert Syst. Appl. 195, 116552 (2022).","journal-title":"Expert Syst. Appl."},{"key":"44516_CR93","doi-asserted-by":"crossref","unstructured":"D.\u00a0Maharana & P.\u00a0Kotecha, Optimization of job shop scheduling problem with grey wolf optimizer and jaya algorithm, in: Smart Innovations in Communication and Computational Sciences, 47\u201358 (Springer, 2019).","DOI":"10.1007\/978-981-10-8968-8_5"},{"issue":"2","key":"44516_CR94","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/S0166-3615(99)00046-9","volume":"41","author":"CAC Coello","year":"2000","unstructured":"Coello, C. A. C. Use of a self-adaptive penalty approach for engineering optimization problems. Comput. Ind. 41(2), 113\u2013127 (2000).","journal-title":"Comput. Ind."},{"key":"44516_CR95","unstructured":"L.\u00a0C. Cagnina, S.\u00a0C. Esquivel & C.\u00a0A.\u00a0C. Coello, Solving engineering optimization problems with the simple constrained particle swarm optimizer, Informatica 32\u00a0(3)."},{"issue":"2","key":"44516_CR96","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1115\/1.2919393","volume":"116","author":"B Kannan","year":"1994","unstructured":"Kannan, B. & Kramer, S. N. An augmented Lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. J. Mech. Des. 116(2), 405\u2013411 (1994).","journal-title":"J. Mech. Des."},{"key":"44516_CR97","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1016\/j.advengsoft.2017.05.014","volume":"114","author":"G Dhiman","year":"2017","unstructured":"Dhiman, G. & Kumar, V. Spotted hyena optimizer: A novel bio-inspired based metaheuristic technique for engineering applications. Adv. Eng. Softw. 114, 48\u201370 (2017).","journal-title":"Adv. Eng. Softw."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-44516-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-44516-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-44516-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T05:02:59Z","timestamp":1779426179000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-44516-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,22]]},"references-count":97,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["44516"],"URL":"https:\/\/doi.org\/10.1038\/s41598-026-44516-2","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,22]]},"assertion":[{"value":"15 January 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 March 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 May 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"15985"}}