{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T20:08:38Z","timestamp":1779912518792,"version":"3.53.1"},"reference-count":56,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T00:00:00Z","timestamp":1779840000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T00:00:00Z","timestamp":1779840000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2023YFB2703900"],"award-info":[{"award-number":["2023YFB2703900"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"DOI":"10.1007\/s11227-026-08586-3","type":"journal-article","created":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T20:01:16Z","timestamp":1779912076000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Crmpa-timesnet: hyperparameter optimization with a modified metaheuristic for time series forecasting"],"prefix":"10.1007","volume":"82","author":[{"given":"Li","family":"Zhao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chundong","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Lin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rui","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongjing","family":"Ma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chaoyang","family":"Guo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,27]]},"reference":[{"key":"8586_CR1","doi-asserted-by":"publisher","unstructured":"Mendis K, Wickramasinghe M, Marasinghe P (2024) Multivariate time series forecasting: a review. In: Proceedings of the 2024 2nd Asia Conference on Computer Vision, Image Processing and Pattern Recognition. Association for Computing Machinery, New York, NY, USA, pp 1\u20139. https:\/\/doi.org\/10.1145\/3663976.3664241","DOI":"10.1145\/3663976.3664241"},{"issue":"11","key":"8586_CR2","doi-asserted-by":"publisher","first-page":"598","DOI":"10.3390\/info14110598","volume":"14","author":"A Casolaro","year":"2023","unstructured":"Casolaro A, Capone V, Iannuzzo G et al (2023) Deep learning for time series forecasting: advances and open problems. Information 14(11):598. https:\/\/doi.org\/10.3390\/info14110598","journal-title":"Information"},{"key":"8586_CR3","unstructured":"Wu H, Hu T, Liu Y et\u00a0al (2023) TimesNet: temporal 2d-variation modeling for general time series analysis. In: Paper presented at the Eleventh International Conference on Learning Representations (ICLR 2023), Kigali, Rwanda, pp 1\u20135"},{"issue":"3","key":"8586_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3506695","volume":"31","author":"L Liao","year":"2022","unstructured":"Liao L, Li H, Shang W et al (2022) An empirical study of the impact of hyperparameter tuning and model optimization on the performance properties of deep neural networks. ACM Trans Softw Eng Methodol 31(3):1\u201340. https:\/\/doi.org\/10.1145\/3506695","journal-title":"ACM Trans Softw Eng Methodol"},{"key":"8586_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.uclim.2024.102233","volume":"59","author":"S Qian","year":"2025","unstructured":"Qian S, Peng T, He R et al (2025) A novel ensemble framework based on intelligent weight optimization and multi-model fusion for air quality index prediction. Urban Climate 59:102233. https:\/\/doi.org\/10.1016\/j.uclim.2024.102233","journal-title":"Urban Climate"},{"key":"8586_CR6","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/s10915-022-02083-4","volume":"94","author":"P Novello","year":"2023","unstructured":"Novello P, Po\u00ebtte G, Lugato D et al (2023) Goal-oriented sensitivity analysis of hyperparameters in deep learning. J Sci Comput 94:45. https:\/\/doi.org\/10.1007\/s10915-022-02083-4","journal-title":"J Sci Comput"},{"issue":"11","key":"8586_CR7","doi-asserted-by":"publisher","first-page":"7129","DOI":"10.1109\/TKDE.2024.3400008","volume":"36","author":"L Han","year":"2024","unstructured":"Han L, Ye HJ, Zhan DC (2024) The capacity and robustness trade-off: revisiting the channel independent strategy for multivariate time series forecasting. IEEE Trans Knowl Data Eng 36(11):7129\u20137142. https:\/\/doi.org\/10.1109\/TKDE.2024.3400008","journal-title":"IEEE Trans Knowl Data Eng"},{"key":"8586_CR8","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/j.neucom.2019.05.023","volume":"360","author":"K Wang","year":"2019","unstructured":"Wang K, Li K, Zhou L et al (2019) Multiple convolutional neural networks for multivariate time series prediction. Neurocomputing 360:107\u2013119. https:\/\/doi.org\/10.1016\/j.neucom.2019.05.023","journal-title":"Neurocomputing"},{"key":"8586_CR9","doi-asserted-by":"publisher","first-page":"1421","DOI":"10.1007\/s10994-019-05815-0","volume":"108","author":"SY Shih","year":"2019","unstructured":"Shih SY, Sun FK, Hy L (2019) Temporal pattern attention for multivariate time series forecasting. Mach Learn 108:1421\u20131441. https:\/\/doi.org\/10.1007\/s10994-019-05815-0","journal-title":"Mach Learn"},{"issue":"10","key":"8586_CR10","doi-asserted-by":"publisher","first-page":"6516","DOI":"10.1109\/TII.2022.3161990","volume":"18","author":"J Geng","year":"2022","unstructured":"Geng J, Yang C, Li Y et al (2022) Mpa-rnn: a novel attention-based recurrent neural networks for total nitrogen prediction. IEEE Trans Ind Inf 18(10):6516\u20136525. https:\/\/doi.org\/10.1109\/TII.2022.3161990","journal-title":"IEEE Trans Ind Inf"},{"key":"8586_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2023.127865","volume":"278","author":"YM Zhang","year":"2023","unstructured":"Zhang YM, Wang H (2023) Multi-head attention-based probabilistic cnn-bilstm for day-ahead wind speed forecasting. Energy 278:127865. https:\/\/doi.org\/10.1016\/j.energy.2023.127865","journal-title":"Energy"},{"key":"8586_CR12","doi-asserted-by":"publisher","first-page":"6775","DOI":"10.1007\/s00500-023-09531-9","volume":"28","author":"H Balti","year":"2024","unstructured":"Balti H, Ben Abbes A, Farah IR (2024) A bi-gru-based encoder\u2013decoder framework for multivariate time series forecasting. Soft Comput 28:6775\u20136786. https:\/\/doi.org\/10.1007\/s00500-023-09531-9","journal-title":"Soft Comput"},{"key":"8586_CR13","doi-asserted-by":"publisher","unstructured":"Zhou H, Zhang S, Peng J et\u00a0al (2021) Informer: beyond efficient transformer for long sequence time-series forecasting. In: Proceedings of the AAAI Conference on Artificial Intelligence, pp 11106\u201311115. https:\/\/doi.org\/10.1609\/aaai.v35i12.17325","DOI":"10.1609\/aaai.v35i12.17325"},{"key":"8586_CR14","doi-asserted-by":"publisher","first-page":"28401","DOI":"10.1007\/s10489-023-04980-z","volume":"53","author":"S Ma","year":"2023","unstructured":"Ma S, Zhang T, Zhao YB et al (2023) Tcln: a transformer-based conv-lstm network for multivariate time series forecasting. Appl Intell 53:28401\u201328417. https:\/\/doi.org\/10.1007\/s10489-023-04980-z","journal-title":"Appl Intell"},{"key":"8586_CR15","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/s40747-023-01099-z","volume":"10","author":"H Yang","year":"2024","unstructured":"Yang H, Li Z, Qi Y (2024) Predicting traffic propagation flow in urban road network with multi-graph convolutional network. Complex Intell Syst 10:23\u201335. https:\/\/doi.org\/10.1007\/s40747-023-01099-z","journal-title":"Complex Intell Syst"},{"key":"8586_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2024.120316","volume":"664","author":"H Lin","year":"2024","unstructured":"Lin H, Wang C (2024) Digwo-n-beats: an evolutionary time series prediction method for situation prediction. Inf Sci 664:120316. https:\/\/doi.org\/10.1016\/j.ins.2024.120316","journal-title":"Inf Sci"},{"key":"8586_CR17","doi-asserted-by":"publisher","first-page":"78423","DOI":"10.1109\/ACCESS.2022.3193643","volume":"10","author":"A Pranolo","year":"2022","unstructured":"Pranolo A, Mao Y, Wibawa AP et al (2022) Robust lstm with tuned-pso and bifold-attention mechanism for analyzing multivariate time-series. IEEE Access 10:78423\u201378434. https:\/\/doi.org\/10.1109\/ACCESS.2022.3193643","journal-title":"IEEE Access"},{"key":"8586_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.apenergy.2023.121638","volume":"349","author":"M Abou Houran","year":"2023","unstructured":"Abou Houran M, Salman Bukhari SM, Zafar MH et al (2023) Coa-cnn-lstm: coati optimization algorithm-based hybrid deep learning model for pv\/wind power forecasting in smart grid applications. Appl Energy 349:121638. https:\/\/doi.org\/10.1016\/j.apenergy.2023.121638","journal-title":"Appl Energy"},{"issue":"6","key":"8586_CR19","doi-asserted-by":"publisher","first-page":"908","DOI":"10.1049\/rpg2.12934","volume":"18","author":"R Li","year":"2024","unstructured":"Li R, Wang M, Li X et al (2024) Short-term photovoltaic prediction based on cnn-gru optimized by improved similar day extraction, decomposition noise reduction and ssa optimization. IET Renew Power Gener 18(6):908\u2013928. https:\/\/doi.org\/10.1049\/rpg2.12934","journal-title":"IET Renew Power Gener"},{"key":"8586_CR20","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/2814\/1\/012019","volume":"2814","author":"X Feng","year":"2024","unstructured":"Feng X, Fu J, Zhang Z et al (2024) A study on long-term industrial electricity consumption and carbon emission forecasting methods based on timesnet models. J Phys: Conf Ser 2814:012019. https:\/\/doi.org\/10.1088\/1742-6596\/2814\/1\/012019","journal-title":"J Phys: Conf Ser"},{"key":"8586_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.renene.2023.119706","volume":"220","author":"H Zhao","year":"2024","unstructured":"Zhao H, Huang X, Xiao Z et al (2024) Week-ahead hourly solar irradiation forecasting method based on iceemdan and timesnet networks. Renew Energy 220:119706. https:\/\/doi.org\/10.1016\/j.renene.2023.119706","journal-title":"Renew Energy"},{"key":"8586_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2024.124851","volume":"255","author":"HG Souto","year":"2024","unstructured":"Souto HG (2024) Charting new avenues in financial forecasting with timesnet: the impact of intraperiod and interperiod variations on realized volatility prediction. Expert Syst Appl 255:124851. https:\/\/doi.org\/10.1016\/j.eswa.2024.124851","journal-title":"Expert Syst Appl"},{"issue":"3","key":"8586_CR23","doi-asserted-by":"publisher","first-page":"1659","DOI":"10.1109\/TSTE.2025.3525498","volume":"16","author":"M Yang","year":"2025","unstructured":"Yang M, Huang Y, Wang Z et al (2025) A framework of day-ahead wind supply power forecasting by risk scenario perception. IEEE Trans Sustain Energy 16(3):1659\u20131672. https:\/\/doi.org\/10.1109\/TSTE.2025.3525498","journal-title":"IEEE Trans Sustain Energy"},{"issue":"4","key":"8586_CR24","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1016\/j.jnlssr.2023.07.001","volume":"4","author":"T Shi","year":"2023","unstructured":"Shi T, Fu J, Hu X (2023) Tse-tran: prediction method of telecommunication-network fraud crime based on time series representation and transformer. J Saf Sci Resil 4(4):340\u2013347. https:\/\/doi.org\/10.1016\/j.jnlssr.2023.07.001","journal-title":"J Saf Sci Resil"},{"key":"8586_CR25","doi-asserted-by":"publisher","DOI":"10.1016\/j.apenergy.2025.125645","volume":"388","author":"S Yu","year":"2025","unstructured":"Yu S, He B, Fang L (2025) Multi-step short-term forecasting of photovoltaic power utilizing timesnet with enhanced feature extraction and a novel loss function. Appl Energy 388:125645. https:\/\/doi.org\/10.1016\/j.apenergy.2025.125645","journal-title":"Appl Energy"},{"key":"8586_CR26","doi-asserted-by":"publisher","unstructured":"Huang Y, Zhou Z, Wang Z et\u00a0al (2023) Timesnet-pm2.5: interpretable timesnet for disentangling intraperiod and interperiod variations in pm2.5 prediction. Atmosphere 14(11):1604. https:\/\/doi.org\/10.3390\/atmos14111604","DOI":"10.3390\/atmos14111604"},{"key":"8586_CR27","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1016\/j.aej.2025.09.018","volume":"130","author":"X Cai","year":"2025","unstructured":"Cai X (2025) An attention-enhanced timesnet time series model for predicting the commodity price. Alex Eng J 130:447\u2013458. https:\/\/doi.org\/10.1016\/j.aej.2025.09.018","journal-title":"Alex Eng J"},{"key":"8586_CR28","doi-asserted-by":"publisher","first-page":"642","DOI":"10.1016\/j.aej.2025.05.066","volume":"128","author":"Y Wang","year":"2025","unstructured":"Wang Y (2025) Evaluating economic policy uncertainty forecasts via timesnet time series modeling of iot and digital circular economy historical indicators. Alex Eng J 128:642\u2013651. https:\/\/doi.org\/10.1016\/j.aej.2025.05.066","journal-title":"Alex Eng J"},{"key":"8586_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.apenergy.2024.122669","volume":"359","author":"C Zhang","year":"2024","unstructured":"Zhang C, Zhang Y, Li Z et al (2024) Enhancing state of charge and state of energy estimation in lithium-ion batteries based on a timesnet model with gaussian data augmentation and error correction. Appl Energy 359:122669. https:\/\/doi.org\/10.1016\/j.apenergy.2024.122669","journal-title":"Appl Energy"},{"issue":"6","key":"8586_CR30","doi-asserted-by":"publisher","first-page":"775","DOI":"10.1177\/01436244241274924","volume":"45","author":"Q Tan","year":"2024","unstructured":"Tan Q, Xue G, Xie W (2024) Heat load forecasting model considering two dimensional changes of time series. Build Serv Eng Res Technol 45(6):775\u2013794. https:\/\/doi.org\/10.1177\/01436244241274924","journal-title":"Build Serv Eng Res Technol"},{"key":"8586_CR31","doi-asserted-by":"publisher","DOI":"10.1016\/j.enconman.2023.118045","volume":"301","author":"C Zhang","year":"2024","unstructured":"Zhang C, Wang Y, Fu Y et al (2024) A novel dwtimesnet-based short-term multi-step wind power forecasting model using feature selection and auto-tuning methods. Energy Convers Manage 301:118045. https:\/\/doi.org\/10.1016\/j.enconman.2023.118045","journal-title":"Energy Convers Manage"},{"key":"8586_CR32","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 et al (2020) Marine predators algorithm: a nature-inspired metaheuristic. Expert Syst Appl 152:113377. https:\/\/doi.org\/10.1016\/j.eswa.2020.113377","journal-title":"Expert Syst Appl"},{"key":"8586_CR33","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.matcom.2024.01.012","volume":"220","author":"JS Pan","year":"2024","unstructured":"Pan JS, Zhang Z, Chu SC et al (2024) A parallel compact marine predators algorithm applied in time series prediction of backpropagation neural network (bnn) and engineering optimization. Math Comput Simul 220:65\u201388. https:\/\/doi.org\/10.1016\/j.matcom.2024.01.012","journal-title":"Math Comput Simul"},{"key":"8586_CR34","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/s10922-022-09650-y","volume":"30","author":"N Firouz","year":"2022","unstructured":"Firouz N, Masdari M, Sangar AB et al (2022) A hybrid multi-objective algorithm for imbalanced controller placement in software-defined networks. J Netw Syst Manage 30:51. https:\/\/doi.org\/10.1007\/s10922-022-09650-y","journal-title":"J Netw Syst Manage"},{"key":"8586_CR35","doi-asserted-by":"publisher","first-page":"3133","DOI":"10.1007\/s11831-023-09897-x","volume":"30","author":"R Rai","year":"2023","unstructured":"Rai R, Dhal KG, Das A et al (2023) Correction to: an inclusive survey on marine predators algorithm: variants and applications. Arch Comput Methods Eng 30:3133\u20133172. https:\/\/doi.org\/10.1007\/s11831-023-09897-x","journal-title":"Arch Comput Methods Eng"},{"key":"8586_CR36","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2022.109615","volume":"254","author":"G Hu","year":"2022","unstructured":"Hu G, Zhu X, Wang X et al (2022) Multi-strategy boosted marine predators algorithm for optimizing approximate developable surface. Knowl Based Syst 254:109615. https:\/\/doi.org\/10.1016\/j.knosys.2022.109615","journal-title":"Knowl Based Syst"},{"key":"8586_CR37","doi-asserted-by":"publisher","first-page":"3269","DOI":"10.1007\/s00366-021-01319-5","volume":"38","author":"Q Fan","year":"2022","unstructured":"Fan Q, Huang H, Chen Q et al (2022) A modified self-adaptive marine predators algorithm: framework and engineering applications. Eng Comput 38:3269\u20133294. https:\/\/doi.org\/10.1007\/s00366-021-01319-5","journal-title":"Eng Comput"},{"key":"8586_CR38","doi-asserted-by":"publisher","DOI":"10.1016\/j.enconman.2020.113692","volume":"228","author":"D Yousri","year":"2021","unstructured":"Yousri D, Hasanien HM, Fathy A (2021) Parameters identification of solid oxide fuel cell for static and dynamic simulation using comprehensive learning dynamic multi-swarm marine predators algorithm. Energy Convers Manage 228:113692. https:\/\/doi.org\/10.1016\/j.enconman.2020.113692","journal-title":"Energy Convers Manage"},{"issue":"2","key":"8586_CR39","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1088\/0253-6102\/38\/2\/168","volume":"38","author":"Y Li-Jiang","year":"2002","unstructured":"Li-Jiang Y, Tian-Lun C (2002) Application of chaos in genetic algorithms. Commun Theor Phys 38(2):168. https:\/\/doi.org\/10.1088\/0253-6102\/38\/2\/168","journal-title":"Commun Theor Phys"},{"issue":"5","key":"8586_CR40","doi-asserted-by":"publisher","first-page":"2095","DOI":"10.1109\/TSC.2024.3384094","volume":"17","author":"S Nazemi","year":"2024","unstructured":"Nazemi S, Khorsand R (2024) C-khcs: multi-objective workflow scheduling using chaotic krill herd optimization and improved cuckoo search in fog computing. IEEE Trans Serv Comput 17(5):2095\u20132108. https:\/\/doi.org\/10.1109\/TSC.2024.3384094","journal-title":"IEEE Trans Serv Comput"},{"key":"8586_CR41","doi-asserted-by":"publisher","DOI":"10.1016\/j.jobe.2023.107635","volume":"78","author":"T Peng","year":"2023","unstructured":"Peng T, Fu Y, Wang Y et al (2023) An intelligent hybrid approach for photovoltaic power forecasting using enhanced chaos game optimization algorithm and locality sensitive hashing based informer model. J Build Eng 78:107635. https:\/\/doi.org\/10.1016\/j.jobe.2023.107635","journal-title":"J Build Eng"},{"key":"8586_CR42","doi-asserted-by":"publisher","DOI":"10.1016\/j.compeleceng.2022.108219","volume":"102","author":"X Xiang","year":"2022","unstructured":"Xiang X, Yan X, Gao C et al (2022) A circle chaos random search strategy particle swarm optimization with its application. Comput Electr Eng 102:108219. https:\/\/doi.org\/10.1016\/j.compeleceng.2022.108219","journal-title":"Comput Electr Eng"},{"key":"8586_CR43","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2022.103212","volume":"173","author":"S Xian","year":"2022","unstructured":"Xian S, Chen K, Cheng Y (2022) Improved seagull optimization algorithm of partition and xgboost of prediction for fuzzy time series forecasting of covid-19 daily confirmed. Adv Eng Softw 173:103212. https:\/\/doi.org\/10.1016\/j.advengsoft.2022.103212","journal-title":"Adv Eng Softw"},{"key":"8586_CR44","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2023.101457","volume":"84","author":"J Li","year":"2024","unstructured":"Li J, Gao L, Li X (2024) Multi-operator opposition-based learning with the neighborhood structure for numerical optimization problems and its applications. Swarm Evol Comput 84:101457. https:\/\/doi.org\/10.1016\/j.swevo.2023.101457","journal-title":"Swarm Evol Comput"},{"key":"8586_CR45","doi-asserted-by":"publisher","unstructured":"Shi Y, RC E (1998) A modified particle swarm optimizer. In: Proceedings of the IEEE Conference on Evolutionary Computation, ICEC, pp 69\u201373. https:\/\/doi.org\/10.1109\/ICEC.1998.699146","DOI":"10.1109\/ICEC.1998.699146"},{"issue":"4","key":"8586_CR46","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1023\/A:1008202821328","volume":"11","author":"R Storn","year":"1997","unstructured":"Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341\u2013359. https:\/\/doi.org\/10.1023\/A:1008202821328","journal-title":"J Global Optim"},{"issue":"3","key":"8586_CR47","doi-asserted-by":"publisher","first-page":"1155","DOI":"10.1016\/j.ejor.2006.06.046","volume":"185","author":"K Socha","year":"2008","unstructured":"Socha K, Dorigo M (2008) Ant colony optimization for continuous domains. Eur J Oper Res 185(3):1155\u20131173. https:\/\/doi.org\/10.1016\/j.ejor.2006.06.046","journal-title":"Eur J Oper Res"},{"issue":"2","key":"8586_CR48","first-page":"281","volume":"13","author":"J Bergstra","year":"2012","unstructured":"Bergstra J, Bengio Y (2012) Random search for hyper-parameter optimization. J Mach Learn Res 13(2):281\u2013305","journal-title":"J Mach Learn Res"},{"key":"8586_CR49","unstructured":"Bergstra J, Bardenet R, Bengio Y et\u00a0al (2011) Algorithms for hyper-parameter optimization. In: Advances in Neural Information Processing Systems, vol\u00a024. Curran Associates, Inc., pp 2546\u20132554. https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2011\/file\/86e8f7ab32cfd12577bc2619bc635690-Paper.pdf"},{"issue":"185","key":"8586_CR50","first-page":"1","volume":"18","author":"L Li","year":"2018","unstructured":"Li L, Jamieson K, DeSalvo G et al (2018) Hyperband: a novel bandit-based approach to hyperparameter optimization. J Mach Learn Res 18(185):1\u201352","journal-title":"J Mach Learn Res"},{"key":"8586_CR51","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysarc.2023.102871","volume":"139","author":"N Van Thieu","year":"2023","unstructured":"Van Thieu N, Mirjalili S (2023) Mealpy: an open-source library for latest meta-heuristic algorithms in python. J Syst Archit 139:102871. https:\/\/doi.org\/10.1016\/j.sysarc.2023.102871","journal-title":"J Syst Archit"},{"issue":"11","key":"8586_CR52","doi-asserted-by":"publisher","first-page":"7665","DOI":"10.1007\/s00521-018-3592-0","volume":"31","author":"K Hussain","year":"2019","unstructured":"Hussain K, Salleh MNM, Cheng S et al (2019) On the exploration and exploitation in popular swarm-based metaheuristic algorithms. Neural Comput Appl 31(11):7665\u20137683. https:\/\/doi.org\/10.1007\/s00521-018-3592-0","journal-title":"Neural Comput Appl"},{"key":"8586_CR53","unstructured":"Babichev SA, Ries J, Lvovsky AI (2022) Less is more: fast multivariate time series forecasting with light sampling-oriented mlp structures. Preprint at https:\/\/arxiv.org\/abs\/2207.01186"},{"key":"8586_CR54","doi-asserted-by":"publisher","unstructured":"Zeng A, Chen M, Zhang L et\u00a0al (2023) Are transformers effective for time series forecasting? In: Proceedings of the AAAI conference on artificial intelligence, pp 11121\u201311128. https:\/\/doi.org\/10.1609\/aaai.v37i9.26317","DOI":"10.1609\/aaai.v37i9.26317"},{"issue":"10","key":"8586_CR55","doi-asserted-by":"publisher","first-page":"10748","DOI":"10.1109\/TKDE.2023.3268199","volume":"35","author":"L Chen","year":"2023","unstructured":"Chen L, Chen D, Shang Z et al (2023) Multi-scale adaptive graph neural network for multivariate time series forecasting. IEEE Trans Knowl Data Eng 35(10):10748\u201310761. https:\/\/doi.org\/10.1109\/TKDE.2023.3268199","journal-title":"IEEE Trans Knowl Data Eng"},{"key":"8586_CR56","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2024.120712","volume":"675","author":"H Gao","year":"2024","unstructured":"Gao H, Ren Q, Li J (2024) Distillation enhanced time series forecasting network with momentum contrastive learning. Inf Sci 675:120712. https:\/\/doi.org\/10.1016\/j.ins.2024.120712","journal-title":"Inf Sci"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-026-08586-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-026-08586-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-026-08586-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T20:01:19Z","timestamp":1779912079000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-026-08586-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,27]]},"references-count":56,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["8586"],"URL":"https:\/\/doi.org\/10.1007\/s11227-026-08586-3","relation":{},"ISSN":["1573-0484"],"issn-type":[{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,27]]},"assertion":[{"value":"9 December 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 May 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 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 have no conflict of interest to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"458"}}