{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T16:32:19Z","timestamp":1778776339881,"version":"3.51.4"},"reference-count":52,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T00:00:00Z","timestamp":1778716800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T00:00:00Z","timestamp":1778716800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"DOI":"10.1007\/s11227-026-08551-0","type":"journal-article","created":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T16:03:36Z","timestamp":1778774616000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Short-term solar irradiance forecasting based on AGCRIME-optimized VMD decomposition and BiLSTM-SA"],"prefix":"10.1007","volume":"82","author":[{"given":"Ziqiong","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengjun","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yun","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinru","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,5,14]]},"reference":[{"key":"8551_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.scitotenv.2019.134602","volume":"718","author":"A Dhar","year":"2020","unstructured":"Dhar A, Naeth MA, Jennings PD, El-Din MG (2020) Perspectives on environmental impacts and a land reclamation strategy for solar and wind energy systems. Sci Total Environ 718:134602. https:\/\/doi.org\/10.1016\/j.scitotenv.2019.134602","journal-title":"Sci Total Environ"},{"key":"8551_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apenergy.2020.115786","volume":"279","author":"Y Yang","year":"2020","unstructured":"Yang Y, Campana PE, Stridh B, Yan J (2020) Potential analysis of roof-mounted solar photovoltaics in Sweden. Appl Energy 279:115786. https:\/\/doi.org\/10.1016\/j.apenergy.2020.115786","journal-title":"Appl Energy"},{"key":"8551_CR3","doi-asserted-by":"publisher","first-page":"8560","DOI":"10.1007\/s11227-021-04244-y","volume":"78","author":"KN Reddy","year":"2022","unstructured":"Reddy KN, Thillaikarasi M, Kumar BS et al (2022) A novel elephant herd optimization model with a deep extreme learning machine for solar radiation prediction using weather forecasts. J Supercomput 78:8560\u20138576. https:\/\/doi.org\/10.1007\/s11227-021-04244-y","journal-title":"J Supercomput"},{"key":"8551_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/s11227-025-07360-1","volume":"81","author":"G Liu","year":"2025","unstructured":"Liu G (2025) DARVFL-LSTM: a time series prediction model integrating dynamic regularization and attention mechanism. J Supercomput 81:905. https:\/\/doi.org\/10.1007\/s11227-025-07360-1","journal-title":"J Supercomput"},{"key":"8551_CR5","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1016\/j.scs.2018.05.027","volume":"41","author":"S Twaha","year":"2018","unstructured":"Twaha S, Ramli MAM (2018) A review of optimization approaches for hybrid distributed energy generation systems: off-grid and grid-connected systems. Sustain Cities Soc 41:320\u2013331. https:\/\/doi.org\/10.1016\/j.scs.2018.05.027","journal-title":"Sustain Cities Soc"},{"key":"8551_CR6","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2023.106986","volume":"126","author":"Y Gao","year":"2023","unstructured":"Gao Y, Li P, Yang H, Wang J (2023) A solar irradiance intelligent forecasting framework based on feature selection and multivariable fuzzy time series. Eng Appl Artif Intell 126:106986. https:\/\/doi.org\/10.1016\/j.engappai.2023.106986","journal-title":"Eng Appl Artif Intell"},{"key":"8551_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/j.apenergy.2024.124844","volume":"378","author":"Y Gao","year":"2025","unstructured":"Gao Y, Hu Z, Chen W-A, Liu M, Ruan Y (2025) A revolutionary neural network architecture with interpretabil-ity and flexibility based on Kolmogorov-Arnold for solar irradiance and temperature forecasting. Appl Energy 378:124844. https:\/\/doi.org\/10.1016\/j.apenergy.2024.124844","journal-title":"Appl Energy"},{"key":"8551_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.enconman.2020.112642","volume":"209","author":"W Yao","year":"2020","unstructured":"Yao W, Xu C, Zhao J, Wang X, Wang Y, Li X, Cao J (2020) The modified ASHRAE model based on the mechanism of multi-parameter coupling. Energy Convers Manag 209:112642. https:\/\/doi.org\/10.1016\/j.enconman.2020.112642","journal-title":"Energy Convers Manag"},{"key":"8551_CR9","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1016\/j.renene.2018.02.102","volume":"123","author":"FH Gandoman","year":"2018","unstructured":"Gandoman FH, Abdel Aleem SHE, Omar N, Ahmadi A, Alenezi FQ (2018) Short-term solar power fore-casting considering cloud coverage and ambient temperature variation effects. Renew Energy 123:793\u2013805. https:\/\/doi.org\/10.1016\/j.renene.2018.02.102","journal-title":"Renew Energy"},{"key":"8551_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.renene.2024.121639","volume":"237","author":"J Huang","year":"2024","unstructured":"Huang J, Yuan C, Boland J, Guo S, Liu W (2024) One-step ahead short-term hourly global solar radiation forecasting with a dynamical system based on classification of days. Renew Energy 237:121639. https:\/\/doi.org\/10.1016\/j.renene.2024.121639","journal-title":"Renew Energy"},{"key":"8551_CR11","doi-asserted-by":"publisher","first-page":"170957","DOI":"10.1016\/j.ijleo.2023.170957","volume":"286","author":"PG Neeraj","year":"2023","unstructured":"Neeraj PG, Tomar A (2023) Multi-model approach applied to meteorological data for solar irradiance forecasting using data-driven approaches. Optik 286:170957\u2013171016. https:\/\/doi.org\/10.1016\/j.ijleo.2023.170957","journal-title":"Optik"},{"key":"8551_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.apenergy.2024.124409","volume":"377","author":"Y Li","year":"2025","unstructured":"Li Y, Zhou W, Wang Y, Miao S, Yao W, Gao W (2025) Interpretable deep learning framework for hourly solar radiation forecasting based on decomposing multi-scale variations. Appl Energy 377:124409. https:\/\/doi.org\/10.1016\/j.apenergy.2024.124409","journal-title":"Appl Energy"},{"key":"8551_CR13","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.solener.2016.03.064","volume":"133","author":"M David","year":"2016","unstructured":"David M, Ramahatana F, Trombe PJ, Lauret P (2016) Probabilistic forecasting of the solar irradiance with recursive ARMA and GARCH models. Sol Energy 133:55\u201372. https:\/\/doi.org\/10.1016\/j.solener.2016.03.064. (ISSN 0038-092X)","journal-title":"Sol Energy"},{"key":"8551_CR14","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1016\/j.enconman.2014.12.072","volume":"92","author":"H Sun","year":"2015","unstructured":"Sun H, Yan D, Zhao N, Zhou J (2015) Empirical investigation on modeling solar irradiance series with ARMA-GARCH models. Energy Convers Manag 92:385\u2013395. https:\/\/doi.org\/10.1016\/j.enconman.2014.12.072. (ISSN 0196-8904)","journal-title":"Energy Convers Manag"},{"key":"8551_CR15","doi-asserted-by":"publisher","DOI":"10.1016\/j.rsase.2020.100427","volume":"20","author":"A Shadab","year":"2020","unstructured":"Shadab A, Ahmad S, Said S (2020) Spatial forecasting of solar irradiance using ARIMA model. Remote Sens Appl Soc Environ 20:100427. https:\/\/doi.org\/10.1016\/j.rsase.2020.100427. (ISSN 2352-9385)","journal-title":"Remote Sens Appl Soc Environ"},{"key":"8551_CR16","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1016\/j.solener.2013.10.002","volume":"98","author":"M Bouzerdoum","year":"2013","unstructured":"Bouzerdoum M, Mellit A, Massi Pavan A (2013) A hybrid model (SARIMA-SVM) for short-term power forecasting of a small-scale grid-connected photovoltaic plant. Sol Energy 98:226\u2013235. https:\/\/doi.org\/10.1016\/j.solener.2013.10.002. (ISSN 0038-092X)","journal-title":"Sol Energy"},{"key":"8551_CR17","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1016\/j.energy.2016.04.115","volume":"109","author":"L Ferbar Tratar","year":"2016","unstructured":"Ferbar Tratar L, Strm\u010dnik E (2016) The comparison of Holt-Winters method and multiple regression method: a case study. Energy 109:266\u2013276. https:\/\/doi.org\/10.1016\/j.energy.2016.04.115. (ISSN 0360-5442)","journal-title":"Energy"},{"key":"8551_CR18","doi-asserted-by":"publisher","first-page":"880","DOI":"10.1016\/j.enconman.2015.08.045","volume":"105","author":"H Sun","year":"2015","unstructured":"Sun H, Zhao N, Zeng X, Yan D (2015) Study of solar irradiance prediction and modeling of relationships between solar irradiance and meteorological variables. Energy Convers Manag 105:880\u2013890. https:\/\/doi.org\/10.1016\/j.enconman.2015.08.045. (ISSN 0196-8904)","journal-title":"Energy Convers Manag"},{"key":"8551_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.rser.2022.112473","volume":"162","author":"Y Tang","year":"2022","unstructured":"Tang Y, Yang K, Zhang S, Zhang Z (2022) Photo-voltaic power forecasting: a hybrid deep learning model incorporating transfer learning strategy. Renew Sustain Energy Rev 162:112473. https:\/\/doi.org\/10.1016\/j.rser.2022.112473. (ISSN 1364-0321)","journal-title":"Renew Sustain Energy Rev"},{"key":"8551_CR20","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.121273","volume":"236","author":"SS Prasad","year":"2024","unstructured":"Prasad SS, Deo RC, Downs NJ, Casillas-P\u00e9rez D, Salcedo-Sanz S, Parisi AV (2024) Very short-term solar ultraviolet-A radiation forecasting system with cloud cover images and a Bayesian optimized interpretable artificial intelligence model. Expert Syst Appl 236:121273. https:\/\/doi.org\/10.1016\/j.eswa.2023.121273. (ISSN 0957-4174)","journal-title":"Expert Syst Appl"},{"key":"8551_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2024.131071","volume":"295","author":"X Wang","year":"2024","unstructured":"Wang X, Ma W (2024) A hybrid deep learning model with an optimal strategy based on improved VMD and transformer for short-term photovoltaic power forecasting. Energy 295:131071. https:\/\/doi.org\/10.1016\/j.energy.2024.131071. (ISSN 0360-5442)","journal-title":"Energy"},{"key":"8551_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclepro.2022.135680","volume":"385","author":"M Guermoui","year":"2023","unstructured":"Guermoui M, Gairaa K, Ferkous K, Santos DSdO, Arrif T, Belaid A (2023) Potential assessment of the TVF-EMD algorithm in forecasting hourly global solar irradiance: review and case studies. J Clean Prod 385:135680. https:\/\/doi.org\/10.1016\/j.jclepro.2022.135680. (ISSN 0959-6526)","journal-title":"J Clean Prod"},{"key":"8551_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2024.133309","volume":"311","author":"X Dong","year":"2024","unstructured":"Dong X, Guo W, Zhou C, Luo Y, Tian Z, Zhang L, Wu X, Liu B (2024) Hybrid model for robust and accurate forecasting building electricity demand combining physical and data-driven methods. Energy 311:133309. https:\/\/doi.org\/10.1016\/j.energy.2024.133309. (ISSN 0360-5442)","journal-title":"Energy"},{"key":"8551_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/j.renene.2024.121732","volume":"237","author":"F Yuan","year":"2024","unstructured":"Yuan F, Chen Z, Liang Y (2024) Precise solar irradiance forecasting for sustainable energy integration: a hybrid model for day-ahead power and hydrogen production. Renew Energy 237:121732. https:\/\/doi.org\/10.1016\/j.renene.2024.121732. (ISSN 0960-1481)","journal-title":"Renew Energy"},{"key":"8551_CR25","doi-asserted-by":"publisher","DOI":"10.1016\/j.rineng.2025.104267","volume":"25","author":"S Pourebrahim","year":"2025","unstructured":"Pourebrahim S, Seifi A, Ehteram M, Hadipour M, Chen JE (2025) The CEEMDAN-EWT-CNN-GRU-SVM model: a robust framework for decomposing non-stationary time series, extracting data features, and predicting solar irradiance. Results Eng 25:104267. https:\/\/doi.org\/10.1016\/j.rineng.2025.104267. (ISSN 2590-1230)","journal-title":"Results Eng"},{"key":"8551_CR26","doi-asserted-by":"publisher","first-page":"1665","DOI":"10.1016\/j.renene.2020.09.141","volume":"162","author":"B Gao","year":"2020","unstructured":"Gao B, Huang X, Shi J, Tai Y, Zhang J (2020) Hourly forecasting of solar irradiance based on CEEMDAN and multi-strategy CNN-LSTM neural networks. Renew Energy 162:1665\u20131683. https:\/\/doi.org\/10.1016\/j.renene.2020.09.141. (ISSN 0960-1481)","journal-title":"Renew Energy"},{"key":"8551_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2025.134847","volume":"318","author":"D Zhou","year":"2025","unstructured":"Zhou D, Liu Y, Wang X, Wang F, Jia Y (2025) Combined ultra-short-term photovoltaic power prediction based on CEEMDAN decomposition and RIME optimized AM-TCN-BiLSTM. Energy 318:134847. https:\/\/doi.org\/10.1016\/j.energy.2025.134847. (ISSN 0360-5442)","journal-title":"Energy"},{"key":"8551_CR28","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2021.119887","volume":"221","author":"T Peng","year":"2021","unstructured":"Peng T, Zhang C, Zhou J, Nazir MS (2021) An integrated framework of Bi-directional Long-Short Term Memory (BiLSTM) based on sine cosine algorithm for hourly solar irradiance forecasting. Energy 221:119887. https:\/\/doi.org\/10.1016\/j.energy.2021.119887. (ISSN 0360-5442)","journal-title":"Energy"},{"key":"8551_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.compeleceng.2023.108691","volume":"108","author":"M Sivakumar","year":"2023","unstructured":"Sivakumar M, S JP, George ST, Subathra MSP, Leebanon R, Kumar NM (2023) Nine novel ensemble models for solar irradiance forecasting in Indian cities based on VMD and DWT integration with the machine and deep learning algorithms. Comput Electr Eng 108:108691. https:\/\/doi.org\/10.1016\/j.compeleceng.2023.108691. (ISSN 0045-7906)","journal-title":"Comput Electr Eng"},{"key":"8551_CR30","doi-asserted-by":"publisher","DOI":"10.1016\/j.enconman.2023.116804","volume":"280","author":"J Liu","year":"2023","unstructured":"Liu J, Huang X, Li Q, Chen Z, Liu G, Tai Y (2023) Hourly stepwise forecasting for solar irradiance using integrated hybrid models CNN-LSTM-MLP combined with error correction and VMD. Energy Convers Manag 280:116804. https:\/\/doi.org\/10.1016\/j.enconman.2023.116804. (ISSN 0196-8904)","journal-title":"Energy Convers Manag"},{"key":"8551_CR31","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.renene.2020.05.150","volume":"160","author":"H Zang","year":"2020","unstructured":"Zang H, Liu L, Sun L, Cheng L, Wei Z, Sun G (2020) Short-term global horizontal irradiance forecasting based on a hybrid CNN-LSTM model with spatiotemporal correlations. Renew Energy 160:26\u201341. https:\/\/doi.org\/10.1016\/j.renene.2020.05.150. (ISSN 0960-1481)","journal-title":"Renew Energy"},{"key":"8551_CR32","doi-asserted-by":"publisher","DOI":"10.1016\/j.renene.2024.119943","volume":"222","author":"NE Michael","year":"2024","unstructured":"Michael NE, Bansal RC, Ismail AAA, Elnady A, Hasan S (2024) A cohesive structure of bi-directional long-short-term memory (BiLSTM) -GRU for predicting hourly solar irradiance. Renew Energy 222:119943. https:\/\/doi.org\/10.1016\/j.renene.2024.119943. (ISSN 0960-1481)","journal-title":"Renew Energy"},{"key":"8551_CR33","doi-asserted-by":"publisher","DOI":"10.1016\/j.apenergy.2022.118801","volume":"313","author":"D Niu","year":"2022","unstructured":"Niu D, Yu M, Sun L, Gao T, Wang K (2022) Short-term multi-energy load forecasting for integrated energy systems based on cnn-bigru optimized by attention mechanism. Appl Energy 313:118801. https:\/\/doi.org\/10.1016\/j.apenergy.2022.118801","journal-title":"Appl Energy"},{"key":"8551_CR34","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2024.132228","volume":"305","author":"X Sun","year":"2024","unstructured":"Sun X, Liu H (2024) Multivariate short-term wind speed prediction based on pso-vmd-se-iceemdan two-stage decomposition and att-s2s. Energy 305:132228. https:\/\/doi.org\/10.1016\/j.energy.2024.132228","journal-title":"Energy"},{"key":"8551_CR35","doi-asserted-by":"publisher","first-page":"3470","DOI":"10.1016\/j.egyr.2024.09.025","volume":"12","author":"Y Zhao","year":"2024","unstructured":"Zhao Y, Peng X, Tu T, Li Z, Yan P, Li C (2024) Woa-vmd-scinet: hybrid model for accurate prediction of ultra-short-term photovoltaic generation power considering seasonal variations. Energy Rep 12:3470\u20133487. https:\/\/doi.org\/10.1016\/j.egyr.2024.09.025","journal-title":"Energy Rep"},{"key":"8551_CR36","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2024.132766","volume":"307","author":"S Cui","year":"2024","unstructured":"Cui S, Lyu S, Ma Y, Wang K (2024) Improved informer pv power short-term prediction model based on weather typing and aha-vmd-mpe. Energy 307:132766. https:\/\/doi.org\/10.1016\/j.energy.2024.132766","journal-title":"Energy"},{"key":"8551_CR37","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecoinf.2023.102270","volume":"77","author":"C Lin","year":"2023","unstructured":"Lin C, Li X, Shi T, Sheng J, Sun S, Wang Y, Li D (2023) Forecasting of wind speed under wind-fire coupling scenarios by combining hs-vmd and am-lstm. Ecol Inform 77:102270. https:\/\/doi.org\/10.1016\/j.ecoinf.2023.102270","journal-title":"Ecol Inform"},{"key":"8551_CR38","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, Zhao D, Heidari AA, Liu L, Zhang X, Mafarja M, Chen H (2023) Rime: a physics-based optimization. Neurocomputing 532:183\u2013214. https:\/\/doi.org\/10.1016\/j.neucom.2023.02.010","journal-title":"Neurocomputing"},{"issue":"10","key":"8551_CR39","doi-asserted-by":"publisher","first-page":"1363","DOI":"10.21275\/ART20162488","volume":"5","author":"E Hariyanto","year":"2016","unstructured":"Hariyanto E, Rahim R (2016) Arnold\u2019s cat map algorithm in digital image encryption. Int J Sci Res (IJSR) 5(10):1363\u20131365. https:\/\/doi.org\/10.21275\/ART20162488","journal-title":"Int J Sci Res (IJSR)"},{"issue":"3","key":"8551_CR40","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/s002000050061","volume":"8","author":"GD Cohen","year":"1997","unstructured":"Cohen GD, Litsyn SN, Lobstein AC, Mattson HF Jr. (1997) Covering radius 1985-1994. Appl Algebra Eng Commun Comput 8(3):173\u2013239. https:\/\/doi.org\/10.1007\/s002000050061","journal-title":"Appl Algebra Eng Commun Comput"},{"issue":"4","key":"8551_CR41","doi-asserted-by":"publisher","first-page":"445","DOI":"10.2307\/1931034","volume":"35","author":"PJ Clark","year":"1954","unstructured":"Clark PJ, Evans FC (1954) Distance to nearest neighbor as a measure of spatial relationships in populations. Ecology 35(4):445\u2013453. https:\/\/doi.org\/10.2307\/1931034","journal-title":"Ecology"},{"issue":"3","key":"8551_CR42","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"CE Shannon","year":"1948","unstructured":"Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(3):379\u2013423. https:\/\/doi.org\/10.1002\/j.1538-7305.1948.tb01338.x","journal-title":"Bell Syst Tech J"},{"key":"8551_CR43","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2023.111211","volume":"152","author":"F Yu","year":"2024","unstructured":"Yu F, Guan J, Wu H, Chen Y, Xia X (2024) Lens imaging opposition-based learning for differential evolution with Cauchy perturbation. Appl Soft Comput 152:111211. https:\/\/doi.org\/10.1016\/j.asoc.2023.111211","journal-title":"Appl Soft Comput"},{"issue":"3","key":"8551_CR44","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","volume":"62","author":"K Dragomiretskiy","year":"2014","unstructured":"Dragomiretskiy K, Zosso D (2014) Variational mode decomposition. IEEE Trans Signal Process 62(3):531\u2013544. https:\/\/doi.org\/10.1109\/TSP.2013.2288675","journal-title":"IEEE Trans Signal Process"},{"key":"8551_CR45","unstructured":"Huang Z, Xu W, and Yu K (2015), Bidirectional lstm-crf models for sequence tagging. https:\/\/arxiv.org\/abs\/1508.01991."},{"key":"8551_CR46","unstructured":"Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez AN, Kaiser L, and Polosukhin I (2017), Attention is all you need, https:\/\/arxiv.org\/abs\/1706.03762."},{"key":"8551_CR47","doi-asserted-by":"publisher","unstructured":"Kennedy J and Eberhart R (1995) Particle swarm optimization. In Proceedings of ICNN\u201995 - International Conference on Neural Networks, volume 4 of ICNN-95, page 1942\u20131948. IEEE. https:\/\/doi.org\/10.1109\/ICNN.1995.488968.","DOI":"10.1109\/ICNN.1995.488968"},{"issue":"1","key":"8551_CR48","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1145\/234313.234350","volume":"28","author":"S Forrest","year":"1996","unstructured":"Forrest S (1996) Genetic algorithms. ACM Comput Surv 28(1):77\u201380. https:\/\/doi.org\/10.1145\/234313.234350","journal-title":"ACM Comput Surv"},{"key":"8551_CR49","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 SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46\u201361. https:\/\/doi.org\/10.1016\/j.advengsoft.2013.12.007","journal-title":"Adv Eng Softw"},{"key":"8551_CR50","doi-asserted-by":"publisher","unstructured":"Dorigo M and Di Caro G (1999), Ant colony optimization: a new metaheuristic. In Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), CEC-99, page1470\u20131477. IEEE. https:\/\/doi.org\/10.1109\/CEC.1999.782657.","DOI":"10.1109\/CEC.1999.782657"},{"issue":"7","key":"8551_CR51","doi-asserted-by":"publisher","first-page":"7305","DOI":"10.1007\/s11227-022-04959-6","volume":"79","author":"J Xue","year":"2022","unstructured":"Xue J, Shen B (2022) Dung beetle optimizer: a new metaheuristic algorithm for global optimization. J Supercomput 79(7):7305\u20137336. https:\/\/doi.org\/10.1007\/s11227-022-04959-6","journal-title":"J Supercomput"},{"key":"8551_CR52","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 (2016) The whale optimization algorithm. Adv Eng Softw 95:51\u201367. https:\/\/doi.org\/10.1016\/j.advengsoft.2016.01.008","journal-title":"Adv Eng Softw"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-026-08551-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-026-08551-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-026-08551-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T16:03:38Z","timestamp":1778774618000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-026-08551-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,14]]},"references-count":52,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["8551"],"URL":"https:\/\/doi.org\/10.1007\/s11227-026-08551-0","relation":{},"ISSN":["1573-0484"],"issn-type":[{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,14]]},"assertion":[{"value":"8 October 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 April 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 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":"419"}}