{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T05:10:28Z","timestamp":1779167428093,"version":"3.51.4"},"reference-count":56,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,5,3]],"date-time":"2026-05-03T00:00:00Z","timestamp":1777766400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Accurate forecasting of agricultural product prices is crucial for informed decision-making in agricultural markets; however, such time series are inherently characterized by non-stationarity, multi-scale dynamics, and substantial noise, posing significant challenges to conventional methods. To overcome these limitations, this study proposes a novel hybrid framework, termed TOC-CNN-BiLSTM-SA, built upon a \u201cquadratic decomposition\u2013clustering\u2013optimization\u201d paradigm. Specifically, a composite CEEMDAN\u2013K-means++\u2013VMD approach is first employed to hierarchically decompose the raw price series via coarse decomposition, feature clustering, and refined decomposition, enabling effective noise suppression and multi-scale feature extraction. Subsequently, a deep learning architecture integrating Convolutional Neural Networks (CNNs), Bidirectional Long Short-Term Memory networks (BiLSTM), and a self-attention mechanism is developed, where CNN captures local patterns, BiLSTM models bidirectional temporal dependencies, and the attention mechanism enhances global feature representation. Furthermore, the Tornado Optimizer with Coriolis force (TOC) is introduced to adaptively tune key hyperparameters, thereby improving model robustness and generalization capability. Empirical results based on wheat price data from Henan Province, China, demonstrate that the proposed model achieves outstanding predictive performance, with RMSE, MAE, MAPE, and R2 values of 4.425, 3.9372, 0.16%, and 99.97%, respectively, significantly outperforming existing benchmark models. These research indicate that the proposed framework effectively captures complex price dynamics and offers a reliable and practical solution for agricultural price forecasting.<\/jats:p>","DOI":"10.3390\/a19050357","type":"journal-article","created":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T01:12:09Z","timestamp":1777857129000},"page":"357","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Agricultural Product Price Prediction Model Based on Quadratic Clustering Decomposition and TOC-Optimized Deep Learning"],"prefix":"10.3390","volume":"19","author":[{"given":"Fengkai","family":"Ye","sequence":"first","affiliation":[{"name":"College of Mining Engineering, North China University of Science and Technology, Tangshan 063210, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruoqian","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mining Engineering, North China University of Science and Technology, Tangshan 063210, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Danping","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Science, North China University of Science and Technology, Tangshan 063210, China"},{"name":"Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China"},{"name":"The Key Laboratory of Engineering Computing in Tangshan City, North China University of Science and Technology, Tangshan 063210, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mengyang","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mining Engineering, North China University of Science and Technology, Tangshan 063210, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Paredes-Garcia, W.J., Ocampo-Vel\u00e1zquez, R.V., Torres-Pacheco, I., and Cedillo-Jim\u00e9nez, C.A. (2019). Price forecasting and span commercialization opportunities for Mexican agricultural products. Agronomy, 9.","DOI":"10.3390\/agronomy9120826"},{"key":"ref_2","unstructured":"Antonaci, L., Demeke, M., and Vezzani, A. (2014). The Challenges of Managing Agricultural Price and Production Risks in Sub-Saharan Africa, FAO."},{"key":"ref_3","unstructured":"Harwood, J.L. (1999). Managing Risk in Farming: Concepts, Research, and Analysis, US Department of Agriculture, ERS."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"101820","DOI":"10.1016\/j.intfin.2023.101820","article-title":"Tail dependence structure and extreme risk spillover effects between the international agricultural futures and spot markets","volume":"88","author":"Dai","year":"2023","journal-title":"J. Int. Financ. Mark. Inst. Money"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Sun, F., Meng, X., Zhang, Y., Wang, Y., Jiang, H., and Liu, P. (2023). Agricultural product price forecasting methods: A review. Agriculture, 13.","DOI":"10.3390\/agriculture13091671"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2204600","DOI":"10.1080\/08839514.2023.2204600","article-title":"Agricultural products price prediction based on improved RBF neural network model","volume":"37","author":"Wang","year":"2023","journal-title":"Appl. Artif. Intell."},{"key":"ref_7","first-page":"201","article-title":"Agricultural policy and wheat production: A case study of Pakistan","volume":"27","author":"Ali","year":"2011","journal-title":"Sarhad J. Agric."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Bezat-Jarz\u0119bowska, A., Rembisz, W., and Jarz\u0119bowski, S. (2024). Maintaining Agricultural Production Profitability\u2014A Simulation Approach to Wheat Market Dynamics. Agriculture, 14.","DOI":"10.3390\/agriculture14111910"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2121","DOI":"10.1108\/BFJ-09-2019-0683","article-title":"Agricultural product price forecasting methods: Research advances and trend","volume":"122","author":"Wang","year":"2020","journal-title":"Br. Food J."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Theofilou, A., Nastis, S.A., Michailidis, A., Bournaris, T., and Mattas, K. (2025). Predicting prices of staple crops using machine learning: A systematic review of studies on wheat, corn, and rice. Sustainability, 17.","DOI":"10.3390\/su17125456"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Tatarintsev, M., Korchagin, S., Nikitin, P., Gorokhova, R., Bystrenina, I., and Serdechnyy, D. (2021). Analysis of the forecast price as a factor of sustainable development of agriculture. Agronomy, 11.","DOI":"10.3390\/agronomy11061235"},{"key":"ref_12","first-page":"85","article-title":"Forecasting of Wheatprice Based on Multi-scale Analysis","volume":"24","author":"Wang","year":"2016","journal-title":"China Manag. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Shumway, R.H., and Stoffer, D.S. (2017). ARIMA models. Time Series Analysis and Its Applications: With R Examples, Springer.","DOI":"10.1007\/978-3-319-52452-8"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"KumarMahto, A., Biswas, R., and Alam, M.A. (2019). Short term forecasting of agriculture commodity price by using ARIMA: Based on Indian market. Advances in Computing and Data Sciences: Third International Conference, ICACDS 2019, Ghaziabad, India, 12\u201313 April 2019, Revised Selected Papers, Part I 3, Springer.","DOI":"10.1007\/978-981-13-9939-8_40"},{"key":"ref_15","first-page":"50","article-title":"Application of ARIMA model for forecasting agricultural productivity in India","volume":"8","author":"Padhan","year":"2012","journal-title":"J. Agric. Soc. Sci."},{"key":"ref_16","first-page":"981","article-title":"Application of ARIMA model for forecasting agricultural prices","volume":"19","author":"Jadhav","year":"2017","journal-title":"J. Agric. Sci. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/s43546-020-00020-x","article-title":"Forecasting the red lentils commodity market price using SARIMA models","volume":"1","author":"Divisekara","year":"2020","journal-title":"SN Bus. Econ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"132306","DOI":"10.1016\/j.physd.2019.132306","article-title":"Fundamentals of recurrent neural network (RNN) and long short-term memory (LSTM) network","volume":"404","author":"Sherstinsky","year":"2020","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Paul, R.K., Yeasin, M., Kumar, P., Kumar, P., Balasubramanian, M., Roy, H.S., Paul, A.K., and Gupta, A. (2022). Machine learning techniques for forecasting agricultural prices: A case of brinjal in Odisha, India. PLoS ONE, 17.","DOI":"10.1371\/journal.pone.0270553"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1162\/neco_a_01199","article-title":"A review of recurrent neural networks: LSTM cells and network architectures","volume":"31","author":"Yu","year":"2019","journal-title":"Neural Comput."},{"key":"ref_21","first-page":"72","article-title":"Forecasting spot prices of agricultural commodities in India: Application of deep-learning models","volume":"28","author":"RL","year":"2021","journal-title":"Intell. Syst. Account. Financ. Manag."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4661","DOI":"10.1007\/s00521-021-06621-3","article-title":"Deep long short-term memory based model for agricultural price forecasting","volume":"34","author":"Jaiswal","year":"2022","journal-title":"Neural Comput. Appl."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Gu, Y.H., Jin, D., Yin, H., Zheng, R., Piao, X., and Yoo, S.J. (2022). Forecasting agricultural commodity prices using dual input attention LSTM. Agriculture, 12.","DOI":"10.3390\/agriculture12020256"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zhang, T., and Tang, Z. (2024). Agricultural commodity futures prices prediction based on a new hybrid forecasting model combining quadratic decomposition technology and LSTM model. Front. Sustain. Food Syst., 8.","DOI":"10.3389\/fsufs.2024.1334098"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"109833","DOI":"10.1016\/j.asoc.2022.109833","article-title":"Optimal forecast combination based on PSO-CS approach for daily agricultural future prices forecasting","volume":"132","author":"Zeng","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2196","DOI":"10.1109\/TIM.2007.907967","article-title":"EMD-based signal filtering","volume":"56","author":"Boudraa","year":"2007","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2655","DOI":"10.1007\/s11269-015-0962-6","article-title":"Improving forecasting accuracy of annual runoff time series using ARIMA based on EEMD decomposition","volume":"29","author":"Wang","year":"2015","journal-title":"Water Resour. Manag."},{"key":"ref_28","unstructured":"Feng, Y., Wang, Z.H., and Li, Q.Y. (2024). Agricultural product price prediction model based on CEEMD-LSTM under the digital background. Price Mon., 1\u20138."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.physa.2018.11.061","article-title":"Financial time series forecasting model based on CEEMDAN and LSTM","volume":"519","author":"Cao","year":"2019","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational mode decomposition","volume":"62","author":"Dragomiretskiy","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Li, Y., Zhang, T., Yu, X., Sun, F., Liu, P., and Zhu, K. (2024). Research on agricultural product price prediction based on improved PSO-GA. Appl. Sci., 14.","DOI":"10.3390\/app14166862"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"85275","DOI":"10.1109\/ACCESS.2024.3415349","article-title":"Combining seasonal and trend decomposition using LOESS with a gated recurrent unit for climate time series forecasting","volume":"12","author":"Liu","year":"2024","journal-title":"IEEE Access"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1002\/for.2665","article-title":"Optimal forecast combination based on ensemble empirical mode decomposition for agricultural commodity futures prices","volume":"39","author":"Fang","year":"2020","journal-title":"J. Forecast."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Liu, D., Tang, Z., and Cai, Y. (2022). A Hybrid Model for China\u2019s Soybean Spot Price Prediction by Integrating CEEMDAN with Fuzzy Entropy Clustering and CNN-GRU-Attention. Sustainability, 14.","DOI":"10.3390\/su142315522"},{"key":"ref_35","first-page":"256","article-title":"Agricultural product price prediction based on signal decomposition and deep learning","volume":"38","author":"Wang","year":"2022","journal-title":"Trans. Chin. Soc. Agric. Eng. (Trans. CSAE)"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Ahmed, M., Seraj, R., and Islam, S.M.S. (2020). The k-means algorithm: A comprehensive survey and performance evaluation. Electronics, 9.","DOI":"10.3390\/electronics9081295"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"H\u00e4m\u00e4l\u00e4inen, J., K\u00e4rkk\u00e4inen, T., and Rossi, T. (2020). Improving scalable K-means++. Algorithms, 14.","DOI":"10.3390\/a14010006"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"112254","DOI":"10.1016\/j.enconman.2019.112254","article-title":"A new prediction method based on VMD-PRBF-ARMA-E model considering wind speed characteristic","volume":"203","author":"Zhang","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_39","first-page":"1285","article-title":"Prediction of COD Concentration in Sewage Treatment Plant Effluent Based on Quadratic Decomposition and BiLSTM","volume":"46","author":"Zhang","year":"2025","journal-title":"J. Chem. Ind. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Bhatt, D., Patel, C., Talsania, H., Patel, J., Vaghela, R., Pandya, S., Modi, K., and Ghayvat, H. (2021). CNN variants for computer vision: History, architecture, application, challenges and future scope. Electronics, 10.","DOI":"10.3390\/electronics10202470"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Siami-Namini, S., Tavakoli, N., and Namin, A.S. (2019). The performance of LSTM and BiLSTM in forecasting time series. 2019 IEEE International Conference on Big Data (Big Data), IEEE.","DOI":"10.1109\/BigData47090.2019.9005997"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s10462-025-11118-9","article-title":"Tornado optimizer with Coriolis force: A novel bio-inspired meta-heuristic algorithm for solving engineering problems","volume":"58","author":"Braik","year":"2025","journal-title":"Artif. Intell. Rev."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"e1484","DOI":"10.1002\/widm.1484","article-title":"Hyperparameter optimization: Foundations, algorithms, best practices, and open challenges","volume":"13","author":"Bischl","year":"2023","journal-title":"Wiley Interdiscip. Rev. Data Min. Knowl. Discov."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"5481","DOI":"10.5194\/gmd-15-5481-2022","article-title":"Root mean square error (RMSE) or mean absolute error (MAE): When to use them or not","volume":"15","author":"Hodson","year":"2022","journal-title":"Geosci. Model Dev. Discuss."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Fu, R., Zhang, Z., and Li, L. (2016). Using LSTM and GRU neural network methods for traffic flow prediction. 2016 31st Youth Academic Annual Conference of Chinese Association of Automation (YAC), IEEE.","DOI":"10.1109\/YAC.2016.7804912"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/S0893-6080(03)00169-2","article-title":"Practical selection of SVM parameters and noise estimation for SVM regression","volume":"17","author":"Cherkassky","year":"2004","journal-title":"Neural Netw."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s10462-011-9208-z","article-title":"An optimizing BP neural network algorithm based on genetic algorithm","volume":"36","author":"Ding","year":"2011","journal-title":"Artif. Intell. Rev."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Wang, W., Cui, X., Qi, Y., Xue, K., Liang, R., and Bai, C. (2024). Prediction model of coal gas permeability based on improved DBO optimized BP neural network. Sensors, 24.","DOI":"10.3390\/s24092873"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"109215","DOI":"10.1016\/j.knosys.2022.109215","article-title":"Beluga whale optimization: A novel nature-inspired metaheuristic algorithm","volume":"251","author":"Zhong","year":"2022","journal-title":"Knowl.-Based Syst."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1007\/s00521-017-3272-5","article-title":"Grey wolf optimizer: A review of recent variants and applications","volume":"30","author":"Faris","year":"2018","journal-title":"Neural Comput. Appl."},{"key":"ref_51","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_52","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.neucom.2023.02.010","article-title":"RIME: A physics-based optimization","volume":"532","author":"Su","year":"2023","journal-title":"Neurocomputing"},{"key":"ref_53","first-page":"e03807","article-title":"Prediction of permanent deformation of subgrade soils under FT cycles using SABO-optimized CNN-BiLSTM network","volume":"21","author":"Liu","year":"2024","journal-title":"Case Stud. Constr. Mater."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"2627","DOI":"10.1007\/s00366-022-01604-x","article-title":"Sand Cat swarm optimization: A nature-inspired algorithm to solve global optimization problems","volume":"39","author":"Seyyedabbasi","year":"2023","journal-title":"Eng. Comput."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1596","DOI":"10.1002\/for.2794","article-title":"On stock volatility forecasting based on text mining and deep learning under high-frequency data","volume":"40","author":"Lei","year":"2021","journal-title":"J. Forecast."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1186\/s40537-025-01240-4","article-title":"Metal commodity futures price forecasting based on a hybrid secondary decomposition error-corrected model","volume":"12","author":"Zhang","year":"2025","journal-title":"J. Big Data"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/5\/357\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T04:28:11Z","timestamp":1779164891000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/5\/357"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,3]]},"references-count":56,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["a19050357"],"URL":"https:\/\/doi.org\/10.3390\/a19050357","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,3]]}}}