{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T07:14:17Z","timestamp":1761808457497,"version":"build-2065373602"},"reference-count":60,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T00:00:00Z","timestamp":1624838400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","award":["MOST-109-2622-E-324-004"],"award-info":[{"award-number":["MOST-109-2622-E-324-004"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Design: At the heart of time series forecasting, if nonlinear and nonstationary data are analyzed using traditional time series, the results will be biased. At the same time, if just using machine learning without any consideration given to input from traditional time series, not much information can be obtained from the results because the machine learning model is a black box. Purpose: In order to better study time series forecasting, we extend the combination of traditional time series and machine learning and propose a hybrid cascade neural network considering a metaheuristic optimization genetic algorithm in space\u2013time forecasting. Finding: To further show the utility of the cascade neural network genetic algorithm, we use various scenarios for training and testing while also extending simulations by considering the activation functions SoftMax, radbas, logsig, and tribas on space\u2013time forecasting of pollution data. During the simulation, we perform numerical metric evaluations using the root-mean-square error (RMSE), mean absolute error (MAE), and symmetric mean absolute percentage error (sMAPE) to demonstrate that our models provide high accuracy and speed up time-lapse computing.<\/jats:p>","DOI":"10.3390\/sym13071158","type":"journal-article","created":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T13:39:22Z","timestamp":1624887562000},"page":"1158","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Evolving Hybrid Cascade Neural Network Genetic Algorithm Space\u2013Time Forecasting"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1812-7478","authenticated-orcid":false,"given":"Rezzy Eko","family":"Caraka","sequence":"first","affiliation":[{"name":"Faculty of Economics and Business, Campus UI Depok, Universitas Indonesia, Depok 16426, Indonesia"},{"name":"Bioinformatics and Data Science Research Center, Bina Nusantara University, Jakarta 11480, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4887-9646","authenticated-orcid":false,"given":"Hasbi","family":"Yasin","sequence":"additional","affiliation":[{"name":"Department of Statistics, Diponegoro University, Semarang 50275, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7621-1988","authenticated-orcid":false,"given":"Rung-Ching","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Information Management, College of Informatics, Chaoyang University of Technology, Taichung 41349, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Noor Ell","family":"Goldameir","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Riau University, Pekanbaru 28293, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Budi Darmawan","family":"Supatmanto","sequence":"additional","affiliation":[{"name":"Weather Modification Technology Center, Agency for the Assessment and Application of Technology (BPPT), Jakarta 10340, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6077-0881","authenticated-orcid":false,"given":"Toni","family":"Toharudin","sequence":"additional","affiliation":[{"name":"Department of Statistics, Padjadjaran University, Bandung 16426, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1120-8571","authenticated-orcid":false,"given":"Mohammad","family":"Basyuni","sequence":"additional","affiliation":[{"name":"Department of Forestry, Faculty of Forestry, Universitas Sumatera Utara, Medan 20155, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Prana Ugiana","family":"Gio","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Universitas Sumatera Utara, Medan 20155, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7404-9005","authenticated-orcid":false,"given":"Bens","family":"Pardamean","sequence":"additional","affiliation":[{"name":"Bioinformatics and Data Science Research Center, Bina Nusantara University, Jakarta 11480, Indonesia"},{"name":"Computer Science Department, Bina Nusantara University, Jakarta 11480, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6547","DOI":"10.1016\/j.atmosenv.2004.08.037","article-title":"Speciation and origin of PM10 and PM2.5 in selected European cities","volume":"38","author":"Querol","year":"2004","journal-title":"Atmos. 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