{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T02:15:56Z","timestamp":1783044956776,"version":"3.54.6"},"reference-count":39,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T00:00:00Z","timestamp":1777852800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004385","name":"Universiteit Gent","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004385","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100019771","name":"European Union&apos;s Research and Innovation","doi-asserted-by":"publisher","award":["101070080"],"award-info":[{"award-number":["101070080"]}],"id":[{"id":"10.13039\/100019771","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Expert Systems with Applications"],"published-print":{"date-parts":[[2026,9]]},"DOI":"10.1016\/j.eswa.2026.132705","type":"journal-article","created":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T00:56:53Z","timestamp":1777942613000},"page":"132705","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Constraint-aware reinforcement learning for energy-efficient and regulation-compliant wastewater treatment"],"prefix":"10.1016","volume":"325","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7478-419X","authenticated-orcid":false,"given":"Omid","family":"Sobhani","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5611-6331","authenticated-orcid":false,"given":"Thomas","family":"Huybrechts","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-9351-811X","authenticated-orcid":false,"given":"Hamid","family":"Toliati","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4364-0377","authenticated-orcid":false,"given":"Cristian Camilo","family":"Gomez Cortes","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4812-4841","authenticated-orcid":false,"given":"Kevin","family":"Mets","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9355-6566","authenticated-orcid":false,"given":"Siegfried","family":"Mercelis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.eswa.2026.132705_bib0001","series-title":"Proceedings of the 34th international conference on machine learning","first-page":"22","article-title":"Constrained policy optimization","volume":"vol. 70","author":"Achiam","year":"2017"},{"issue":"13","key":"10.1016\/j.eswa.2026.132705_bib0002","doi-asserted-by":"crossref","DOI":"10.3390\/w15132349","article-title":"Unlocking the potential of wastewater treatment: Machine learning based energy consumption prediction","volume":"15","author":"Alali","year":"2023","journal-title":"Water"},{"key":"10.1016\/j.eswa.2026.132705_bib0003","unstructured":"Alex, J., Benedetti, L., Copp, J. B., Gernaey, K. V., Jeppsson, U., Nopens, I., Pons, M.-N., Rieger, L., Rosen, C., Steyer, J. P. et al. (2008). Benchmark simulation model no. 1 (BSM1): Technical Report TEIE-7229. Lund University. https:\/\/www2.iea.lth.se\/publications\/Reports\/LTH-IEA-7229.pdf."},{"key":"10.1016\/j.eswa.2026.132705_bib0004","series-title":"Constrained Markov decision processes","author":"Altman","year":"1999"},{"issue":"11","key":"10.1016\/j.eswa.2026.132705_bib0005","doi-asserted-by":"crossref","first-page":"2374","DOI":"10.2166\/wst.2013.139","article-title":"Aeration control\u2013a review","volume":"67","author":"\u00c5mand","year":"2013","journal-title":"Water Science and Technology"},{"issue":"3","key":"10.1016\/j.eswa.2026.132705_bib0006","doi-asserted-by":"crossref","first-page":"396","DOI":"10.2166\/aqua.2024.209","article-title":"Total ammonia aeration control (TAAC) theory - an innovative ammonia-based aeration controller","volume":"73","author":"Budzynski","year":"2024","journal-title":"AQUA - Water Infrastructure, Ecosystems and Society"},{"key":"10.1016\/j.eswa.2026.132705_bib0007","doi-asserted-by":"crossref","DOI":"10.1016\/j.chemosphere.2021.130498","article-title":"Optimal control towards sustainable wastewater treatment plants based on multi-agent reinforcement learning","volume":"279","author":"Chen","year":"2021","journal-title":"Chemosphere"},{"issue":"20","key":"10.1016\/j.eswa.2026.132705_bib0008","doi-asserted-by":"crossref","first-page":"1775","DOI":"10.1080\/10643389.2023.2183699","article-title":"Reinforcement learning applied to wastewater treatment process control optimization: Approaches, challenges, and path forward","volume":"53","author":"Croll","year":"2023","journal-title":"Critical Reviews in Environmental Science and Technology"},{"issue":"46","key":"10.1016\/j.eswa.2026.132705_bib0009","doi-asserted-by":"crossref","first-page":"18382","DOI":"10.1021\/acs.est.3c00353","article-title":"Systematic performance evaluation of reinforcement learning algorithms applied to wastewater treatment control optimization","volume":"57","author":"Croll","year":"2023","journal-title":"Environmental Science & Technology"},{"key":"10.1016\/j.eswa.2026.132705_bib0010","doi-asserted-by":"crossref","DOI":"10.1016\/j.jwpe.2024.106658","article-title":"Reinforcement learning optimization of a water resource recovery facility: Evaluating the impact of reward function design on agent training, control optimization, and treatment risk","volume":"69","author":"Croll","year":"2025","journal-title":"Journal of Water Process Engineering"},{"issue":"1","key":"10.1016\/j.eswa.2026.132705_bib0011","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1038\/s41545-020-0072-8","article-title":"Sustainable sanitation and gaps in global climate policy and financing","volume":"3","author":"Dickin","year":"2020","journal-title":"NPJ Clean Water"},{"issue":"11","key":"10.1016\/j.eswa.2026.132705_bib0012","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1016\/j.envsoft.2011.06.001","article-title":"Dynamic influent pollutant disturbance scenario generation using a phenomenological modelling approach","volume":"26","author":"Gernaey","year":"2011","journal-title":"Environmental Modelling & Software"},{"key":"10.1016\/j.eswa.2026.132705_bib0013","series-title":"Convex optimization: Saddle points characterization and introduction to duality","first-page":"243","author":"Giorgi","year":"2023"},{"key":"10.1016\/j.eswa.2026.132705_bib0014","doi-asserted-by":"crossref","DOI":"10.1016\/j.jclepro.2023.138008","article-title":"Optimization and control strategies of aeration in WWTPs: A review","volume":"418","author":"Gu","year":"2023","journal-title":"Journal of Cleaner Production"},{"key":"10.1016\/j.eswa.2026.132705_bib0015","series-title":"Proceedings of the 35th international conference on machine learning","first-page":"1861","article-title":"Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor","volume":"vol. 80","author":"Haarnoja","year":"2018"},{"key":"10.1016\/j.eswa.2026.132705_bib0016","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2021.109689","article-title":"Reinforcement learning control of constrained dynamic systems with uniformly ultimate boundedness stability guarantee","volume":"129","author":"Han","year":"2021","journal-title":"Automatica"},{"key":"10.1016\/j.eswa.2026.132705_bib0017","series-title":"Activated sludge models ASM1, ASM2, ASM2d and ASM3","author":"Henze","year":"2006"},{"issue":"1","key":"10.1016\/j.eswa.2026.132705_bib0018","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1061\/(ASCE)0733-9372(2003)129:1(52)","article-title":"Oxidation\u2013reduction potential as a monitoring tool in a low dissolved oxygen wastewater treatment process","volume":"129","author":"Holman","year":"2003","journal-title":"Journal of Environmental Engineering"},{"issue":"24","key":"10.1016\/j.eswa.2026.132705_bib0019","doi-asserted-by":"crossref","DOI":"10.3390\/w16243710","article-title":"Real-time control of A2O process in wastewater treatment through fast deep reinforcement learning based on data-driven simulation model","volume":"16","author":"Hu","year":"2024","journal-title":"Water"},{"issue":"13","key":"10.1016\/j.eswa.2026.132705_bib0020","doi-asserted-by":"crossref","DOI":"10.3390\/en17133162","article-title":"Modeling and control strategies for energy management in a wastewater center: A review on aeration","volume":"17","author":"Jamaludin","year":"2024","journal-title":"Energies"},{"key":"10.1016\/j.eswa.2026.132705_bib0021","series-title":"Proceedings of the thirtieth international joint conference on artificial intelligence, IJCAI-21","first-page":"4508","article-title":"Policy learning with constraints in model-free reinforcement learning: A survey","author":"Liu","year":"2021"},{"key":"10.1016\/j.eswa.2026.132705_bib0022","doi-asserted-by":"crossref","first-page":"6349","DOI":"10.1016\/j.egyr.2025.05.045","article-title":"Energy management model for wastewater treatment plants","volume":"13","author":"Miederer","year":"2025","journal-title":"Energy Reports"},{"key":"10.1016\/j.eswa.2026.132705_bib0023","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2025.127180","article-title":"Application of soft actor-critic algorithms in optimizing wastewater treatment with time delays integration","volume":"277","author":"Mohammadi","year":"2025","journal-title":"Expert Systems with Applications"},{"issue":"1","key":"10.1016\/j.eswa.2026.132705_bib0024","doi-asserted-by":"crossref","first-page":"140","DOI":"10.2166\/wpt.2022.154","article-title":"Modelling and optimization of energy consumption in the activated sludge biological aeration unit","volume":"18","author":"Muloiwa","year":"2022","journal-title":"Water Practice and Technology"},{"key":"10.1016\/j.eswa.2026.132705_bib0025","doi-asserted-by":"crossref","DOI":"10.1016\/j.jclepro.2020.125772","article-title":"Artificial intelligence based ensemble modeling of wastewater treatment plant using jittered data","volume":"291","author":"Nourani","year":"2021","journal-title":"Journal of Cleaner Production"},{"key":"10.1016\/j.eswa.2026.132705_bib0026","series-title":"New challenges on bioinspired applications","first-page":"215","article-title":"Reinforcement learning techniques for the control of wastewater treatment plants","author":"Hernandez-del Olmo","year":"2011"},{"issue":"14","key":"10.1016\/j.eswa.2026.132705_bib0027","doi-asserted-by":"crossref","DOI":"10.3390\/s19143139","article-title":"Machine learning weather soft-sensor for advanced control of wastewater treatment plants","volume":"19","author":"Hern\u00e1ndez-del Olmo","year":"2019","journal-title":"Sensors"},{"issue":"2","key":"10.1016\/j.eswa.2026.132705_bib0028","doi-asserted-by":"crossref","first-page":"189","DOI":"10.3390\/bioengineering11020189","article-title":"Dynamic modelling, process control, and monitoring of selected biological and advanced oxidation processes for wastewater treatment: A review of recent developments","volume":"11","author":"Parsa","year":"2024","journal-title":"Bioengineering"},{"key":"10.1016\/j.eswa.2026.132705_bib0029","series-title":"Constrained reinforcement learning has zero duality gap","first-page":"7555","author":"Paternain","year":"2019"},{"issue":"268","key":"10.1016\/j.eswa.2026.132705_bib0030","first-page":"1","article-title":"Stable-baselines3: Reliable reinforcement learning implementations","volume":"22","author":"Raffin","year":"2021","journal-title":"Journal of Machine Learning Research"},{"key":"10.1016\/j.eswa.2026.132705_bib0031","series-title":"Technical Report","article-title":"Generating wastewater treatment plant influent data for realistic evaluation of future scenarios \u2013 case study for WWTPs in stockholm, Sweden","author":"Saagi","year":"2017"},{"key":"10.1016\/j.eswa.2026.132705_bib0032","series-title":"Weftec 2010","first-page":"3333","article-title":"Energy efficiency in wastewater treatment in north america: A WERF compendium of best practices and case studies of novel approaches","author":"Sandino","year":"2010"},{"issue":"1","key":"10.1016\/j.eswa.2026.132705_bib0033","doi-asserted-by":"crossref","first-page":"63","DOI":"10.2166\/wst.2019.032","article-title":"Ammonia-based aeration control with optimal SRT control: Improved performance and lower energy consumption","volume":"79","author":"Schraa","year":"2019","journal-title":"Water Science and Technology"},{"key":"10.1016\/j.eswa.2026.132705_bib0034","series-title":"Reinforcement learning: An introduction","author":"Sutton","year":"2018"},{"issue":"10","key":"10.1016\/j.eswa.2026.132705_bib0035","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1016\/0043-1354(91)90066-Y","article-title":"A dynamic model of the clarification-thickening process","volume":"25","author":"Tak\u00e1cs","year":"1991","journal-title":"Water Research"},{"key":"10.1016\/j.eswa.2026.132705_bib0036","series-title":"The thirty-ninth annual conference on neural information processing systems datasets and benchmarks track","article-title":"Gymnasium: A standard interface for reinforcement learning environments","author":"Towers","year":"2025"},{"key":"10.1016\/j.eswa.2026.132705_bib0037","doi-asserted-by":"crossref","DOI":"10.1016\/j.scitotenv.2021.147138","article-title":"A machine learning framework to improve effluent quality control in wastewater treatment plants","volume":"784","author":"Wang","year":"2021","journal-title":"Science of The Total Environment"},{"issue":"1","key":"10.1016\/j.eswa.2026.132705_bib0038","doi-asserted-by":"crossref","first-page":"2822","DOI":"10.1080\/09540091.2022.2151567","article-title":"Safe reinforcement learning for dynamical systems using barrier certificates","volume":"34","author":"Zhao","year":"2022","journal-title":"Connection Science"},{"key":"10.1016\/j.eswa.2026.132705_bib0039","series-title":"Development of data-driven models for influent prediction at wastewater treatment plants","author":"Zhou","year":"2019"}],"container-title":["Expert Systems with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0957417426016180?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0957417426016180?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T01:20:00Z","timestamp":1783041600000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0957417426016180"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9]]},"references-count":39,"alternative-id":["S0957417426016180"],"URL":"https:\/\/doi.org\/10.1016\/j.eswa.2026.132705","relation":{},"ISSN":["0957-4174"],"issn-type":[{"value":"0957-4174","type":"print"}],"subject":[],"published":{"date-parts":[[2026,9]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Constraint-aware reinforcement learning for energy-efficient and regulation-compliant wastewater treatment","name":"articletitle","label":"Article Title"},{"value":"Expert Systems with Applications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.eswa.2026.132705","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}],"article-number":"132705"}}