{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T09:38:56Z","timestamp":1769074736988,"version":"3.49.0"},"reference-count":26,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,18]],"date-time":"2023-06-18T00:00:00Z","timestamp":1687046400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers"],"abstract":"<jats:p>Optimizing water distribution both from an energy-saving perspective and from a quality of service perspective is a challenging task since it involves a complex system with many nodes, many hidden variables and many operational constraints. For this reason, water distribution systems need to handle a delicate trade-off between the effectiveness and computational time of the solution. In this paper, we propose a new computationally efficient method, named rule-based control, to optimize water distribution networks without the need for a rigorous formulation of the optimization problem. As a matter of fact, since it is based on a machine learning approach, the proposed method employs only a set of historical data, where the configuration can be labeled according to a quality criterion. Since it is a data-driven approach, it could be applied to any complex network where historical labeled data are available. In particular, rule-based control exploits a rule-based classification method that allows us to retrieve the rules leading to good or bad performances of the system, even without any information about its physical laws. The evaluation of the results on some simulated scenarios shows that the proposed approach is able to reduce energy consumption while ensuring a good quality of the service. The proposed approach is currently used in the water distribution system of the Milan (Italy) water main.<\/jats:p>","DOI":"10.3390\/computers12060123","type":"journal-article","created":{"date-parts":[[2023,6,19]],"date-time":"2023-06-19T01:31:14Z","timestamp":1687138274000},"page":"123","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Optimizing Water Distribution through Explainable AI and Rule-Based Control"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0666-6597","authenticated-orcid":false,"given":"Enrico","family":"Ferrari","sequence":"first","affiliation":[{"name":"Rulex Innovation Labs, Rulex Inc., 16122 Genoa, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9912-3454","authenticated-orcid":false,"given":"Damiano","family":"Verda","sequence":"additional","affiliation":[{"name":"Rulex Innovation Labs, Rulex Inc., 16122 Genoa, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5947-8728","authenticated-orcid":false,"given":"Nicol\u00f2","family":"Pinna","sequence":"additional","affiliation":[{"name":"Rulex Innovation Labs, Rulex Inc., 16122 Genoa, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9999-2331","authenticated-orcid":false,"given":"Marco","family":"Muselli","sequence":"additional","affiliation":[{"name":"Institute of Electronics, Computer and Telecommunication Engineering, Italian National Research Council, 16149 Genova, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"04016023","DOI":"10.1061\/(ASCE)WR.1943-5452.0000665","article-title":"Pressure standards in water distribution systems: Reflection on current practice with consideration of some unresolved issues","volume":"142","author":"Ghorbanian","year":"2016","journal-title":"J. Water Resour. Plan. Manag."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Stinson, M., and Vitasovic, Z. (2006, January 21\u201325). Real time control of sewers: US EPA manual. Proceedings of the World Environmental and Water Resource Congress 2006: Examining the Confluence of Environmental and Water Concerns, Omaha, NE, USA.","DOI":"10.1061\/40856(200)406"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Mala-Jetmarova, H., Sultanova, N., and Savic, D. (2018). Lost in Optimisation of Water Distribution Systems? A Literature Review of System Design. Water, 10.","DOI":"10.3390\/w10030307"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1061\/(ASCE)0733-9496(2003)129:3(210)","article-title":"Optimization of water distribution network design using the shuffled frog leaping algorithm","volume":"129","author":"Eusuff","year":"2003","journal-title":"J. Water Resour. Plan. Manag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1002\/net.21673","article-title":"An iterated local search algorithm for water distribution network design optimization","volume":"67","year":"2016","journal-title":"Networks"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"875","DOI":"10.2166\/ws.2013.074","article-title":"A new algorithm for real-time pressure control in water distribution networks","volume":"13","author":"Creaco","year":"2013","journal-title":"Water Sci. Technol. Water Supply"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Page, P.R., and Creaco, E. (2019). Comparison of flow-dependent controllers for remote real-time pressure control in a water distribution system with stochastic consumption. Water, 11.","DOI":"10.3390\/w11030422"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"04017045","DOI":"10.1061\/(ASCE)WR.1943-5452.0000807","article-title":"Pressure management of water distribution systems via the remote real-time control of variable speed pumps","volume":"143","author":"Page","year":"2017","journal-title":"J. Water Resour. Plan. Manag."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Mosetlhe, T., Hamam, Y., Du, S., and Monacelli, E. (2020). A Survey of Pressure Control Approaches in Water Supply Systems. Water, 12.","DOI":"10.3390\/w12061732"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1109\/TCNS.2019.2939651","article-title":"Optimal scheduling of water distribution systems","volume":"7","author":"Singh","year":"2019","journal-title":"IEEE Trans. Control. Netw. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5:1","DOI":"10.1147\/JRD.2009.5429018","article-title":"The energy-efficiency benefits of pump-scheduling optimization for potable water supplies","volume":"53","author":"Bunn","year":"2009","journal-title":"IBM J. Res. Dev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"15","DOI":"10.2166\/hydro.2006.014","article-title":"Use of an artificial neural network to capture the domain knowledge of a conventional hydraulic simulation model","volume":"9","author":"Rao","year":"2007","journal-title":"J. Hydroinform."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"25","DOI":"10.2166\/hydro.2006.015","article-title":"Development of a real-time, near-optimal control process for water-distribution networks","volume":"9","author":"Rao","year":"2006","journal-title":"J. Hydroinform."},{"key":"ref_14","unstructured":"Rylander, S., and Gotshall, B. (2002, January 10\u201314). Optimal population size and the genetic algorithm. Proceedings of the World Scientific and Engineering Academy and Society (WSEAS) International Conference on Soft Computing, Optimization, Simulation and Manufacturing Systems (SOSM 2002), Shanghai, China."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.envsoft.2017.02.009","article-title":"Lost in Optimisation of Water Distribution Systems? A Literature Review of System Operation","volume":"93","author":"Sultanova","year":"2017","journal-title":"Environ. Model. Softw."},{"key":"ref_16","unstructured":"Lopez-Ibanez, M., Devi Prasad, T., and Paechter, B. (2005, January 2\u20135). Multi-objective optimisation of the pump scheduling problem using SPEA2. Proceedings of the 2005 IEEE Congress on Evolutionary Computation, Edinburgh, UK."},{"key":"ref_17","unstructured":"Murphy, L., Dandy, G., and Simpson, A. (1994, January 15\u201317). Optimum Design and Operation of Pumped Water Distribution Systems. Proceedings of the 1994 Conference on Hydraulics in Civil Engineering, Brisbane, Australia."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1016\/j.envsoft.2014.11.004","article-title":"A computational software tool for the minimization of costs and greenhouse gas emissions associated with water distribution systems","volume":"69","author":"Stokes","year":"2015","journal-title":"Environ. Model. Softw."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Patriksson, M., Bagloee, S., and Asadi, M. (2018). Minimization of water pumps\u2019 electricity usage: A hybrid approach of regression models with optimization. Expert Syst. Appl., 107.","DOI":"10.1016\/j.eswa.2018.04.027"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/0893-6080(91)90009-T","article-title":"Approximation capabilities of multilayer feedforward networks","volume":"4","author":"Hornik","year":"1991","journal-title":"Neural Netw."},{"key":"ref_21","unstructured":"Rossman, L.A. (2000). EPANET 2 Users Manual."},{"key":"ref_22","unstructured":"Apolloni, B., Marinaro, M., Nicosia, G., and Tagliaferri, R. Switching Neural Networks: A New Connectionist Model for Classification. Proceedings of the 16th Italian Workshop on Neural Nets, WIRN 2005, International Workshop on Natural and Artificial Immune Systems (NAIS 2005), Vietri sul Mare, Italy, 8\u201311 June 2005."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1109\/TKDE.2009.206","article-title":"Coupling Logical Analysis of Data and Shadow Clustering for Partially Defined Positive Boolean Function Reconstruction","volume":"23","author":"Muselli","year":"2011","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF00116251","article-title":"Induction of decision trees","volume":"1","author":"Quinlan","year":"1986","journal-title":"Mach. Learn."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random Forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"04014009","DOI":"10.1061\/(ASCE)WR.1943-5452.0000378","article-title":"Battle of the Water Networks II","volume":"140","author":"Monteiro","year":"2014","journal-title":"J. Water Resour. Plan. Manag."}],"container-title":["Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-431X\/12\/6\/123\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:55:47Z","timestamp":1760126147000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-431X\/12\/6\/123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,18]]},"references-count":26,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["computers12060123"],"URL":"https:\/\/doi.org\/10.3390\/computers12060123","relation":{},"ISSN":["2073-431X"],"issn-type":[{"value":"2073-431X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,18]]}}}