{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T23:46:11Z","timestamp":1776123971006,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2021,9,30]],"date-time":"2021-09-30T00:00:00Z","timestamp":1632960000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this study, the numerical computation heuristic of the environmental and economic system using the artificial neural networks (ANNs) structure together with the capabilities of the heuristic global search genetic algorithm (GA) and the quick local search interior-point algorithm (IPA), i.e., ANN-GA-IPA. The environmental and economic system is dependent of three categories, execution cost of control standards and new technical diagnostics elimination costs of emergencies values and the competence of the system of industrial elements. These three elements form a nonlinear differential environmental and economic system. The optimization of an error-based objective function is performed using the differential environmental and economic system and its initial conditions. The optimization of an error-based objective function is performed using the differential environmental and economic system and its initial conditions.<\/jats:p>","DOI":"10.3390\/s21196567","type":"journal-article","created":{"date-parts":[[2021,10,10]],"date-time":"2021-10-10T21:37:49Z","timestamp":1633901869000},"page":"6567","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Numerical Study of the Environmental and Economic System through the Computational Heuristic Based on Artificial Neural Networks"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8092-4665","authenticated-orcid":false,"given":"Kashif","family":"Nisar","sequence":"first","affiliation":[{"name":"Faculty of Computing and Informatics, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu Sabah 88400, Malaysia"}]},{"given":"Zulqurnain","family":"Sabir","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Hazara University, Mansehra 21120, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9953-822X","authenticated-orcid":false,"given":"Muhammad Asif","family":"Zahoor Raja","sequence":"additional","affiliation":[{"name":"Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou 64002, Taiwan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1793-5905","authenticated-orcid":false,"given":"Ag Asri Ag","family":"Ibrahim","sequence":"additional","affiliation":[{"name":"Faculty of Computing and Informatics, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu Sabah 88400, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7008-1366","authenticated-orcid":false,"given":"Samy Refahy","family":"Mahmoud","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"given":"Mohammed","family":"Balubaid","sequence":"additional","affiliation":[{"name":"GRC Department, Faculty of Applied studies, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3638-3464","authenticated-orcid":false,"given":"Danda B.","family":"Rawat","sequence":"additional","affiliation":[{"name":"Data Science and Cybersecurity Center, Deptartment of Electrical Engineering and Computer Science, Howard University, Washington, DC 20059, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8657-3800","authenticated-orcid":false,"given":"Joel J. 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