{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T09:16:03Z","timestamp":1767863763712,"version":"3.49.0"},"reference-count":63,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T00:00:00Z","timestamp":1621555200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006242","name":"Universiti Malaysia Sabah","doi-asserted-by":"publisher","award":["GUN55443"],"award-info":[{"award-number":["GUN55443"]}],"id":[{"id":"10.13039\/501100006242","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>In this work, a new heuristic computing design is presented with an artificial intelligence approach to exploit the models with feed-forward (FF) Gudermannian neural networks (GNN) accomplished with global search capability of genetic algorithms (GA) combined with local convergence aptitude of active-set method (ASM), i.e., FF-GNN-GAASM to solve the second kind of Lane\u2013Emden nonlinear singular models (LE-NSM). The proposed method based on the computing intelligent Gudermannian kernel is incorporated with the hidden layer configuration of FF-GNN models of differential operatives of the LE-NSM, which are arbitrarily associated with presenting an error-based objective function that is used to optimize by the hybrid heuristics of GAASM. Three LE-NSM-based examples are numerically solved to authenticate the effectiveness, accurateness, and efficiency of the suggested FF-GNN-GAASM. The reliability of the scheme via statistical valuations is verified in order to authenticate the stability, accuracy, and convergence.<\/jats:p>","DOI":"10.3390\/app11114725","type":"journal-article","created":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T13:15:15Z","timestamp":1621602915000},"page":"4725","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Evolutionary Integrated Heuristic with Gudermannian Neural Networks for Second Kind of Lane\u2013Emden Nonlinear Singular Models"],"prefix":"10.3390","volume":"11","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, Yunlin 64002, Taiwan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1793-5905","authenticated-orcid":false,"given":"Ag. Asri","family":"Ag. Ibrahim","sequence":"additional","affiliation":[{"name":"Faculty of Computing and Informatics, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu, Sabah 88400, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8657-3800","authenticated-orcid":false,"given":"Joel J. P. C.","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"Post-Graduation Program in Electrical Engineering, Federal University of Piau\u00ed (UFPI), Teresina-PI 64049-550, Brazil"},{"name":"Covilh\u00e3 Delegation, Instituto de Telecomunica\u00e7\u00f5es, 6201-001 Covilh\u00e3, Portugal"}]},{"given":"Adnan","family":"Shahid Khan","sequence":"additional","affiliation":[{"name":"Faculty of Computer Science and Information Technology, Universiti Malaysia Sarawak, Kota Samarahan 94300, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4274-4927","authenticated-orcid":false,"given":"Manoj","family":"Gupta","sequence":"additional","affiliation":[{"name":"Department of Electronics and Communication Engineering, JECRC University Jaipur, Rajasthan 303905, India"}]},{"given":"Aldawoud","family":"Kamal","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Mutah University Jordan, Mu\u2019tah 61710, Jordan"}]},{"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, Dept of Electrical Engineering and Computer Science, Howard University, Washington, DC 20059, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"57","DOI":"10.2475\/ajs.s2-50.148.57","article-title":"On the Theoretical Temperature of the Sun, under the Hypothesis of a gaseous Mass maintaining its Volume by its internal Heat and depending on the laws of gases as known to terrestrial Experiment","volume":"148","author":"Lane","year":"1870","journal-title":"Am. 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