{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T21:29:06Z","timestamp":1772832546065,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,6,21]],"date-time":"2022-06-21T00:00:00Z","timestamp":1655769600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Xiamen University Malaysia Research Fund","award":["XMUMRF\/2022-C9\/IECE\/0033"],"award-info":[{"award-number":["XMUMRF\/2022-C9\/IECE\/0033"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Simulation-based optimization design is becoming increasingly important in engineering. However, carrying out multi-point, multi-variable, and multi-objective optimization work is faced with the \u201cCurse of Dimensionality\u201d, which is highly time-consuming and often limited by computational burdens as in aerodynamic optimization problems. In this paper, an active subspace dimensionality reduction method and the adaptive surrogate model were proposed to reduce such computational costs while keeping a high precision. In this method, the active subspace dimensionality reduction technique, three-layer radial basis neural network approach, and polynomial fitting process were presented. For the model evaluation, a NASA standard test function problem and RAE2822 airfoil drag reduction optimization were investigated in the experimental design problem. The efficacy of the method was proved by both the experimental examples in which the adaptive surrogate model in a dominant one-dimensional active subspace is given and the optimization efficiency was improved by two orders. Furthermore, the results show that the constructed surrogate model reduced dimensionality and alleviated the complexity of conventional multivariate surrogate modeling with high precision.<\/jats:p>","DOI":"10.3390\/sym14071282","type":"journal-article","created":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T23:11:19Z","timestamp":1655939479000},"page":"1282","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Dimensionality Reduction, Modelling, and Optimization of Multivariate Problems Based on Machine Learning"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0580-6954","authenticated-orcid":false,"given":"Mohammed","family":"Alswaitti","sequence":"first","affiliation":[{"name":"School of Computing and Data Science, Xiamen University Malaysia, Sepang 43900, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2286-1728","authenticated-orcid":false,"given":"Kamran","family":"Siddique","sequence":"additional","affiliation":[{"name":"School of Computing and Data Science, Xiamen University Malaysia, Sepang 43900, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shulei","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Computing and Data Science, Xiamen University Malaysia, Sepang 43900, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2937-4327","authenticated-orcid":false,"given":"Waleed","family":"Alomoush","sequence":"additional","affiliation":[{"name":"School of Information Technology, Skyline University College, Sharjah P.O. Box 1797, United Arab Emirates"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ayat","family":"Alrosan","sequence":"additional","affiliation":[{"name":"School of Information Technology, Skyline University College, Sharjah P.O. Box 1797, United Arab Emirates"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,21]]},"reference":[{"key":"ref_1","first-page":"4434","article-title":"Cuckoo Search Algorithm based Dynamic Parameter Adjustment Mechanism for Solving Global Optimization Problems","volume":"14","author":"Alomoush","year":"2019","journal-title":"Int. J. Appl. Eng. 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