{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T14:49:54Z","timestamp":1772722194818,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T00:00:00Z","timestamp":1772668800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FEDER funds"},{"DOI":"10.13039\/501100001871","name":"Portuguese Foundation for Science and Technology","doi-asserted-by":"publisher","award":["UID-P\/05256\/2020"],"award-info":[{"award-number":["UID-P\/05256\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Portuguese Foundation for Science and Technology","doi-asserted-by":"publisher","award":["UID-B\/05256\/2020"],"award-info":[{"award-number":["UID-B\/05256\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>Injection molding is widely used for plastic parts, but its performance is limited by the cooling stage, which dominates cycle time and affects dimensional stability and energy consumption. Conformal cooling channels, which can be manufactured using additive technologies, improve thermal efficiency but introduce a high-dimensional design problem. This work proposes an integrated methodology for optimizing injection molds with conformal cooling channels that combines parametric CAD (Computer-Aided Drawing), simulation, non-linear principal component analysis, artificial neural network, and multi-objective evolutionary optimization. The workflow is applied to a case study with five cooling layouts. An initial set of 36 metrics related to temperature gradients, warpage, shrinkage, and energy is reduced to a small number of latent objectives, simplifying the search space while preserving the main physical trends. Artificial neural networks surrogates accurately reproduce numerical results, enabling exploration of the design space at a fraction of the computational cost. The optimization yields diverse Pareto-optimal solutions that balance cycle time, dimensional stability, and energy consumption, assisting the design of more sustainable injection molds. Sensitivity analysis identifies mold temperature and channel position\/diameter as key design levers. The proposed methodology reduces dependence on expensive simulations and is readily transferable to industrial mold design.<\/jats:p>","DOI":"10.3390\/math14050877","type":"journal-article","created":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T13:11:22Z","timestamp":1772716282000},"page":"877","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Data-Driven Multi-Objective Optimization of Conformal Cooling Channels for Energy-Efficient Injection Molding"],"prefix":"10.3390","volume":"14","author":[{"given":"Carlos","family":"Pereira","sequence":"first","affiliation":[{"name":"Department of Polymer Engineering, University of Minho, 4800-058 Guimar\u00e3es, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8964-400X","authenticated-orcid":false,"given":"Ant\u00f3nio J.","family":"Pontes","sequence":"additional","affiliation":[{"name":"Department of Polymer Engineering, University of Minho, 4800-058 Guimar\u00e3es, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7777-7625","authenticated-orcid":false,"given":"Ant\u00f3nio","family":"Gaspar-Cunha","sequence":"additional","affiliation":[{"name":"Department of Polymer Engineering, University of Minho, 4800-058 Guimar\u00e3es, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Rosato, D.V., Rosato, D.V., and Rosato, M.G. (2000). Injection Molding Handbook, Springer.","DOI":"10.1007\/978-1-4615-4597-2"},{"key":"ref_2","unstructured":"Osswald, T.A., Turng, L.-S., and Gramann, P. (2007). Injection Molding Handbook, Hanser."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Kazmer, D.O. (2022). Injection Mold Design Engineering, Hanser Publishers. [3rd ed.].","DOI":"10.3139\/9781569908921.fm"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Gaspar-Cunha, A., Melo, J., Marques, T., and Pontes, A. (2025). A review on injection molding: Conformal cooling channels, modelling, surrogate models and multi-objective optimization. Polymers, 17.","DOI":"10.20944\/preprints202503.1555.v1"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Kanbur, B.B., Zhou, Y., Shen, S., and Duan, F. (2020). Neural network-integrated multiobjective optimization of 3D-printed conformal cooling channels. Proceedings of the 2020 5th International Conference on Smart and Sustainable Technologies (SpliTech), IEEE.","DOI":"10.23919\/SpliTech49282.2020.9243730"},{"key":"ref_6","first-page":"672","article-title":"Additive manufacturing of conformal cooling channels for injection mold tools: Current progress and challenges","volume":"21","author":"Chung","year":"2018","journal-title":"Addit. Manuf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3887","DOI":"10.1093\/bioinformatics\/bti634","article-title":"Non-linear PCA: A missing data approach","volume":"21","author":"Scholz","year":"2005","journal-title":"Bioinformatics"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1109\/TEVC.2013.2281535","article-title":"NSGA-III: An evolutionary many-objective optimization algorithm based on reference points","volume":"18","author":"Deb","year":"2014","journal-title":"IEEE Trans. Evol. 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[2nd ed.]."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"20150202","DOI":"10.1098\/rsta.2015.0202","article-title":"Principal component analysis: A review and recent developments","volume":"374","author":"Jolliffe","year":"2016","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_15","first-page":"18","article-title":"A multi-objective evolutionary algorithm using neural networks to approximate fitness evaluations","volume":"6","author":"Vieira","year":"2005","journal-title":"Int. J. Comput. Syst. Signals"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"201","DOI":"10.3795\/KSME-B.2019.43.3.201","article-title":"Effects of mold heat transfer coefficient on numerical simulation of injection molding","volume":"43","author":"Park","year":"2019","journal-title":"Trans. Korean Soc. Mech. Eng. B"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2029","DOI":"10.1016\/j.applthermaleng.2003.12.027","article-title":"Analysis of thermal contact resistance between polymer and mold in injection molding","volume":"24","author":"Bendada","year":"2004","journal-title":"Appl. Therm. Eng."},{"key":"ref_18","unstructured":"Chang, P. (2026, January 10). Quick Setting of Localized Heat Resistance Throughout the Molding Process. Moldex3D Blog, 4 January 2021. Available online: https:\/\/www.moldex3d.com\/blog\/tips-and-tricks\/quick-setting-of-localized-heat-resistance-throughout-the-molding-process\/."},{"key":"ref_19","unstructured":"Shawe-Taylor, J., Zemel, R., Bartlett, P., Pereira, F., and Weinberger, K.Q. (2011). Algorithms for Hyper-Parameter Optimization. Advances in Neural Information Processing Systems, Curran Associates, Inc."},{"key":"ref_20","unstructured":"Pereira, C., and Gaspar-Cunha, A. (2026, January 15). Surrogate-Assisted Multi-Objective Optimization of Conformal Cooling in Injection Molding. Available online: https:\/\/datarepositorium.uminho.pt\/dataset.xhtml?persistentId=doi:10.34622\/datarepositorium\/HUBDNN."}],"container-title":["Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-7390\/14\/5\/877\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T13:46:40Z","timestamp":1772718400000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-7390\/14\/5\/877"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,5]]},"references-count":20,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["math14050877"],"URL":"https:\/\/doi.org\/10.3390\/math14050877","relation":{},"ISSN":["2227-7390"],"issn-type":[{"value":"2227-7390","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,5]]}}}