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Nonetheless, challenges persist in attaining both high learning efficiency and optimal solution quality. To address this issue, we propose a novel multi-objective optimization algorithm grounded in information geometry and machine learning principles, which integrates adaptive gradient descent with meta-reinforcement learning techniques to effectively tackle MOCOPs. In this paper, we present a meta-learning framework aimed at enhancing model performance in multi-objective combinatorial optimization through tensor remodeling, preconditioned gradient descent, and entropy regularization strategies. Experimental results demonstrate that the proposed method yields significant performance improvements across several classic multi-objective combinatorial optimization challenges, including the Multi-objective Traveling Salesman Problem (MOTSP), Multi-objective Vehicle Routing Problem (MOCVRP), and Multi-objective Knapsack Problem (MOKP).<\/jats:p>","DOI":"10.1177\/17248035251388509","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T17:36:47Z","timestamp":1762191407000},"page":"53-66","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Adaptive Geometry Based Meta-Learning for Multi-Objective Combinatorial Optimization Problems"],"prefix":"10.1177","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1821-0204","authenticated-orcid":false,"given":"Fangzhen","family":"Ge","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Huaibei Normal University, Anhui, China"},{"name":"Anhui Engineering Research Center for Intelligent Computing and Application on Cognitive Behavior (ICACB), Anhui, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-6562-1809","authenticated-orcid":false,"given":"Mingshi","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Huaibei Normal University, Anhui, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Debao","family":"Chen","sequence":"additional","affiliation":[{"name":"Anhui Engineering Research Center for Intelligent Computing and Application on Cognitive Behavior (ICACB), Anhui, China"},{"name":"School of Physics and Electronic Information, Huaibei Normal University, Huaibei, Anhui, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Longfeng","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Huaibei Normal University, Anhui, China"},{"name":"Anhui Engineering Research Center for Intelligent Computing and Application on Cognitive Behavior (ICACB), Anhui, China"},{"name":"Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Huaibei, Anhui, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huaiyu","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Huaibei Normal University, Anhui, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2025,11,3]]},"reference":[{"key":"e_1_3_3_2_1","doi-asserted-by":"publisher","DOI":"10.1162\/089976698300017746"},{"key":"e_1_3_3_3_1","unstructured":"Amari S. 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