{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T12:05:33Z","timestamp":1770897933495,"version":"3.50.1"},"publisher-location":"California","reference-count":0,"publisher":"International Joint Conferences on Artificial Intelligence Organization","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p>Recent neural heuristics for the Vehicle Routing Problem (VRP) primarily rely on node coordinates as input, which may be less effective in practical scenarios where real cost metrics\u2014such as edge-based distances\u2014are more relevant. To address this limitation, we introduce EFormer, an Edge-based Transformer model that uses edge as the sole input for VRPs. Our approach employs a precoder module with a mixed-score attention mechanism to convert edge information into temporary node embeddings. We also present a parallel encoding strategy characterized by a graph encoder and a node encoder, each responsible for processing graph and node embeddings in distinct feature spaces, respectively. This design yields a more comprehensive representation of the global relationships among edges. In the decoding phase, parallel context embedding and multi-query integration are used to compute separate attention mechanisms over the two encoded embeddings, facilitating efficient path construction. We train EFormer using reinforcement learning in an autoregressive manner. Extensive experiments on the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) reveal that EFormer outperforms established baselines on synthetic datasets, including large-scale and diverse distributions. Moreover, EFormer demonstrates strong generalization on real-world instances from TSPLib and CVRPLib. These findings confirm the effectiveness of EFormer\u2019s core design in solving VRPs.<\/jats:p>","DOI":"10.24963\/ijcai.2025\/954","type":"proceedings-article","created":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T08:10:40Z","timestamp":1758269440000},"page":"8582-8590","source":"Crossref","is-referenced-by-count":1,"title":["EFormer: An Effective Edge-based Transformer for Vehicle Routing Problems"],"prefix":"10.24963","author":[{"given":"Dian","family":"Meng","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Dalian University of Technology"},{"name":"Key Laboratory of Social Computing and Cognitive Intelligence (Dalian university of Technology), Ministry of Education, China"}]},{"given":"Zhiguang","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Computing and Information Systems, Singapore Management University"}]},{"given":"Yaoxin","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Innovation Sciences, Eindhoven University of Technology"}]},{"given":"Yaqing","family":"Hou","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Dalian University of Technology"},{"name":"Key Laboratory of Social Computing and Cognitive Intelligence (Dalian university of Technology), Ministry of Education, China"}]},{"given":"Hongwei","family":"Ge","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Dalian University of Technology"},{"name":"Key Laboratory of Social Computing and Cognitive Intelligence (Dalian university of Technology), Ministry of Education, China"}]},{"given":"Qiang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Dalian University of Technology"},{"name":"Key Laboratory of Social Computing and Cognitive Intelligence (Dalian university of Technology), Ministry of Education, China"}]}],"member":"10584","event":{"name":"Thirty-Fourth International Joint Conference on Artificial Intelligence {IJCAI-25}","theme":"Artificial Intelligence","location":"Montreal, Canada","acronym":"IJCAI-2025","number":"34","sponsor":["International Joint Conferences on Artificial Intelligence Organization (IJCAI)"],"start":{"date-parts":[[2025,8,16]]},"end":{"date-parts":[[2025,8,22]]}},"container-title":["Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence"],"original-title":[],"deposited":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T11:35:36Z","timestamp":1758627336000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ijcai.org\/proceedings\/2025\/954"}},"subtitle":[],"proceedings-subject":"Artificial Intelligence Research Articles","short-title":[],"issued":{"date-parts":[[2025,9]]},"references-count":0,"URL":"https:\/\/doi.org\/10.24963\/ijcai.2025\/954","relation":{},"subject":[],"published":{"date-parts":[[2025,9]]}}}