{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T13:15:58Z","timestamp":1778159758558,"version":"3.51.4"},"reference-count":46,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"12","license":[{"start":{"date-parts":[[2024,12,1]],"date-time":"2024-12-01T00:00:00Z","timestamp":1733011200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2024,12,1]],"date-time":"2024-12-01T00:00:00Z","timestamp":1733011200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2024,12,1]],"date-time":"2024-12-01T00:00:00Z","timestamp":1733011200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"name":"National Key R&D Project of China","award":["2020YFA0714300"],"award-info":[{"award-number":["2020YFA0714300"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62473098"],"award-info":[{"award-number":["62473098"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62203108"],"award-info":[{"award-number":["62203108"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Jiangsu Province Excellent Postdoctoral Program","award":["2022ZB131"],"award-info":[{"award-number":["2022ZB131"]}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2022M720720"],"award-info":[{"award-number":["2022M720720"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2023T160105"],"award-info":[{"award-number":["2023T160105"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Artif. Intell."],"published-print":{"date-parts":[[2024,12]]},"DOI":"10.1109\/tai.2024.3461630","type":"journal-article","created":{"date-parts":[[2024,9,19]],"date-time":"2024-09-19T13:32:23Z","timestamp":1726752743000},"page":"6699-6708","source":"Crossref","is-referenced-by-count":14,"title":["Reinforcement Learning for Solving Colored Traveling Salesman Problems: An Entropy-Insensitive Attention Approach"],"prefix":"10.1109","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-8591-5741","authenticated-orcid":false,"given":"Tianyu","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Cyber Science and Engineering, Southeast University, Nanjing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4443-608X","authenticated-orcid":false,"given":"Xinli","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Cyber Science and Engineering, Southeast University, Nanjing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8676-0195","authenticated-orcid":false,"given":"Xiangping","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mathematics, Southeast University, Nanjing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3133-7119","authenticated-orcid":false,"given":"Jinde","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Mathematics, Southeast University, Nanjing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2004.10.004"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/tits.2018.2808179"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2017.12.031"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2014.2371918"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/JAS.2017.7510415"},{"key":"ref6","article-title":"Application of colored traveling salesman problems into scheduling and coordination of multiple material handling robots","author":"Wang","year":"2019"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.3182\/20140824-6-ZA-1003.01403"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/tsmc.2016.2591267"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TITS.2017.2706720"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TITS.2020.2972389"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v35i8.16916"},{"key":"ref12","article-title":"Learning a latent search space for routing problems using variational autoencoders","volume-title":"Proc. Int. Conf. Learn. Represent.","author":"Hottung","year":"2021"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2021.3068828"},{"key":"ref14","first-page":"465","article-title":"Learning 2-opt heuristics for the traveling salesman problem via deep rein forcement learning","volume-title":"Proc. Asian Conf. Mach. Learn.","author":"Costa","year":"2020"},{"key":"ref15","article-title":"Neural combinatorial optimization with reinforcement learning","author":"Bello","year":"2016"},{"key":"ref16","article-title":"Attention, learn to solve routing problems","volume-title":"Proc. Int. Conf. Learn. Represent.","author":"Kool","year":"2019"},{"key":"ref17","first-page":"9861","article-title":"Reinforcement learning for solving the vehicle routing problem","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","volume":"31","author":"Nazari","year":"2018"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/TAI.2023.3297988"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2024.111652"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2023.3329530"},{"key":"ref21","first-page":"2692","article-title":"Pointer networks","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","volume":"28","author":"Vinyals","year":"2015"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.48550\/ARXIV.1706.03762"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v35i13.17430"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2023.05.003"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/TITS.2020.3003163"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/TAI.2021.3087666"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1145\/321043.321046"},{"key":"ref28","volume-title":"Reinforcement Learning: An Introduction","author":"Sutton","year":"2018"},{"key":"ref29","article-title":"Train short, test long: Attention with linear biases enables input length extrapolation","author":"Press","year":"2021"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.18653\/v1\/2023.acl-long.816"},{"key":"ref31","article-title":"Consider the scale operation in attention mechanism from the perspective of entropy invariance","author":"Su","year":"2021"},{"key":"ref32","first-page":"7487","article-title":"Stabilizing transformers for reinforcement learning","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Parisotto","year":"2020"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/BF00992696"},{"key":"ref35","article-title":"Adam: A method for stochastic optimization","volume-title":"Proc. Int. Conf. Learn. Represent.","author":"Kingma","year":"2014"},{"key":"ref36","article-title":"Gurobi optimizer reference manual","author":"Gurobi Optimization","year":"2023"},{"key":"ref37","article-title":"Or-tools","author":"Perron","year":"2023"},{"key":"ref38","article-title":"Cardinal optimizer (COPT) user guide","author":"Ge","year":"2022"},{"key":"ref39","article-title":"The SCIP optimization suite 8.0","author":"Bestuzheva","year":"2021"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-91086-4_4"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1109\/TITS.2016.2542264"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1166\/jctn.2009.1230"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1109\/IITSI.2010.144"},{"key":"ref44","first-page":"86","article-title":"Nearest neighbor insertion algorithm for solving capacitated vehicle routing problem","volume-title":"Proc. 2nd Int. Conf. Comput. Sustain. Global Develop. (INDIACom)","author":"Joshi","year":"2015"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1109\/TAI.2024.3452678"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2024.106432"}],"container-title":["IEEE Transactions on Artificial Intelligence"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/9078688\/10794552\/10684320.pdf?arnumber=10684320","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,23]],"date-time":"2025-08-23T01:09:23Z","timestamp":1755911363000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/10684320\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12]]},"references-count":46,"journal-issue":{"issue":"12"},"URL":"https:\/\/doi.org\/10.1109\/tai.2024.3461630","relation":{},"ISSN":["2691-4581"],"issn-type":[{"value":"2691-4581","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12]]}}}