{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T10:50:15Z","timestamp":1761130215403,"version":"3.44.0"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2025,7,18]],"date-time":"2025-07-18T00:00:00Z","timestamp":1752796800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,7,18]],"date-time":"2025-07-18T00:00:00Z","timestamp":1752796800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62306201"],"award-info":[{"award-number":["62306201"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018542","name":"Natural Science Foundation of Sichuan Province","doi-asserted-by":"publisher","award":["2025ZNSFSC1466"],"award-info":[{"award-number":["2025ZNSFSC1466"]}],"id":[{"id":"10.13039\/501100018542","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2025,9]]},"DOI":"10.1007\/s40747-025-02018-0","type":"journal-article","created":{"date-parts":[[2025,7,18]],"date-time":"2025-07-18T07:12:27Z","timestamp":1752822747000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Learning to solving vehicle routing problems via local\u2013global feature fusion transformer"],"prefix":"10.1007","volume":"11","author":[{"given":"Wei","family":"Li","sequence":"first","affiliation":[]},{"given":"Bing Tian","family":"Dai","sequence":"additional","affiliation":[]},{"given":"Xueming","family":"Yan","sequence":"additional","affiliation":[]},{"given":"Junying","family":"Zou","sequence":"additional","affiliation":[]},{"given":"Zhijie","family":"Liang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8661-5695","authenticated-orcid":false,"given":"Jingwen","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,18]]},"reference":[{"key":"2018_CR1","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1007\/s10107-008-0218-9","volume":"120","author":"R Baldacci","year":"2009","unstructured":"Baldacci R, Mingozzi A (2009) A unified exact method for solving different classes of vehicle routing problems. Math Program 120:347\u2013380","journal-title":"Math Program"},{"key":"2018_CR2","unstructured":"Bello I, Pham H, Le QV et al (2017) Neural combinatorial optimization with reinforcement learning. In: 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24\u201326, 2017, Workshop Track Proceedings. OpenReview.net. https:\/\/openreview.net\/forum?id=Bk9mxlSFx"},{"issue":"1","key":"2018_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TCIAIG.2012.2186810","volume":"4","author":"CB Browne","year":"2012","unstructured":"Browne CB, Powley E, Whitehouse D et al (2012) A survey of Monte Carlo tree search methods. IEEE Trans Comput Intell AI Games 4(1):1\u201343. https:\/\/doi.org\/10.1109\/TCIAIG.2012.2186810","journal-title":"IEEE Trans Comput Intell AI Games"},{"key":"2018_CR4","doi-asserted-by":"crossref","unstructured":"Chen W, Men Y, Fuster N et al (2024) Artificial intelligence in logistics optimization with sustainable criteria: A review. Sustainability 16(21):9145","DOI":"10.3390\/su16219145"},{"key":"2018_CR5","unstructured":"Chen X, Tian Y (2019) Learning to perform local rewriting for combinatorial optimization. In: Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, December 8\u201314, 2019, Vancouver, BC, Canada, pp 6278\u20136289. https:\/\/proceedings.neurips.cc\/paper\/2019\/hash\/131f383b434fdf48079bff1e44e2d9a5-Abstract.html"},{"key":"2018_CR6","unstructured":"da Costa PRdO, Rhuggenaath J, Zhang Y et al (2020) Learning 2-opt heuristics for the traveling salesman problem via deep reinforcement learning. In: Proceedings of The 12th Asian Conference on Machine Learning, ACML 2020, 18\u201320 November 2020, Bangkok, Thailand, Proceedings of Machine Learning Research, vol 129. PMLR, pp 465\u2013480"},{"key":"2018_CR7","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/j.tre.2014.09.003","volume":"71","author":"\u00c1 Felipe","year":"2014","unstructured":"Felipe \u00c1, Ortu\u00f1o MT, Righini G et al (2014) A heuristic approach for the green vehicle routing problem with multiple technologies and partial recharges. Transp Res Part E Logist Transp Rev 71:111\u2013128","journal-title":"Transp Res Part E Logist Transp Rev"},{"issue":"9","key":"2018_CR8","doi-asserted-by":"publisher","first-page":"1150","DOI":"10.1057\/palgrave.jors.2602597","volume":"59","author":"R Fildes","year":"2008","unstructured":"Fildes R, Nikolopoulos K, Crone SF et al (2008) Forecasting and operational research: a review. J Oper Res Soc 59(9):1150\u20131172. https:\/\/doi.org\/10.1057\/palgrave.jors.2602597","journal-title":"J Oper Res Soc"},{"key":"2018_CR9","doi-asserted-by":"crossref","unstructured":"Gao C, Shang H, Xue K et al (2024) Towards generalizable neural solvers for vehicle routing problems via ensemble with transferrable local policy. In: Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence, IJCAI 2024, Jeju, South Korea, August 3\u20139, 2024. ijcai.org, pp 6914\u20136922","DOI":"10.24963\/ijcai.2024\/764"},{"key":"2018_CR10","doi-asserted-by":"crossref","unstructured":"Hastie T, Tibshirani R, Friedman J et al (2009) Overview of supervised learning. In: The elements of statistical learning: Data mining, inference, and prediction. Springer, New York, pp 9\u201341","DOI":"10.1007\/978-0-387-84858-7_2"},{"key":"2018_CR11","first-page":"966","volume-title":"An extension of the Lin\u2013Kernighan\u2013Helsgaun TSP solver for constrained traveling salesman and vehicle routing problems","author":"K Helsgaun","year":"2017","unstructured":"Helsgaun K (2017) An extension of the Lin\u2013Kernighan\u2013Helsgaun TSP solver for constrained traveling salesman and vehicle routing problems, vol 12. Roskilde University, Roskilde, pp 966\u2013980"},{"key":"2018_CR12","doi-asserted-by":"crossref","unstructured":"Hottung A, Tierney K (2020) Neural large neighborhood search for the capacitated vehicle routing problem. In: ECAI 2020. IOS Press, pp 443\u2013450","DOI":"10.3233\/FAIA200124"},{"key":"2018_CR13","unstructured":"Huang Z, Zhou J, Cao Z et al (2025) Rethinking light decoder-based solvers for vehicle routing problems. In: 13th International Conference on Learning Representations, ICLR 2025, Singapore, April 24\u201328, 2025, pp 27471\u201327491"},{"issue":"10","key":"2018_CR14","doi-asserted-by":"publisher","first-page":"10855","DOI":"10.1109\/TCYB.2021.3069942","volume":"52","author":"YH Jia","year":"2021","unstructured":"Jia YH, Mei Y, Zhang M (2021) A bilevel ant colony optimization algorithm for capacitated electric vehicle routing problem. IEEE Trans Cybern 52(10):10855\u201310868","journal-title":"IEEE Trans Cybern"},{"key":"2018_CR15","doi-asserted-by":"crossref","unstructured":"Jin Y, Ding Y, Pan X et al (2023) Pointerformer: Deep reinforced multi-pointer transformer for the traveling salesman problem. Proceedings of the AAAI Conference on Artificial Intelligence, Washington, DC, USA, February 7\u201314, 2023 37(7):8132\u20138140","DOI":"10.1609\/aaai.v37i7.25982"},{"issue":"1\u20132","key":"2018_CR16","first-page":"70","volume":"27","author":"CK Joshi","year":"2020","unstructured":"Joshi CK, Cappart Q, Rousseau LM (2020) Learning travelling salesperson problem requires rethinking generalization. Constraints An Int J 27(1\u20132):70\u201398","journal-title":"Constraints An Int J"},{"key":"2018_CR17","first-page":"225","volume":"7","author":"M J\u00fcnger","year":"1995","unstructured":"J\u00fcnger M, Reinelt G, Rinaldi G (1995) The traveling salesman problem. Handb Oper Res Manag Sci 7:225\u2013330","journal-title":"Handb Oper Res Manag Sci"},{"key":"2018_CR18","unstructured":"Khalil EB, Dai H, Zhang Y et al (2017) Learning combinatorial optimization algorithms over graphs. In: Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, December 4\u20139, 2017, Long Beach, CA, USA, pp 6348\u20136358"},{"key":"2018_CR19","first-page":"10418","volume":"34","author":"M Kim","year":"2021","unstructured":"Kim M, Park J et al (2021) Learning collaborative policies to solve NP-hard routing problems. Adv Neural Inf Process Syst 34:10418\u201310430","journal-title":"Adv Neural Inf Process Syst"},{"key":"2018_CR20","unstructured":"Kool W, van Hoof H, Welling M (2019) Attention, learn to solve routing problems! In: 7th International Conference on Learning Representations, ICLR 2019, New Orleans, LA, USA, May 6\u20139, 2019. OpenReview.net. https:\/\/openreview.net\/forum?id=ByxBFsRqYm"},{"key":"2018_CR21","unstructured":"Kwon Y, Choo J, Kim B et al (2020) POMO: policy optimization with multiple optima for reinforcement learning. In: Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6\u201312, 2020, virtual"},{"key":"2018_CR22","first-page":"5138","volume":"34","author":"YD Kwon","year":"2021","unstructured":"Kwon YD, Choo J, Yoon I et al (2021) Matrix encoding networks for neural combinatorial optimization. Adv Neural Inf Process Syst 34:5138\u20135149","journal-title":"Adv Neural Inf Process Syst"},{"issue":"7985","key":"2018_CR23","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1038\/s41586-023-06668-3","volume":"623","author":"BM Lake","year":"2023","unstructured":"Lake BM, Baroni M (2023) Human-like systematic generalization through a meta-learning neural network. Nature 623(7985):115\u2013121","journal-title":"Nature"},{"issue":"3","key":"2018_CR24","doi-asserted-by":"publisher","first-page":"1860","DOI":"10.1109\/TSG.2022.3142961","volume":"13","author":"H Li","year":"2022","unstructured":"Li H, He H (2022) Learning to operate distribution networks with safe deep reinforcement learning. IEEE Trans Smart Grid 13(3):1860\u20131872. https:\/\/doi.org\/10.1109\/TSG.2022.3142961","journal-title":"IEEE Trans Smart Grid"},{"key":"2018_CR25","unstructured":"Li H, Liu F, Zheng Z et\u00a0al (2024) CaDA: cross-problem routing solver with constraint-aware dual-attention. arXiv preprint. arXiv:2412.00346"},{"key":"2018_CR26","doi-asserted-by":"crossref","unstructured":"Li J, Ma Y, Cao Z et\u00a0al (2023) Learning feature embedding refiner for solving vehicle routing problems. IEEE Trans Neural Netw Learn Syst","DOI":"10.1109\/TNNLS.2023.3285077"},{"key":"2018_CR27","unstructured":"Lu H, Zhang X, Yang S (2020) A learning-based iterative method for solving vehicle routing problems. In: 8th International Conference on Learning Representations, ICLR 2020, Addis Ababa, Ethiopia, April 26\u201330, 2020. OpenReview.net. https:\/\/openreview.net\/forum?id=BJe1334YDH"},{"key":"2018_CR28","doi-asserted-by":"crossref","unstructured":"Manchanda S, Michel S, Drakulic D et\u00a0al (2022) On the generalization of neural combinatorial optimization heuristics. In: Joint European conference on machine learning and knowledge discovery in databases. Springer, Berlin, pp 426\u2013442","DOI":"10.1007\/978-3-031-26419-1_26"},{"key":"2018_CR29","doi-asserted-by":"publisher","unstructured":"Mentzer JT, DeWitt W, Keebler JS et al (2001) Defining supply chain management. J Bus Logist 22(2):1\u201325. https:\/\/doi.org\/10.1002\/j.2158-1592.2001.tb00001.x, https:\/\/onlinelibrary.wiley.com\/doi\/abs\/10.1002\/j.2158-1592.2001.tb00001.x","DOI":"10.1002\/j.2158-1592.2001.tb00001.x"},{"issue":"3","key":"2018_CR30","first-page":"66","volume":"4","author":"S Nanda Kumar","year":"2012","unstructured":"Nanda Kumar S, Panneerselvam R (2012) A survey on the vehicle routing problem and its variants. Intell Inf Manag 4(3):66\u201374","journal-title":"Intell Inf Manag"},{"key":"2018_CR31","unstructured":"Narayanan A, Misra P, Ojha A et al (2022) A reinforcement learning approach for electric vehicle routing problem with vehicle-to-grid supply. arXiv preprint arXiv:2204.05545"},{"key":"2018_CR32","unstructured":"Nazari M, Oroojlooy A, Snyder L et\u00a0al (2018) Reinforcement learning for solving the vehicle routing problem. In: Bengio S, Wallach H, Larochelle H et\u00a0al (eds) Advances in neural information processing systems, vol\u00a031. Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, December 3\u20138, 2018, Montr\u00e9al, Canada, pp 9861\u20139871"},{"issue":"7","key":"2018_CR33","doi-asserted-by":"publisher","first-page":"1613","DOI":"10.1068\/a4230","volume":"42","author":"T Neutens","year":"2010","unstructured":"Neutens T, Schwanen T, Witlox F et al (2010) Equity of urban service delivery: a comparison of different accessibility measures. Environ Plan A 42(7):1613\u20131635. https:\/\/doi.org\/10.1068\/a4230","journal-title":"Environ Plan A"},{"issue":"4","key":"2018_CR34","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1287\/ijoc.3.4.376","volume":"3","author":"G Reinelt","year":"1991","unstructured":"Reinelt G (1991) TSPLIB\u2014a traveling salesman problem library. ORSA J Comput 3(4):376\u2013384","journal-title":"ORSA J Comput"},{"key":"2018_CR35","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/s11721-007-0005-x","volume":"1","author":"AE Rizzoli","year":"2007","unstructured":"Rizzoli AE, Montemanni R, Lucibello E et al (2007) Ant colony optimization for real-world vehicle routing problems: from theory to applications. Swarm Intell 1:135\u2013151","journal-title":"Swarm Intell"},{"key":"2018_CR36","unstructured":"Sutskever I, Vinyals O, Le QV (2014) Sequence to sequence learning with neural networks. In: Advances in Neural Information Processing Systems 27: Annual Conference on Neural Information Processing Systems 2014, December 8\u201313 2014, Montreal, Quebec, Canada, pp 3104\u20133112"},{"issue":"3","key":"2018_CR37","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1016\/S0954-1810(01)00005-X","volume":"15","author":"KC Tan","year":"2001","unstructured":"Tan KC, Lee LH, Zhu Q et al (2001) Heuristic methods for vehicle routing problem with time windows. Artif Intell Eng 15(3):281\u2013295","journal-title":"Artif Intell Eng"},{"key":"2018_CR38","doi-asserted-by":"publisher","unstructured":"Uchoa E, Pecin D, Pessoa A et al (2017) New benchmark instances for the capacitated vehicle routing problem. Eur J Oper Res 257(3):845\u2013858. https:\/\/doi.org\/10.1016\/j.ejor.2016.08.012. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0377221716306270","DOI":"10.1016\/j.ejor.2016.08.012"},{"key":"2018_CR39","unstructured":"Vaswani A, Shazeer N, Parmar N et\u00a0al (2017) Attention is all you need. In: Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, December 4\u20139, 2017, Long Beach, CA, USA, pp 5998\u20136008"},{"key":"2018_CR40","unstructured":"Vinyals O, Fortunato M, Jaitly N (2015) Pointer networks. In: Advances in Neural Information Processing Systems 28: Annual Conference on Neural Information Processing Systems 2015, December 7\u201312, 2015, Montreal, Quebec, Canada, pp 2692\u20132700"},{"key":"2018_CR41","unstructured":"Wang C, Cheng P, Li J et\u00a0al (2024) Leader reward for POMO-based neural combinatorial optimization. arXiv preprint. arXiv:2405.13947"},{"issue":"6","key":"2018_CR42","doi-asserted-by":"publisher","first-page":"4644","DOI":"10.1109\/TPWRS.2020.2990179","volume":"35","author":"S Wang","year":"2020","unstructured":"Wang S, Duan J, Shi D et al (2020) A data-driven multi-agent autonomous voltage control framework using deep reinforcement learning. IEEE Trans Power Syst 35(6):4644\u20134654. https:\/\/doi.org\/10.1109\/TPWRS.2020.2990179","journal-title":"IEEE Trans Power Syst"},{"key":"2018_CR43","doi-asserted-by":"crossref","unstructured":"Wu F, He Z, Hu K, et\u00a0al (2024) Learning to solve single-batch-processing machine scheduling problem with two-dimensional packing constraints. Available at SSRN 4714938","DOI":"10.2139\/ssrn.4714938"},{"issue":"9","key":"2018_CR44","doi-asserted-by":"publisher","first-page":"5057","DOI":"10.1109\/TNNLS.2021.3068828","volume":"33","author":"Y Wu","year":"2021","unstructured":"Wu Y, Song W, Cao Z et al (2021) Learning improvement heuristics for solving routing problems. IEEE Trans Neural Netw Learn Syst 33(9):5057\u20135069","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"4","key":"2018_CR45","doi-asserted-by":"publisher","first-page":"1624","DOI":"10.1109\/TITS.2011.2158001","volume":"12","author":"J Zhang","year":"2011","unstructured":"Zhang J, Wang FY, Wang K et al (2011) Data-driven intelligent transportation systems: a survey. IEEE Trans Intell Transp Syst 12(4):1624\u20131639. https:\/\/doi.org\/10.1109\/TITS.2011.2158001","journal-title":"IEEE Trans Intell Transp Syst"},{"issue":"10","key":"2018_CR46","doi-asserted-by":"publisher","first-page":"7978","DOI":"10.1109\/TNNLS.2022.3148435","volume":"34","author":"Z Zhang","year":"2023","unstructured":"Zhang Z, Wu Z, Zhang H et al (2023) Meta-learning-based deep reinforcement learning for multiobjective optimization problems. IEEE Trans Neural Netw Learn Syst 34(10):7978\u20137991. https:\/\/doi.org\/10.1109\/TNNLS.2022.3148435","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"2018_CR47","unstructured":"Zheng Z, Yao S, Wang Z et\u00a0al (2024) DPN: decoupling partition and navigation for neural solvers of min-max vehicle routing problems. In: Proceedings of the 41st international conference on machine learning, pp 61559\u201361592"},{"key":"2018_CR48","unstructured":"Zheng Z, Zhou C, Tong X, et\u00a0al (2024) UDC: A unified neural divide-and-conquer framework for large-scale combinatorial optimization problems. In: Globerson A, Mackey L, Belgrave D, et\u00a0al (eds) Advances in Neural Information Processing Systems, vol\u00a038. Annual Conference on Neural Information Processing Systems 2024, NeurIPS 2024, Vancouver, BC, Canada, December 10\u201315, 2024"},{"key":"2018_CR49","unstructured":"Zhou C, Lin X, Wang Z et\u00a0al (2024) Instance-conditioned adaptation for large-scale generalization of neural combinatorial optimization. arXiv preprint. arXiv:2405.01906"},{"key":"2018_CR50","unstructured":"Zhou J, Wu Y, Song W et\u00a0al (2023) Towards omni-generalizable neural methods for vehicle routing problems. In: International Conference on Machine Learning, ICML 2023, 23\u201329 July 2023, Honolulu, Hawaii, USA, Proceedings of Machine Learning Research, vol 202. PMLR, pp 42769\u201342789"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-02018-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-025-02018-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-02018-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,7]],"date-time":"2025-09-07T13:56:23Z","timestamp":1757253383000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-025-02018-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,18]]},"references-count":50,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["2018"],"URL":"https:\/\/doi.org\/10.1007\/s40747-025-02018-0","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"type":"print","value":"2199-4536"},{"type":"electronic","value":"2198-6053"}],"subject":[],"published":{"date-parts":[[2025,7,18]]},"assertion":[{"value":"12 April 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 June 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 July 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"392"}}