{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T16:13:49Z","timestamp":1771949629907,"version":"3.50.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"17","license":[{"start":{"date-parts":[[2023,10,10]],"date-time":"2023-10-10T00:00:00Z","timestamp":1696896000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,10,10]],"date-time":"2023-10-10T00:00:00Z","timestamp":1696896000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2020YFA0907000"],"award-info":[{"award-number":["2020YFA0907000"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"ComputeX center, ICT, CAS"},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["32271297, 62072435, 82130055"],"award-info":[{"award-number":["32271297, 62072435, 82130055"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s00521-023-09042-6","type":"journal-article","created":{"date-parts":[[2023,10,10]],"date-time":"2023-10-10T15:02:33Z","timestamp":1696950153000},"page":"9687-9706","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["NeuralGLS: learning to guide local search with graph convolutional network for the traveling salesman problem"],"prefix":"10.1007","volume":"36","author":[{"given":"Jingyan","family":"Sui","sequence":"first","affiliation":[]},{"given":"Shizhe","family":"Ding","sequence":"additional","affiliation":[]},{"given":"Boyang","family":"Xia","sequence":"additional","affiliation":[]},{"given":"Ruizhi","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Dongbo","family":"Bu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,10,10]]},"reference":[{"key":"9042_CR1","doi-asserted-by":"publisher","unstructured":"La\u00a0Maire BFJ, Mladenov VM (2012) Comparison of neural networks for solving the travelling salesman problem. In: 11th symposium on neural network applications in electrical engineering, pp. 21\u201324. https:\/\/doi.org\/10.1109\/NEUREL.2012.6419953","DOI":"10.1109\/NEUREL.2012.6419953"},{"issue":"2","key":"9042_CR2","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/0377-2217(92)90138-Y","volume":"59","author":"G Laporte","year":"1992","unstructured":"Laporte G (1992) The traveling salesman problem: An overview of exact and approximate algorithms. Eur J Operat Res 59(2):231\u2013247. https:\/\/doi.org\/10.1016\/0377-2217(92)90138-Y","journal-title":"Eur J Operat Res"},{"key":"9042_CR3","doi-asserted-by":"publisher","unstructured":"Matai R, Singh S, Mittal ML (2010) Traveling salesman problem: an overview of applications, formulations, and solution approaches. In: Davendra D (ed) Traveling salesman problem. IntechOpen, Rijeka. Chap. 1. https:\/\/doi.org\/10.5772\/12909","DOI":"10.5772\/12909"},{"issue":"2","key":"9042_CR4","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1016\/j.ejor.2020.07.063","volume":"290","author":"Y Bengio","year":"2021","unstructured":"Bengio Y, Lodi A, Prouvost A (2021) Machine learning for combinatorial optimization: a methodological tour d\u2019horizon. Eur J Operat Res 290(2):405\u2013421. https:\/\/doi.org\/10.1016\/j.ejor.2020.07.063","journal-title":"Eur J Operat Res"},{"key":"9042_CR5","first-page":"56248","volume":"28","author":"O Vinyals","year":"2015","unstructured":"Vinyals O, Fortunato M, Jaitly N (2015) Pointer networks. Adv Neural Inf Process Syst 28:56248","journal-title":"Adv Neural Inf Process Syst"},{"key":"9042_CR6","doi-asserted-by":"publisher","unstructured":"Bello I, Pham H, Le QV, Norouzi M, Bengio S (2016) Neural combinatorial optimization with reinforcement learning. arXiv preprint arXiv:1611.09940. https:\/\/doi.org\/10.48550\/arXiv.1611.09940","DOI":"10.48550\/arXiv.1611.09940"},{"key":"9042_CR7","doi-asserted-by":"publisher","unstructured":"Dai H, Khalil EB, Zhang Y, Dilkina B, Song L (2017) Learning combinatorial optimization algorithms over graphs. arXiv preprint arXiv:1704.01665. https:\/\/doi.org\/10.48550\/arXiv.1704.01665","DOI":"10.48550\/arXiv.1704.01665"},{"key":"9042_CR8","doi-asserted-by":"crossref","unstructured":"Deudon M, Cournut P, Lacoste A, Adulyasak Y, Rousseau LM (2018) Learning heuristics for the tsp by policy gradient. In: International conference on the integration of constraint programming, artificial intelligence, and operations research. Springer, Singapore, pp 170\u2013181","DOI":"10.1007\/978-3-319-93031-2_12"},{"key":"9042_CR9","doi-asserted-by":"publisher","unstructured":"Kool W, Van\u00a0Hoof H, Welling M (2019) Attention, learn to solve routing problems! arXiv preprint arXiv:1803.08475. https:\/\/doi.org\/10.48550\/arXiv.1803.08475","DOI":"10.48550\/arXiv.1803.08475"},{"key":"9042_CR10","doi-asserted-by":"publisher","unstructured":"Ma Q, Ge S, He D, Thaker D, Drori I (2019) Combinatorial optimization by graph pointer networks and hierarchical reinforcement learning. arXiv preprint arXiv:1911.04936. https:\/\/doi.org\/10.48550\/arXiv.1911.04936","DOI":"10.48550\/arXiv.1911.04936"},{"key":"9042_CR11","first-page":"21188","volume":"33","author":"Y-D Kwon","year":"2020","unstructured":"Kwon Y-D, Choo J, Kim B, Yoon I, Gwon Y, Min S (2020) POMO: policy optimization with multiple optima for reinforcement learning. Adv Neural Inf Process Syst 33:21188\u201321198","journal-title":"Adv Neural Inf Process Syst"},{"issue":"10","key":"9042_CR12","doi-asserted-by":"publisher","first-page":"9730","DOI":"10.3934\/mbe.2022452","volume":"19","author":"Y Wang","year":"2022","unstructured":"Wang Y, Chen Z, Chen Z (2022) Dynamic graph conv-lstm model with dynamic positional encoding for the large-scale traveling salesman problem. Math Biosci Eng 19(10):9730\u20139748. https:\/\/doi.org\/10.3934\/mbe.2022452","journal-title":"Math Biosci Eng"},{"key":"9042_CR13","doi-asserted-by":"publisher","unstructured":"Wu Y, Song W, Cao Z, Zhang J, Lim A (2019) Learning improvement heuristics for solving routing problems. arXiv e-prints, 1912. https:\/\/doi.org\/10.48550\/arXiv.1912.05784","DOI":"10.48550\/arXiv.1912.05784"},{"key":"9042_CR14","doi-asserted-by":"crossref","unstructured":"d O\u00a0Costa PR, Rhuggenaath J, Zhang Y, Akcay A (2020) Learning 2-opt heuristics for the traveling salesman problem via deep reinforcement learning. In: Asian conference on machine learning. PMLR, pp 465\u2013480","DOI":"10.1007\/s42979-021-00779-2"},{"key":"9042_CR15","first-page":"11096","volume":"34","author":"Y Ma","year":"2021","unstructured":"Ma Y, Li J, Cao Z, Song W, Zhang L, Chen Z, Tang J (2021) Learning to iteratively solve routing problems with dual-aspect collaborative transformer. Adv Neural Inf Process Syst 34:11096\u201311107","journal-title":"Adv Neural Inf Process Syst"},{"key":"9042_CR16","unstructured":"Sui J, Ding S, Liu R, Xu L, Bu D (2021) Learning 3-opt heuristics for traveling salesman problem via deep reinforcement learning. In: Asian conference on machine learning. PMLR, pp 1301\u20131316"},{"key":"9042_CR17","doi-asserted-by":"publisher","unstructured":"Joshi CK, Laurent T, Bresson X (2019) An efficient graph convolutional network technique for the travelling salesman problem. arXiv preprint arXiv:1906.01227. https:\/\/doi.org\/10.48550\/arXiv.1906.01227","DOI":"10.48550\/arXiv.1906.01227"},{"key":"9042_CR18","doi-asserted-by":"publisher","unstructured":"Hudson B, Li Q, Malencia M, Prorok A (2021) Graph neural network guided local search for the traveling salesperson problem. In: International conference on learning representations. https:\/\/doi.org\/10.48550\/arXiv.2110.05291","DOI":"10.48550\/arXiv.2110.05291"},{"key":"9042_CR19","doi-asserted-by":"crossref","unstructured":"Fu Z, Qiu K, Zha H (2021) Generalize a small pre-trained model to arbitrarily large TSP instances. In: Proceedings of the AAAI conference on artificial intelligence, vol 35, pp 7474\u20137482","DOI":"10.1609\/aaai.v35i8.16916"},{"key":"9042_CR20","first-page":"7472","volume":"34","author":"L Xin","year":"2021","unstructured":"Xin L, Song W, Cao Z, Zhang J (2021) Neurolkh: combining deep learning model with Lin-Kernighan-Helsgaun heuristic for solving the traveling salesman problem. Adv Neural Inf Process Syst 34:7472\u20137483","journal-title":"Adv Neural Inf Process Syst"},{"issue":"12","key":"9042_CR21","doi-asserted-by":"publisher","first-page":"5408","DOI":"10.1109\/TCAD.2022.3164330","volume":"41","author":"S Sanyal","year":"2022","unstructured":"Sanyal S, Roy K (2022) Neuro-ising: accelerating large-scale traveling salesman problems via graph neural network guided localized ising solvers. IEEE Trans Comput Aided Design Integr Circ Syst 41(12):5408\u20135420. https:\/\/doi.org\/10.1109\/TCAD.2022.3164330","journal-title":"IEEE Trans Comput Aided Design Integr Circ Syst"},{"key":"9042_CR22","doi-asserted-by":"publisher","first-page":"110144","DOI":"10.1016\/j.knosys.2022.110144","volume":"260","author":"J Zheng","year":"2023","unstructured":"Zheng J, He K, Zhou J, Jin Y, Li C-M (2023) Reinforced Lin-Kernighan-Helsgaun algorithms for the traveling salesman problems. Knowl Based Syst 260:110144. https:\/\/doi.org\/10.1016\/j.knosys.2022.110144","journal-title":"Knowl Based Syst"},{"issue":"4","key":"9042_CR23","first-page":"393","volume":"2","author":"G Dantzig","year":"1954","unstructured":"Dantzig G, Fulkerson R, Johnson S (1954) Solution of a large-scale traveling-salesman problem. J Operat Res Soc Am 2(4):393\u2013410","journal-title":"J Operat Res Soc Am"},{"issue":"1","key":"9042_CR24","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1137\/0110015","volume":"10","author":"M Held","year":"1962","unstructured":"Held M, Karp RM (1962) A dynamic programming approach to sequencing problems. J Soc Indust Appl Math 10(1):196\u2013210","journal-title":"J Soc Indust Appl Math"},{"key":"9042_CR25","unstructured":"Applegate D, Bixby R, Chvatal V, Cook W (2006) Concorde TSP solver"},{"issue":"3","key":"9042_CR26","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1137\/0206041","volume":"6","author":"DJ Rosenkrantz","year":"1977","unstructured":"Rosenkrantz DJ, Stearns RE, Lewis PM II (1977) An analysis of several heuristics for the traveling salesman problem. SIAM J Comput 6(3):563\u2013581. https:\/\/doi.org\/10.1137\/0206041","journal-title":"SIAM J Comput"},{"key":"9042_CR27","unstructured":"Cook, W.J.. (2011) In Pursuit of the traveling salesman: mathematics at the limits of computation. Princeton University Press, Princeton"},{"issue":"1","key":"9042_CR28","first-page":"215","volume":"1","author":"DS Johnson","year":"1997","unstructured":"Johnson DS, McGeoch LA (1997) The traveling salesman problem: a case study in local optimization. Local Search Comb Optim 1(1):215\u2013310","journal-title":"Local Search Comb Optim"},{"key":"9042_CR29","doi-asserted-by":"publisher","unstructured":"Gutin G, Punnen AP (2006) The traveling salesman problem and its variations, vol 12. Springer, New York. https:\/\/doi.org\/10.1007\/b101971","DOI":"10.1007\/b101971"},{"key":"9042_CR30","unstructured":"Helsgaun K (2017) An extension of the Lin-Kernighan-Helsgaun TSP solver for constrained traveling salesman and vehicle routing problems. Roskilde University, Roskilde, p 12"},{"key":"9042_CR31","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s001090000086","volume":"8","author":"RJ Williams","year":"1992","unstructured":"Williams RJ (1992) Simple statistical gradient-following algorithms for connectionist reinforcement learning. Mach Learn 8:229\u2013256. https:\/\/doi.org\/10.1007\/s001090000086","journal-title":"Mach Learn"},{"key":"9042_CR32","unstructured":"Mnih V, Kavukcuoglu K, Silver D, Graves A, Antonoglou I, Wierstra D, Riedmiller M (2013) Playing Atari with deep reinforcement learning. arXiv preprint arXiv:1312.5602"},{"key":"9042_CR33","volume":"30","author":"A Vaswani","year":"2017","unstructured":"Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez AN, Kaiser \u0141, Polosukhin I (2017) Attention is all you need. Adv Neural Inf Process Syst 30:462317","journal-title":"Adv Neural Inf Process Syst"},{"key":"9042_CR34","doi-asserted-by":"publisher","unstructured":"Veli\u010dkovi\u0107 P, Cucurull G, Casanova A, Romero A, Li\u00f2 P, Bengio Y. Graph attention networks. In: International conference on learning representations. https:\/\/doi.org\/10.48550\/arXiv.1710.10903","DOI":"10.48550\/arXiv.1710.10903"},{"key":"9042_CR35","first-page":"00085","volume":"38","author":"C Nilsson","year":"2003","unstructured":"Nilsson C (2003) Heuristics for the traveling salesman problem. Linkop Univ 38:00085\u20139","journal-title":"Linkop Univ"},{"key":"9042_CR36","doi-asserted-by":"crossref","unstructured":"Perez E, Strub F, De\u00a0Vries H, Dumoulin V, Courville A (2018) Film: Visual reasoning with a general conditioning layer. In: Proceedings of the AAAI conference on artificial intelligence, vol 32","DOI":"10.1609\/aaai.v32i1.11671"},{"issue":"2","key":"9042_CR37","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1016\/S0377-2217(98)00099-X","volume":"113","author":"C Voudouris","year":"1999","unstructured":"Voudouris C, Tsang E (1999) Guided local search and its application to the traveling salesman problem. Eur J Operat Res 113(2):469\u2013499. https:\/\/doi.org\/10.1016\/S0377-2217(98)00099-X","journal-title":"Eur J Operat Res"},{"key":"9042_CR38","doi-asserted-by":"publisher","unstructured":"Kingma DP, Ba J (2014) Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980. https:\/\/doi.org\/10.48550\/arXiv.1412.6980","DOI":"10.48550\/arXiv.1412.6980"},{"issue":"4","key":"9042_CR39","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"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-023-09042-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-023-09042-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-023-09042-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,27]],"date-time":"2024-05-27T08:08:02Z","timestamp":1716797282000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-023-09042-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,10]]},"references-count":39,"journal-issue":{"issue":"17","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["9042"],"URL":"https:\/\/doi.org\/10.1007\/s00521-023-09042-6","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,10]]},"assertion":[{"value":"17 March 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 September 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 October 2023","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 have no conflict of interests to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}