{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T09:45:14Z","timestamp":1781343914839,"version":"3.54.1"},"reference-count":51,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2022,2,3]],"date-time":"2022-02-03T00:00:00Z","timestamp":1643846400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,2,3]],"date-time":"2022-02-03T00:00:00Z","timestamp":1643846400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. & Cyber."],"published-print":{"date-parts":[[2022,8]]},"DOI":"10.1007\/s13042-022-01516-8","type":"journal-article","created":{"date-parts":[[2022,2,3]],"date-time":"2022-02-03T03:02:53Z","timestamp":1643857373000},"page":"2213-2228","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Learning to optimise general TSP instances"],"prefix":"10.1007","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2919-238X","authenticated-orcid":false,"given":"Nasrin","family":"Sultana","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jeffrey","family":"Chan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tabinda","family":"Sarwar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A. K.","family":"Qin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,2,3]]},"reference":[{"key":"1516_CR1","unstructured":"Applegate DL, Bixby RE, Chvatal V, Cook WJ (2006) The traveling salesman problem: a computational study. Princeton university press,"},{"key":"1516_CR2","unstructured":"Nicos Christofides (1976) Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report, Carnegie-Mellon Univ Pittsburgh Pa Management Sciences Research Group"},{"key":"1516_CR3","first-page":"457474","volume":"2","author":"E Burke","year":"2003","unstructured":"Burke E, Hart E, Kendall G, Newall J, Ross P, Shulenburg S (2003) An emerging direction in modern search technology. Handbook Metaheuristics 2:457474","journal-title":"Handbook Metaheuristics"},{"issue":"7553","key":"1516_CR4","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1038\/nature14539","volume":"521","author":"Yann LeCun","year":"2015","unstructured":"LeCun Yann, Bengio Yoshua, Hinton Geoffrey (2015) Deep learning. Nature 521(7553):436\u2013444","journal-title":"Nature"},{"key":"1516_CR5","unstructured":"Li Ke, Malik Jitendra (2017) Learning to optimize neural nets. arXiv preprint arXiv: 1703.00441,"},{"key":"1516_CR6","unstructured":"Oriol Vinyals, Meire Fortunato, Navdeep Jaitly (2015) Pointer networks. In: Advances in Neural Information Processing Systems, pages 2692\u20132700"},{"key":"1516_CR7","unstructured":"Irwan B, Hieu P, Quoc VL, Mohammad N, Samy B (2016) Neural combinatorial optimization with reinforcement learning. arXiv preprintarXiv:1611.09940,"},{"key":"1516_CR8","doi-asserted-by":"crossref","unstructured":"Michel D, Pierre C, Alexandre L, Yossiri Adulyasak, Louis-Martin Rousseau (2018) Learning heuristics for the tsp by policy gradient. In: International conference on the integration of constraint programming, artificial intelligence, and operations research, pages 170\u2013181. Springer,","DOI":"10.1007\/978-3-319-93031-2_12"},{"key":"1516_CR9","unstructured":"WWM Kool, M\u00a0Welling (2018) Attention solves your tsp. arXiv preprint arXiv:1803.08475,"},{"key":"1516_CR10","unstructured":"Yeong-Dae K, Jinho C, Byoungjip K, Iljoo Y, Seungjai M, Youngjune Gwon (2020) Pomo: Policy optimization with multiple optima for reinforcement learning. arXiv preprint arXiv: 2010.16011,"},{"key":"1516_CR11","doi-asserted-by":"crossref","unstructured":"Nasrin S, Jeffrey C, Tabinda S, Qin AK (2021) Learning to optimise routing problems using policy optimisation. In: 2021 international joint conference on neural networks (IJCNN), pages 1\u20138. IEEE,","DOI":"10.1109\/IJCNN52387.2021.9534010"},{"key":"1516_CR12","unstructured":"Pablo M, Norman MG (1994) An analysis of the performance of traveling salesman heuristics on infinite-size fractal instances in the euclidean plane. ORSA J Comput,"},{"key":"1516_CR13","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1016\/j.asoc.2018.07.010","volume":"71","author":"Miguel C\u00e1rdenas-Montes","year":"2018","unstructured":"C\u00e1rdenas-Montes Miguel (2018) Creating hard-to-solve instances of travelling salesman problem. Appl Soft Comput 71:268\u2013276","journal-title":"Appl Soft Comput"},{"key":"1516_CR14","unstructured":"Thomas F, Thomas S, Holger H, Peter M (2005) An analysis of the hardness of tsp instances for two high performance algorithms. In: Proceedings of the Sixth Metaheuristics International Conference, pages 361\u2013367,"},{"key":"1516_CR15","unstructured":"Matthew C (2018) A comparison of exact and heuristic algorithms to solve the travelling salesman problem. Univ Plymouth J"},{"issue":"4","key":"1516_CR16","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1287\/ijoc.3.4.376","volume":"3","author":"Gerhard Reinelt","year":"1991","unstructured":"Reinelt Gerhard (1991) Tsplib-a traveling salesman problem library. ORSA J Comput 3(4):376\u2013384","journal-title":"ORSA J Comput"},{"key":"1516_CR17","unstructured":"David A (2006) Ribert Bixby, Vasek Chvatal, William Cook (2006) Concorde tsp solver,"},{"key":"1516_CR18","unstructured":"Chaitanya\u00a0KJ, Thomas L, Xavier B ( 2019) An efficient graph convolutional network technique for the travelling salesman problem. arXiv preprintarXiv:1906.01227,"},{"key":"1516_CR19","unstructured":"Yousof HK (2001) On the solution of the traveling salesman problem: a novel heuristic that uses frequency of anchored nearest neighbors. Master\u2019s thesis, Arizona State University"},{"issue":"10","key":"1516_CR20","first-page":"1995","volume":"3361","author":"Yann LeCun","year":"1995","unstructured":"LeCun Yann, Bengio Yoshua et al (1995) Convolutional networks for images, speech, and time series. Handbook Brain Theory Neural Netw 3361(10):1995","journal-title":"Handbook Brain Theory Neural Netw"},{"key":"1516_CR21","doi-asserted-by":"crossref","unstructured":"Saad Albawi, Tareq\u00a0Abed Mohammed, Saad Al-Zawi (2017) Understanding of a convolutional neural network. In: 2017 international conference on engineering and technology (ICET), pages 1\u20136. Ieee,","DOI":"10.1109\/ICEngTechnol.2017.8308186"},{"issue":"4","key":"1516_CR22","doi-asserted-by":"publisher","first-page":"699","DOI":"10.1287\/opre.14.4.699","volume":"14","author":"Eugene L Lawler","year":"1966","unstructured":"Lawler Eugene L, Wood David E (1966) Branch-and-bound methods: a survey. Oper Res 14(4):699\u2013719","journal-title":"Oper Res"},{"issue":"1","key":"1516_CR23","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/S0377-2217(99)00284-2","volume":"126","author":"Keld Helsgaun","year":"2000","unstructured":"Helsgaun Keld (2000) An effective implementation of the lin-kernighan traveling salesman heuristic. Euro J Oper Res 126(1):106\u2013130","journal-title":"Euro J Oper Res"},{"issue":"1","key":"1516_CR24","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s10479-005-3971-7","volume":"140","author":"Michel Gendreau","year":"2005","unstructured":"Gendreau Michel, Potvin Jean-Yves (2005) Metaheuristics in combinatorial optimization. Ann Oper Res 140(1):189\u2013213","journal-title":"Ann Oper Res"},{"key":"1516_CR25","unstructured":"Laurent P, Vincent F (2015). Or-tools"},{"key":"1516_CR26","unstructured":"Elias K, Hanjun D, Yuyu Z, Bistra D, Le S (2017) Learning combinatorial optimization algorithms over graphs. In Advances in neural information processing systems, pages 6348\u20136358,"},{"key":"1516_CR27","unstructured":"Ashish V, Noam S, Niki P, Jakob U, Llion J, Aidan NG, \u0141ukasz K, Illia P (2017) Attention is all you need. In: Advances in neural information processing systems, pages 5998\u20136008,"},{"key":"1516_CR28","unstructured":"Zonghan W, Shirui P, Fengwen C, Guodong L, Chengqi Z, S YP (2020) A comprehensive survey on graph neural networks. IEEE Transactions on Neural Networks and Learning Systems"},{"key":"1516_CR29","doi-asserted-by":"publisher","first-page":"108418","DOI":"10.1109\/ACCESS.2020.3000236","volume":"8","author":"Zhihao Xing","year":"2020","unstructured":"Xing Zhihao, Shikui Tu (2020) A graph neural network assisted monte carlo tree search approach to traveling salesman problem. IEEE Access 8:108418\u2013108428","journal-title":"IEEE Access"},{"key":"1516_CR30","unstructured":"Yaoxin W, Wen S, Zhiguang C, Jie Z, Andrew L (2021) Learning improvement heuristics for solving routing problems. IEEE transactions on neural networks and learning systems"},{"key":"1516_CR31","unstructured":"Paulo R de\u00a0O da\u00a0Costa, Jason R, Yingqian Z, Alp A ( 2020) Learning 2-opt heuristics for the traveling salesman problem via deep reinforcement learning. arXiv preprintarXiv:2004.01608,"},{"key":"1516_CR32","unstructured":"Ruffa AA (2007) A novel solution to the att48 benchmark problem. arXiv preprint arXiv: 0710.0539"},{"key":"1516_CR33","unstructured":"Caldwell JR, Watson RA, Thies C, Knowles JD (2018) Deep optimisation: Solving combinatorial optimisation problems using deep neural networks. arXiv preprint arXiv: 1811.00784,"},{"issue":"5","key":"1516_CR34","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1002\/cplx.6130010511","volume":"1","author":"G Macready William","year":"1996","unstructured":"Macready William G, Wolpert David H (1996) What makes an optimization problem hand? Complexity 1(5):40\u201346","journal-title":"Complexity"},{"key":"1516_CR35","doi-asserted-by":"crossref","unstructured":"Kate S-M, van Hemert V, Xin YL (2010) Understanding tsp difficulty by learning from evolved instances. In: International conference on learning and intelligent optimization, pages 266\u2013280. Springer,","DOI":"10.1007\/978-3-642-13800-3_29"},{"issue":"1","key":"1516_CR36","doi-asserted-by":"publisher","first-page":"38","DOI":"10.2307\/2309088","volume":"64","author":"C Carl Robusto","year":"1957","unstructured":"Carl Robusto C (1957) The cosine-haversine formula. Am Math Mon 64(1):38\u201340","journal-title":"Am Math Mon"},{"key":"1516_CR37","first-page":"4731","volume":"33","author":"M Prates","year":"2019","unstructured":"Prates M, Avelar PHC, Lemos H, Lamb LC, Vardi Moshe Y (2019) Learning to solve np-complete problems: a graph neural network for decision tsp. Proc AAAI Conf Artificial Intell 33:4731\u20134738","journal-title":"Proc AAAI Conf Artificial Intell"},{"key":"1516_CR38","unstructured":"Gerhard R (1995) Tsplib95. Interdisziplin\u00e4res Zentrum f\u00fcr Wissenschaftliches Rechnen (IWR), Heidelberg, 338,"},{"key":"1516_CR39","doi-asserted-by":"crossref","unstructured":"Rennie SJ , Marcheret E, Mroueh Y, Ross J, Goel V (2017) Self-critical sequence training for image captioning. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7008\u20137024,","DOI":"10.1109\/CVPR.2017.131"},{"key":"1516_CR40","unstructured":"Souza LC, Usberti FL, T\u00e9cnico-IC-PFG Relat\u00f3rio , Final de\u00a0Gradua\u00e7\u00e3o Projeto(2019) Two-stage stochastic traveling salesman problem with evolutionary framework. Inst. de Computa\u00e7\u00e3o,"},{"issue":"1\u20132","key":"1516_CR41","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1016\/S0004-3702(96)00030-6","volume":"88","author":"Ian P Gent","year":"1996","unstructured":"Gent Ian P, Walsh Toby (1996) The tsp phase transition. Artificial Intell 88(1\u20132):349\u2013358","journal-title":"Artificial Intell"},{"issue":"8","key":"1516_CR42","doi-asserted-by":"publisher","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","volume":"9","author":"S Hochreiter","year":"1997","unstructured":"Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735\u20131780","journal-title":"Neural Comput"},{"key":"1516_CR43","unstructured":"Dzmitry B, Kyunghyun C, Yoshua B (2014) Neural machine translation by jointly learning to align and translate. arXiv preprint arXiv: 1409.0473"},{"key":"1516_CR44","unstructured":"Xavier B ,Thomas L (2021). The transformer network for the traveling salesman problem. arXiv preprint arXiv:2103.03012,"},{"key":"1516_CR45","unstructured":"Wouter K, Herke van H, Joaquim G, Max W (2021) Deep policy dynamic programming for vehicle routing problems. arXiv preprint arXiv:2102.11756,"},{"key":"1516_CR46","unstructured":"Nasrin S, Jeffrey C, Tabinda S, Babak A, Qin AK (2021) Learning enhanced optimisation for routing problems. arXiv preprintarXiv:2109.08345,"},{"key":"1516_CR47","unstructured":"Kingma DP, Adam JB (2014) A method for stochastic optimization. arXiv preprintarXiv:1412.6980,"},{"key":"1516_CR48","unstructured":"Bresson X , Laurent T ( 2018) An experimental study of neural networks for variable graphs. Arxiv,"},{"key":"1516_CR49","unstructured":"Yoshua B, Andrea L, Antoine P (2020) Machine learning for combinatorial optimization: a methodological tour d\u2019horizon. Euro J Oper Res"},{"key":"1516_CR50","unstructured":"Hao L, Xingwen Z, Shuang Y (2019) A learning-based iterative method for solving vehicle routing problems. In: International conference on learning representations"},{"key":"1516_CR51","unstructured":"Li Z, Quanhong W, Haihua L, Yong Z (2019) End-to-end learning of multi-scale convolutional neural network for stereo matching. arXiv preprint arXiv:1906.10399"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-022-01516-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13042-022-01516-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-022-01516-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,17]],"date-time":"2024-09-17T20:20:35Z","timestamp":1726604435000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13042-022-01516-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,3]]},"references-count":51,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["1516"],"URL":"https:\/\/doi.org\/10.1007\/s13042-022-01516-8","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"value":"1868-8071","type":"print"},{"value":"1868-808X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,3]]},"assertion":[{"value":"28 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 February 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}