{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T09:20:33Z","timestamp":1773480033483,"version":"3.50.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2022,6,20]],"date-time":"2022-06-20T00:00:00Z","timestamp":1655683200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,6,20]],"date-time":"2022-06-20T00:00:00Z","timestamp":1655683200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71971041"],"award-info":[{"award-number":["71971041"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Outstanding Young Scientific and Technological Talents Foundation of Sichuan Province","award":["2020JDJQ0035"],"award-info":[{"award-number":["2020JDJQ0035"]}]},{"name":"Major Program of National Social Science Foundation of China","award":["20&ZD084"],"award-info":[{"award-number":["20&ZD084"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2024,8]]},"DOI":"10.1007\/s10479-022-04788-z","type":"journal-article","created":{"date-parts":[[2022,6,20]],"date-time":"2022-06-20T10:04:07Z","timestamp":1655719447000},"page":"517-536","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["An improved transformer model with multi-head attention and attention to attention for low-carbon multi-depot vehicle routing problem"],"prefix":"10.1007","volume":"339","author":[{"given":"Yang","family":"Zou","sequence":"first","affiliation":[]},{"given":"Hecheng","family":"Wu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5761-6680","authenticated-orcid":false,"given":"Yunqiang","family":"Yin","sequence":"additional","affiliation":[]},{"given":"Lalitha","family":"Dhamotharan","sequence":"additional","affiliation":[]},{"given":"Daqiang","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Aviral Kumar","family":"Tiwari","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,6,20]]},"reference":[{"key":"4788_CR1","unstructured":"Bello, I., Pham, H., Le, Q.V. et al. (2019). Neural combinatorial optimization with reinforcement learning. In 5th International conference on learning representations, ICLR 2017\u2014Workshop track proceedings."},{"key":"4788_CR2","doi-asserted-by":"crossref","unstructured":"Bock, S., & Wei, M. G. (2019, July). A proof of local convergence for the Adam optimizer. In 2019 International joint conference on neural networks (IJCNN) (pp. 1\u20138).","DOI":"10.1109\/IJCNN.2019.8852239"},{"key":"4788_CR3","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s10479-008-0487-y","volume":"180","author":"HC Brand\u00e3o de Oliveira","year":"2010","unstructured":"Brand\u00e3o de Oliveira, H. C., & Vasconcelos, G. C. (2010). A hybrid search method for the vehicle routing problem with time windows. Annals of Operations Research, 180, 125\u2013144.","journal-title":"Annals of Operations Research"},{"key":"4788_CR4","unstructured":"Bresson, X., & Laurent, T. (2021). The transformer network for the traveling salesman problem. arXiv preprint arXiv:2103.03012."},{"issue":"4","key":"4788_CR5","first-page":"1","volume":"12","author":"JF Camacho-Vallejo","year":"2021","unstructured":"Camacho-Vallejo, J. F., L\u00f3pez-Vera, L., et al. (2021). A tabu search algorithm to solve a green logistics bi-objective bi-level problem. Annals of Operations Research, 12(4), 1\u201327.","journal-title":"Annals of Operations Research"},{"key":"4788_CR6","doi-asserted-by":"crossref","unstructured":"Deudon, M., Cournut, P., Lacoste, A. et al. (2018). Learning heuristics for the tsp by policy gradient. In International conference on the integration of constraint programming, artificial intelligence, and operations research (pp. 170\u2013181).","DOI":"10.1007\/978-3-319-93031-2_12"},{"key":"4788_CR7","unstructured":"Eggleston, H. S., Buendia, L., Miwa, K. et al. (2006). 2006 IPCC guidelines for national greenhouse gas inventories."},{"key":"4788_CR8","unstructured":"Facts, E. (2005). Average carbon dioxide emissions resulting from gasoline and diesel fuel, United States Environmental Protection Agency, Seattle, Wash., USA"},{"issue":"1","key":"4788_CR9","doi-asserted-by":"publisher","first-page":"33","DOI":"10.5267\/j.ijiec.2017.5.002","volume":"9","author":"LF Galindres-Guancha","year":"2018","unstructured":"Galindres-Guancha, L. F., Toro-Ocampo, E. M., & Rend\u00f3n, R. A. (2018). Multi-objective MDVRP solution considering route balance and cost using the ILS metaheuristic. International Journal of Industrial Engineering Computations, 9(1), 33\u201346.","journal-title":"International Journal of Industrial Engineering Computations"},{"issue":"6","key":"4788_CR10","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1016\/0305-0483(76)90097-9","volume":"4","author":"BE Gillett","year":"1976","unstructured":"Gillett, B. E., & Johnson, J. G. (1976). Multi-terminal vehicle-dispatch algorithm. Omega, 4(6), 711\u2013718.","journal-title":"Omega"},{"key":"4788_CR11","unstructured":"Haarnoja, T., Zhou, A. et al. (2018). Soft actor-critic algorithms and applications. arXiv preprint arXiv:1812.05905."},{"key":"4788_CR12","doi-asserted-by":"crossref","unstructured":"Huang, L. et al. (2019). Attention on attention for image captioning. In Proceedings of the IEEE\/CVF international conference on computer vision.","DOI":"10.1109\/ICCV.2019.00473"},{"key":"4788_CR13","doi-asserted-by":"crossref","unstructured":"Huang, Z., Liang, D., Xu, P. et al. (2020). Improve transformer models with better relative position embeddings. arXiv preprint arXiv:2009.13658.","DOI":"10.18653\/v1\/2020.findings-emnlp.298"},{"key":"4788_CR14","first-page":"1","volume":"11","author":"P Kalaivaani","year":"2021","unstructured":"Kalaivaani, P., Sathishkumar, V. E., Hatamleh, W. A., et al. (2021). Advanced lightweight feature interaction in deep neural networks for improving the prediction in click through rate. Annals of Operations Research, 11, 1\u201315.","journal-title":"Annals of Operations Research"},{"key":"4788_CR15","unstructured":"Kool, W., Hoof, H. V., & Welling, M. (2019). Attention, learn to solve routing problems! In: 7th International conference on learning representations."},{"key":"4788_CR16","doi-asserted-by":"crossref","unstructured":"Kruk, S. (2018). Practical python AI projects: Mathematical models of optimization problems with Google OR-tools, Apress.","DOI":"10.1007\/978-1-4842-3423-5"},{"issue":"8","key":"4788_CR17","doi-asserted-by":"publisher","first-page":"6949","DOI":"10.1016\/j.eswa.2012.01.024","volume":"39","author":"Y Kuo","year":"2011","unstructured":"Kuo, Y., & Wang, C. (2011). A variable neighborhood search for the multi-depot vehicle routing problem with loading cost. Expert Systems with Applications, 39(8), 6949\u20136954.","journal-title":"Expert Systems with Applications"},{"key":"4788_CR18","unstructured":"Kurbiel, T., & Khaleghian, S. (2017). Training of deep neural networks based on distance measures using RMSProp. arXiv preprint arXiv:1708.01911."},{"key":"4788_CR19","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1016\/j.trd.2018.01.026","volume":"59","author":"J Li","year":"2018","unstructured":"Li, J., Wang, R., Li, T., et al. (2018). Benefit analysis of shared depot resources for multi-depot vehicle routing problem with fuel consumption. Transportation Research Part d: Transport and Environment, 59, 417\u2013432.","journal-title":"Transportation Research Part d: Transport and Environment"},{"key":"4788_CR20","unstructured":"Ma, Q., Ge, S., He, D. et al. (2019). Combinatorial optimization by graph pointer networks and hierarchical reinforcement learning. arXiv preprint arXiv:1911.04936."},{"key":"4788_CR21","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1007\/s10479-021-04046-8","volume":"304","author":"E Marrekchi","year":"2021","unstructured":"Marrekchi, E., Besbes, W., Dhouib, D., et al. (2021). A review of recent advances in the operations research literature on the green routing problem and its variants. Annals of Operations Research, 304, 529\u2013574.","journal-title":"Annals of Operations Research"},{"key":"4788_CR22","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/s10479-016-2366-2","volume":"258","author":"E Mizutani","year":"2017","unstructured":"Mizutani, E., & Dreyfus, S. (2017). Totally model-free actor-critic recurrent neural-network reinforcement learning in non-Markovian domains. Annals of Operations Research, 258, 107\u2013131.","journal-title":"Annals of Operations Research"},{"key":"4788_CR23","unstructured":"Nazari, M., Oroojlooy, A., Tak\u00e1\u010d, M. et al. (2018). Reinforcement learning for solving the vehicle routing problem. In: Advances in neural information processing systems."},{"key":"4788_CR24","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10479-017-2642-9","volume":"273","author":"PHV Penna","year":"2019","unstructured":"Penna, P. H. V., Subramanian, A., Ochi, L. S., et al. (2019). A hybrid heuristic for a broad class of vehicle routing problems with heterogeneous fleet. Annals of Operations Research, 273, 5\u201374.","journal-title":"Annals of Operations Research"},{"key":"4788_CR25","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/BF02125403","volume":"63","author":"JY Potvin","year":"1996","unstructured":"Potvin, J. Y. (1996). Genetic algorithms for the traveling salesman problem. Annals of Operations Research, 63, 337\u2013370.","journal-title":"Annals of Operations Research"},{"key":"4788_CR26","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/s10479-012-1077-6","volume":"241","author":"WB Powell","year":"2016","unstructured":"Powell, W. B. (2016). Perspectives of approximate dynamic programming. Annals of Operations Research, 241, 319\u2013356.","journal-title":"Annals of Operations Research"},{"key":"4788_CR27","doi-asserted-by":"publisher","first-page":"669","DOI":"10.1007\/s10479-019-03501-x","volume":"293","author":"J Roy","year":"2020","unstructured":"Roy, J., Pamu\u010dar, D., & Kar, S. (2020). Evaluation and selection of third party logistics provider under sustainability perspectives: An interval valued fuzzy-rough approach. Annals of Operations Research, 293, 669\u2013714.","journal-title":"Annals of Operations Research"},{"issue":"1","key":"4788_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ejor.2007.10.030","volume":"193","author":"B Sahin","year":"2009","unstructured":"Sahin, B., Yilmaz, H., Ust, Y., et al. (2009). An approach for analysing transportation costs and a case study. European Journal of Operational Research, 193(1), 1\u201311.","journal-title":"European Journal of Operational Research"},{"key":"4788_CR29","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/j.cor.2013.05.011","volume":"52","author":"S Salhi","year":"2014","unstructured":"Salhi, S., Imran, A., & Wassan, N. A. (2014). The multi-depot vehicle routing problem with heterogeneous vehicle fleet: Formulation and a variable neighborhood search implementation. Computers & Operations Research, 52, 315\u2013325.","journal-title":"Computers & Operations Research"},{"key":"4788_CR30","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/s10479-016-2192-6","volume":"258","author":"M Sayli","year":"2017","unstructured":"Sayli, M., & Y\u0131lmaz, E. (2017). Anti-periodic solutions for state-dependent impulsive recurrent neural networks with time-varying and continuously distributed delays. Annals of Operations Research, 258, 159\u2013185.","journal-title":"Annals of Operations Research"},{"issue":"1","key":"4788_CR31","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/s10479-009-0651-z","volume":"175","author":"A Sbihi","year":"2010","unstructured":"Sbihi, A., & Eglese, R. W. (2010). Combinatorial optimization and green logistics. Annals of Operations Research, 175(1), 159\u2013175.","journal-title":"Annals of Operations Research"},{"key":"4788_CR32","unstructured":"Vaswani, A., Shazeer, N., Parmar, N., et al. (2017). Attention is all you need. In: Advances in neural information processing systems (pp. 5998\u20136008)."},{"key":"4788_CR33","unstructured":"Vinyals, O., Fortunato, M., & Jaitly, N. (2015). Pointer networks. arXiv preprint arXiv:1506.03134."},{"key":"4788_CR34","unstructured":"Ward, R., Wu, X., & Bottou, L. (2018). Adagrad stepsizes: Sharp convergence over nonconvex landscapes, from any initialization. arXiv preprint arXiv:1806.01811"},{"issue":"7","key":"4788_CR35","doi-asserted-by":"publisher","first-page":"1419","DOI":"10.1016\/j.cor.2011.08.013","volume":"39","author":"Y Xiao","year":"2012","unstructured":"Xiao, Y., Zhao, Q., et al. (2012). Development of a fuel consumption optimization model for the capacitated vehicle routing problem. Computers & Operations Research, 39(7), 1419\u20131431.","journal-title":"Computers & Operations Research"},{"key":"4788_CR36","doi-asserted-by":"crossref","unstructured":"Yang, H. (2021). Extended attention mechanism for TSP problem. In 2021 International joint conference on neural networks (IJCNN).","DOI":"10.1109\/IJCNN52387.2021.9533472"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-022-04788-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-022-04788-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-022-04788-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T18:24:55Z","timestamp":1722363895000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-022-04788-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,20]]},"references-count":36,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2024,8]]}},"alternative-id":["4788"],"URL":"https:\/\/doi.org\/10.1007\/s10479-022-04788-z","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,20]]},"assertion":[{"value":"17 May 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 June 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}