{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T05:28:20Z","timestamp":1774070900830,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T00:00:00Z","timestamp":1664409600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T00:00:00Z","timestamp":1664409600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001870","name":"Fundacja na rzecz Nauki Polskiej","doi-asserted-by":"publisher","award":["TEAM NET POIR.04.04.00-00-17C1\/18-00"],"award-info":[{"award-number":["TEAM NET POIR.04.04.00-00-17C1\/18-00"]}],"id":[{"id":"10.13039\/501100001870","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004281","name":"Narodowe Centrum Nauki","doi-asserted-by":"publisher","award":["2019\/33\/B\/ST6\/02011"],"award-info":[{"award-number":["2019\/33\/B\/ST6\/02011"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007835","name":"Silesian University of Technology","doi-asserted-by":"publisher","award":["BKM-700\/RT2\/2022 12\/020\/BKM2022\/0233"],"award-info":[{"award-number":["BKM-700\/RT2\/2022 12\/020\/BKM2022\/0233"]}],"id":[{"id":"10.13039\/501100007835","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>As consequences of disruptions in railway traffic affect passenger experience and satisfaction, appropriate rerouting and\/or rescheduling is necessary. These problems are known to be NP-hard, given the numerous restrictions of traffic nature. With the recent advances in quantum technologies, quantum annealing has become an alternative method to solve such optimization problems. To use quantum annealing, the problem needs to be encoded in quadratic unconstrained binary optimization (QUBO) or higher-order binary optimization (HOBO) formulation that can be recast as a QUBO. This paper introduces QUBO and HOBO representations for rescheduling problems of railway traffic management; the latter is a new approach up to our knowledge. This new approach takes into account not only the single-track lines but also the double- and multi-track lines, as well as stations composed of tracks and switches. We consider the conditions of minimal headway between trains, minimal stay on stations, track occupation, and rolling stock circulation. Furthermore, a hybrid quantum-classical procedure is presented that includes rerouting. We demonstrate the proof of concept implementation on the D-Wave Quantum Processing Unit and D-Wave hybrid solver.<\/jats:p>","DOI":"10.1007\/s11128-022-03670-y","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T17:04:01Z","timestamp":1664471041000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Quadratic and higher-order unconstrained binary optimization of railway rescheduling for quantum computing"],"prefix":"10.1007","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7386-5441","authenticated-orcid":false,"given":"Krzysztof","family":"Domino","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3540-1061","authenticated-orcid":false,"given":"Akash","family":"Kundu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2033-2881","authenticated-orcid":false,"given":"\u00d6zlem","family":"Salehi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7447-3447","authenticated-orcid":false,"given":"Krzysztof","family":"Krawiec","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,9,29]]},"reference":[{"key":"3670_CR1","doi-asserted-by":"publisher","DOI":"10.4324\/9780367816698","volume-title":"The Routledge Handbook of Public Transport","author":"C Mulley","year":"2021","unstructured":"Mulley, C., Nelson, J.D., Ison, S., Tsoi, K.H., Loo, B.P.Y.: The Routledge Handbook of Public Transport. Routledge, London (2021)"},{"issue":"2","key":"3670_CR2","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/j.tbs.2014.12.001","volume":"2","author":"P Batty","year":"2015","unstructured":"Batty, P., Palacin, R., Gonz\u00e1lez-Gil, A.: Challenges and opportunities in developing urban modal shift. Travel Behav. Soc. 2(2), 109\u2013123 (2015). https:\/\/doi.org\/10.1016\/j.tbs.2014.12.001","journal-title":"Travel Behav. Soc."},{"key":"3670_CR3","unstructured":"Gawlak, K.: Mapa zdarze\u0144 i wydarze\u0144 kolejowych w roli innowacyjnego projektu wspomagajacego system zarzadzania bezpiecze\u0144stwem regionalnego przewo\u017anika Koleje \u015al\u0105skie sp. z o.o. (Map of railroad events as an innovative project supporting safety management system of the regional carrier Koleje \u015al\u0105skie sp. z o.o.). Urzad Transprotu Kolejowego (Eng. Office of Rail Transport) (2022). https:\/\/utk.gov.pl\/download\/1\/67088\/MKBekran6122021.pdf"},{"issue":"4","key":"3670_CR4","doi-asserted-by":"publisher","first-page":"466","DOI":"10.1007\/s10696-013-9172-9","volume":"26","author":"R Larsen","year":"2014","unstructured":"Larsen, R., Pranzo, M., D\u2019Ariano, A., Corman, F., Pacciarelli, D.: Susceptibility of optimal train schedules to stochastic disturbances of process times. Flex. Serv. Manuf. J. 26(4), 466\u2013489 (2014)","journal-title":"Flex. Serv. Manuf. J."},{"issue":"3","key":"3670_CR5","doi-asserted-by":"publisher","first-page":"342","DOI":"10.1016\/j.trb.2006.06.001","volume":"41","author":"J T\u00f6rnquist","year":"2007","unstructured":"T\u00f6rnquist, J., Persson, J.A.: N-tracked railway traffic re-scheduling during disturbances. Transp. Res. Part B: Methodol. 41(3), 342\u2013362 (2007). https:\/\/doi.org\/10.1016\/j.trb.2006.06.001","journal-title":"Transp. Res. Part B: Methodol."},{"issue":"4","key":"3670_CR6","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1080\/03081060.2011.577152","volume":"34","author":"F Corman","year":"2011","unstructured":"Corman, F., D\u2019Ariano, A., Pranzo, M., Hansen, I.A.: Effectiveness of dynamic reordering and rerouting of trains in a complicated and densely occupied station area. Transp. Plan. Technol. 34(4), 341\u2013362 (2011)","journal-title":"Transp. Plan. Technol."},{"issue":"2","key":"3670_CR7","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1016\/0304-4149(89)90040-9","volume":"33","author":"B Apolloni","year":"1989","unstructured":"Apolloni, B., Carvalho, C., De Falco, D.: Quantum stochastic optimization. Stoch. Process. Appl. 33(2), 233\u2013244 (1989)","journal-title":"Stoch. Process. Appl."},{"issue":"5","key":"3670_CR8","doi-asserted-by":"publisher","first-page":"5355","DOI":"10.1103\/PhysRevE.58.5355","volume":"58","author":"T Kadowaki","year":"1998","unstructured":"Kadowaki, T., Nishimori, H.: Quantum annealing in the transverse Ising model. Phys. Rev. E 58(5), 5355 (1998)","journal-title":"Phys. Rev. E"},{"key":"3670_CR9","unstructured":"Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: Quantum computation by adiabatic evolution. arXiv preprint arXiv:quant-ph\/0001106 (2000)"},{"issue":"7346","key":"3670_CR10","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1038\/nature10012","volume":"473","author":"MW Johnson","year":"2011","unstructured":"Johnson, M.W., et al.: Quantum annealing with manufactured spins. Nature 473(7346), 194\u2013198 (2011)","journal-title":"Nature"},{"key":"3670_CR11","unstructured":"Glover, F., Kochenberger, G., Du, Y.: A tutorial on formulating and using QUBO models. arXiv preprint arXiv:1811.11538 (2018)"},{"key":"3670_CR12","doi-asserted-by":"publisher","first-page":"5","DOI":"10.3389\/fphy.2014.00005","volume":"2","author":"A Lucas","year":"2014","unstructured":"Lucas, A.: Ising formulations of many NP problems. Front. Phys. 2, 5 (2014)","journal-title":"Front. Phys."},{"issue":"1","key":"3670_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41534-022-00546-y","volume":"8","author":"A Glos","year":"2022","unstructured":"Glos, A., Krawiec, A., Zimbor\u00e1s, Z.: Space-efficient binary optimization for variational quantum computing. NPJ Quantum Inf. 8(1), 1\u20138 (2022)","journal-title":"NPJ Quantum Inf."},{"key":"3670_CR14","doi-asserted-by":"crossref","unstructured":"Tabi, Z., El-Safty, K.H., Kallus, Z., H\u00e1ga, P., Kozsik, T., Glos, A., Zimbor\u00e1s, Z.: Quantum optimization for the graph coloring problem with space-efficient embedding. In: 2020 IEEE International Conference on Quantum Computing and Engineering (QCE), pp. 56\u201362. IEEE (2020)","DOI":"10.1109\/QCE49297.2020.00018"},{"issue":"2","key":"3670_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11128-021-03405-5","volume":"21","author":"\u00d6 Salehi","year":"2022","unstructured":"Salehi, \u00d6., Glos, A., Miszczak, J.A.: Unconstrained binary models of the travelling salesman problem variants for quantum optimization. Quantum Inf. Process. 21(2), 1\u201330 (2022)","journal-title":"Quantum Inf. Process."},{"key":"3670_CR16","unstructured":"Domino, K., Koniorczyk, M., Krawiec, K., Ja\u0142owiecki, K., Deffner, S., Gardas, B.: Quantum annealing in the NISQ era: railway conflict management. arXiv preprint arXiv:2112.03674 (2021)"},{"key":"3670_CR17","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1016\/j.tra.2015.06.002","volume":"81","author":"L-G Mattsson","year":"2015","unstructured":"Mattsson, L.-G., Jenelius, E.: Vulnerability and resilience of transport systems\u2014a discussion of recent research. Transp. Res. Part A: Policy Pract. 81, 16\u201334 (2015). https:\/\/doi.org\/10.1016\/j.tra.2015.06.002","journal-title":"Transp. Res. Part A: Policy Pract."},{"key":"3670_CR18","doi-asserted-by":"publisher","first-page":"114547","DOI":"10.1109\/ACCESS.2019.2935106","volume":"7","author":"C Wen","year":"2019","unstructured":"Wen, C., Huang, P., Li, Z., Lessan, J., Fu, L., Jiang, C., Xu, X.: Train dispatching management with data-driven approaches: a comprehensive review and appraisal. IEEE Access 7, 114547\u2013114571 (2019). https:\/\/doi.org\/10.1109\/ACCESS.2019.2935106","journal-title":"IEEE Access"},{"issue":"4","key":"3670_CR19","doi-asserted-by":"publisher","first-page":"380","DOI":"10.1287\/trsc.32.4.380","volume":"32","author":"J-F Cordeau","year":"1998","unstructured":"Cordeau, J.-F., Toth, P., Vigo, D.: A survey of optimization models for train routing and scheduling. Transp. Sci. 32(4), 380\u2013404 (1998). https:\/\/doi.org\/10.1287\/trsc.32.4.380","journal-title":"Transp. Sci."},{"issue":"3","key":"3670_CR20","doi-asserted-by":"publisher","first-page":"1274","DOI":"10.1109\/TITS.2014.2358392","volume":"16","author":"F Corman","year":"2015","unstructured":"Corman, F., Meng, L.: A review of online dynamic models and algorithms for railway traffic management. IEEE Trans. Intell. Transp. Syst. 16(3), 1274\u20131284 (2015). https:\/\/doi.org\/10.1109\/TITS.2014.2358392","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"issue":"10","key":"3670_CR21","doi-asserted-by":"publisher","first-page":"2840","DOI":"10.1016\/j.cor.2008.12.012","volume":"36","author":"SQ Liu","year":"2009","unstructured":"Liu, S.Q., Kozan, E.: Scheduling trains as a blocking parallel-machine job shop scheduling problem. Comput. Oper. Res. 36(10), 2840\u20132852 (2009). https:\/\/doi.org\/10.1016\/j.cor.2008.12.012","journal-title":"Comput. Oper. Res."},{"key":"3670_CR22","doi-asserted-by":"publisher","unstructured":"Corman, F., D\u2019Ariano, A., Hansen, I.A., Pacciarelli, D., Pranzo, M.: Dispatching trains during seriously disrupted traffic situations. In: 2011 International Conference on Networking, Sensing and Control, pp. 323\u2013328. https:\/\/doi.org\/10.1109\/ICNSC.2011.5874901 (2011)","DOI":"10.1109\/ICNSC.2011.5874901"},{"issue":"5","key":"3670_CR23","doi-asserted-by":"publisher","first-page":"830","DOI":"10.1016\/j.tre.2009.03.004","volume":"45","author":"S Harrod","year":"2009","unstructured":"Harrod, S.: Capacity factors of a mixed speed railway network. Transp. Res. Part E: Logist. Transp. Rev. 45(5), 830\u2013841 (2009). https:\/\/doi.org\/10.1016\/j.tre.2009.03.004","journal-title":"Transp. Res. Part E: Logist. Transp. Rev."},{"key":"3670_CR24","doi-asserted-by":"crossref","unstructured":"Borowski, M., et al.: New hybrid quantum annealing algorithms for solving vehicle routing problem. In: International Conference on Computational Science, pp. 546\u2013561. Springer (2020)","DOI":"10.1007\/978-3-030-50433-5_42"},{"key":"3670_CR25","doi-asserted-by":"publisher","first-page":"29","DOI":"10.3389\/fict.2017.00029","volume":"4","author":"F Neukart","year":"2017","unstructured":"Neukart, F., Compostella, G., Seidel, C., Von Dollen, D., Yarkoni, S., Parney, B.: Traffic flow optimization using a quantum annealer. Front. ICT 4, 29 (2017)","journal-title":"Front. ICT"},{"key":"3670_CR26","unstructured":"Farhi, E., Goldstone, J., Gutmann, S.: A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028 (2014)"},{"issue":"2","key":"3670_CR27","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1016\/j.ejor.2006.10.034","volume":"183","author":"A D\u2019Ariano","year":"2007","unstructured":"D\u2019Ariano, A., Pacciarelli, D., Pranzo, M.: A branch and bound algorithm for scheduling trains in a railway network. Eur. J. Oper. Res. 183(2), 643\u2013657 (2007)","journal-title":"Eur. J. Oper. Res."},{"issue":"2","key":"3670_CR28","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/s10951-017-0526-0","volume":"21","author":"J Lange","year":"2018","unstructured":"Lange, J., Werner, F.: Approaches to modeling train scheduling problems as job-shop problems with blocking constraints. J. Sched. 21(2), 191\u2013207 (2018)","journal-title":"J. Sched."},{"key":"3670_CR29","first-page":"344","volume":"72","author":"B Szpigel","year":"1973","unstructured":"Szpigel, B.: Optimal train scheduling on a single line railway. J. Oper. Res. 72, 344\u2013351 (1973)","journal-title":"J. Oper. Res."},{"issue":"3","key":"3670_CR30","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/0166-218X(95)80004-N","volume":"59","author":"YN Sotskov","year":"1995","unstructured":"Sotskov, Y.N., Shakhlevich, N.V.: NP-hardness of shop-scheduling problems with three jobs. Discrete Appl. Math. 59(3), 237\u2013266 (1995)","journal-title":"Discrete Appl. Math."},{"key":"3670_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-2361-4","volume-title":"Scheduling","author":"ML Pinedo","year":"2012","unstructured":"Pinedo, M.L.: Scheduling, vol. 29. Springer, New York (2012)"},{"issue":"1\u20133","key":"3670_CR32","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/S0166-218X(01)00341-9","volume":"123","author":"E Boros","year":"2002","unstructured":"Boros, E., Hammer, P.L.: Pseudo-boolean optimization. Discrete Appl. Math. 123(1\u20133), 155\u2013225 (2002)","journal-title":"Discrete Appl. Math."},{"issue":"3","key":"3670_CR33","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1504\/IJMHEUR.2011.041196","volume":"1","author":"F Glover","year":"2011","unstructured":"Glover, F., Hao, J.-K., Kochenberger, G.: Polynomial unconstrained binary optimisation\u2014part 1. Int. J. Metaheuristics 1(3), 232\u2013256 (2011)","journal-title":"Int. J. Metaheuristics"},{"key":"3670_CR34","volume-title":"Linear and Nonlinear Programming. International Series in Operations Research & Management Science","author":"DG Luenberger","year":"1984","unstructured":"Luenberger, D.G., Ye, Y.: Linear and Nonlinear Programming. International Series in Operations Research & Management Science. Springer, New York (1984)"},{"key":"3670_CR35","doi-asserted-by":"crossref","unstructured":"Mandal, A., Roy, A., Upadhyay, S., Ushijima-Mwesigwa, H.: Compressed quadratization of higher order binary optimization problems. In: Proceedings of the 17th ACM International Conference on Computing Frontiers, pp. 126\u2013131 (2020)","DOI":"10.1145\/3387902.3392627"},{"key":"3670_CR36","unstructured":"Rosenberg, I.G.: Reduction of bivalent maximization to the quadratic case. Cahiers du Centre d\u2019Etudes de Recherche Operationnelle (1975)"},{"key":"3670_CR37","doi-asserted-by":"crossref","unstructured":"Shimada, D., Shibuya, T., Shibasaki, T.: A decomposition method for makespan minimization in job-shop scheduling problem using ising machine. In: IEEE 8th International Conference on Industrial Engineering and Applications (ICIEA), pp. 307\u2013314. IEEE (2021)","DOI":"10.1109\/ICIEA52957.2021.9436798"},{"key":"3670_CR38","volume-title":"PuLP: A Linear Programming Toolkit for Python","author":"S Mitchell","year":"2011","unstructured":"Mitchell, S., Consulting, S.M., Dunning, I.: PuLP: A Linear Programming Toolkit for Python. The University of Auckland, Auckland (2011)"},{"key":"3670_CR39","doi-asserted-by":"crossref","unstructured":"Forrest, J., Lougee-Heimer, R.: CBC user guide: emerging theory, methods, and applications. In: INFORMS TutORials in Operations Research, pp. 257\u2013277 (2005)","DOI":"10.1287\/educ.1053.0020"},{"key":"3670_CR40","unstructured":"Dattani, N., Szalay, S., Chancellor, N.: Pegasus: the second connectivity graph for large-scale quantum annealing hardware. arXiv preprint arXiv:1901.07636 (2019)"},{"key":"3670_CR41","unstructured":"D-Wave: D-Wave Hybrid Solver Service + Advantage: Technology Update [WhitePaper]. https:\/\/www.dwavesys.com\/media\/m2xbmlhs\/14-1048a-a_d-wave_hybrid_solver_service_plus_advantage_technology_update.pdf (2020)"},{"key":"3670_CR42","unstructured":"McGeoch, C., Farr\u00e9, P., Bernoudy, W.: D-Wave Hybrid Solver Service+ Advantage: Technology Update. Technical report, D-Wave Systems Inc, Burnaby, BC, Canada (2020)"},{"issue":"1","key":"3670_CR43","doi-asserted-by":"publisher","first-page":"014004","DOI":"10.1103\/PhysRevApplied.12.014004","volume":"12","author":"A Perdomo-Ortiz","year":"2019","unstructured":"Perdomo-Ortiz, A., Feldman, A., Ozaeta, A., Isakov, S.V., Zhu, Z., O\u2019Gorman, B., Katzgraber, H.G., Diedrich, A., Neven, H., de Kleer, J., et al.: Readiness of quantum optimization machines for industrial applications. Phys. Rev. Appl. 12(1), 014004 (2019)","journal-title":"Phys. Rev. Appl."},{"key":"3670_CR44","unstructured":"Ender, K., ter Hoeven, R., Niehoff, B.E., Drieb-Sch\u00f6n, M., Lechner, W.: Parity quantum optimization: compiler. arXiv preprint arXiv:2105.06233 (2021)"},{"issue":"5","key":"3670_CR45","first-page":"8","volume":"53","author":"S Tsukamoto","year":"2017","unstructured":"Tsukamoto, S., Takatsu, M., Matsubara, S., Tamura, H.: An accelerator architecture for combinatorial optimization problems. Fujitsu Sci. Tech. J. 53(5), 8\u201313 (2017)","journal-title":"Fujitsu Sci. Tech. J."},{"key":"3670_CR46","doi-asserted-by":"crossref","unstructured":"Roch, C., Impertro, A., Linnhoff-Popien, C.: Cross entropy optimization of constrained problem Hamiltonians for quantum annealing. In: International Conference on Computational Science, pp. 60\u201373. Springer (2021)","DOI":"10.1007\/978-3-030-77980-1_5"},{"key":"3670_CR47","doi-asserted-by":"crossref","unstructured":"Ayodele, M., Allmendinger, R., L\u00f3pez-Ib\u00e1\u00f1ez, M., Parizy, M.: Multi-objective QUBO solver: bi-objective quadratic assignment. arXiv preprint arXiv:2205.13399 (2022)","DOI":"10.1145\/3512290.3528698"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03670-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-022-03670-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03670-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,13]],"date-time":"2022-10-13T07:21:06Z","timestamp":1665645666000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-022-03670-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,29]]},"references-count":47,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["3670"],"URL":"https:\/\/doi.org\/10.1007\/s11128-022-03670-y","relation":{},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,29]]},"assertion":[{"value":"25 March 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 August 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 September 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"337"}}