{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T15:23:32Z","timestamp":1772119412663,"version":"3.50.1"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"17-18","license":[{"start":{"date-parts":[[2024,7,31]],"date-time":"2024-07-31T00:00:00Z","timestamp":1722384000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,7,31]],"date-time":"2024-07-31T00:00:00Z","timestamp":1722384000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2024,9]]},"DOI":"10.1007\/s00500-024-09837-2","type":"journal-article","created":{"date-parts":[[2024,7,31]],"date-time":"2024-07-31T15:03:15Z","timestamp":1722438195000},"page":"9857-9882","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Uncertain Chinese postman problem with budget constraint: a robust optimization approach"],"prefix":"10.1007","volume":"28","author":[{"given":"M.","family":"Das","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.","family":"Nahak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. P.","family":"Biswal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,31]]},"reference":[{"key":"9837_CR1","unstructured":"Baoding L (2007) Uncertainty theory. 2"},{"issue":"1","key":"9837_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.orl.2008.09.010","volume":"37","author":"A Beck","year":"2009","unstructured":"Beck A, Ben-Tal A (2009) Duality in robust optimization: primal worst equals dual best. Oper Res Lett 37(1):1\u20136","journal-title":"Oper Res Lett"},{"issue":"4","key":"9837_CR3","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1287\/moor.23.4.769","volume":"23","author":"A Ben-Tal","year":"1998","unstructured":"Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23(4):769\u2013805","journal-title":"Math Oper Res"},{"issue":"3","key":"9837_CR4","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1007\/PL00011380","volume":"88","author":"A Ben-Tal","year":"2000","unstructured":"Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program 88(3):411\u2013424","journal-title":"Math Program"},{"key":"9837_CR5","doi-asserted-by":"publisher","DOI":"10.1515\/9781400831050","volume-title":"Robust optimization","author":"A Ben-Tal","year":"2009","unstructured":"Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton University Press, Princeton"},{"issue":"1","key":"9837_CR6","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1287\/opre.1030.0065","volume":"52","author":"D Bertsimas","year":"2004","unstructured":"Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52(1):35\u201353","journal-title":"Oper Res"},{"issue":"6","key":"9837_CR7","doi-asserted-by":"publisher","first-page":"510","DOI":"10.1016\/j.orl.2003.12.007","volume":"32","author":"D Bertsimas","year":"2004","unstructured":"Bertsimas D, Pachamanova D, Sim M (2004) Robust linear optimization under general norms. Oper Res Lett 32(6):510\u2013516","journal-title":"Oper Res Lett"},{"issue":"3","key":"9837_CR8","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1137\/080734510","volume":"53","author":"D Bertsimas","year":"2011","unstructured":"Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev 53(3):464\u2013501","journal-title":"SIAM Rev"},{"key":"9837_CR9","volume-title":"Multiobjective decision making: theory and methodology","author":"V Chankong","year":"2008","unstructured":"Chankong V, Haimes YY (2008) Multiobjective decision making: theory and methodology. Courier Dover Publications, New York"},{"key":"9837_CR10","volume-title":"An algorithm for the rural postman problem","author":"N Christofides","year":"1981","unstructured":"Christofides N, Campos V, Corbern A, Mota E (1981) An algorithm for the rural postman problem. Imperial College Report, London"},{"issue":"3","key":"9837_CR11","doi-asserted-by":"publisher","first-page":"1109","DOI":"10.1137\/10079731X","volume":"21","author":"AL Cust\u00f3dio","year":"2011","unstructured":"Cust\u00f3dio AL, Madeira JA, Vaz AIF, Vicente LN (2011) Direct multisearch for multiobjective optimization. SIAM J Optim 21(3):1109\u20131140","journal-title":"SIAM J Optim"},{"key":"9837_CR12","doi-asserted-by":"crossref","unstructured":"Deb K (2011) Multi-objective optimisation using evolutionary algorithms: an introduction. In: multi-objective evolutionary optimisation for product design and manufacturing, pp. 3\u201334. Springer, London: Springer London","DOI":"10.1007\/978-0-85729-652-8_1"},{"key":"9837_CR13","unstructured":"Fonseca CM, Fleming PJ et al (1993) Genetic algorithms for multiobjective optimization: formulationdiscussion and generalization. In: Icga, vol. 93, pp. 416\u2013423. Citeseer"},{"key":"9837_CR14","unstructured":"GLJAN MG Graphic programming using odd or even points. Chin J Mufh 1:273\u2013277 (1962)"},{"key":"9837_CR15","doi-asserted-by":"crossref","unstructured":"Golden BL, Wong RT (1981) Capacitated arc routing problems. Networks 11(3):305\u2013315","DOI":"10.1002\/net.3230110308"},{"key":"9837_CR16","doi-asserted-by":"crossref","unstructured":"Grandinetti L, Guerriero F, Lagan\u00e0 D, Pisacane O (2010) An approximate $$\\varepsilon $$-constraint method for the multi-objective undirected capacitated arc routing problem. In: International Symposium on Experimental Algorithms, pp. 214\u2013225. Springer","DOI":"10.1007\/978-3-642-13193-6_19"},{"issue":"1","key":"9837_CR17","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/0166-218X(84)90089-1","volume":"9","author":"M Guan","year":"1984","unstructured":"Guan M (1984) On the windy postman problem. Discret Appl Math 9(1):41\u201346","journal-title":"Discret Appl Math"},{"key":"9837_CR18","first-page":"296","volume":"3","author":"Y Haimes","year":"1971","unstructured":"Haimes Y (1971) On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Trans Syst Man Cybern 3:296\u2013297","journal-title":"IEEE Trans Syst Man Cybern"},{"key":"9837_CR19","doi-asserted-by":"publisher","first-page":"4367","DOI":"10.1007\/s00500-018-3094-0","volume":"23","author":"MB Kar","year":"2019","unstructured":"Kar MB, Kar S, Guo S, Li X, Majumder S (2019) A new bi-objective fuzzy portfolio selection model and its solution through evolutionary algorithms. Soft Comput 23:4367\u20134381","journal-title":"Soft Comput"},{"issue":"1","key":"9837_CR20","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/s10100-018-0598-8","volume":"28","author":"M Kayac\u0131 \u00c7odur","year":"2020","unstructured":"Kayac\u0131 \u00c7odur M, Y\u0131lmaz M (2020) A time-dependent hierarchical Chinese postman problem. CEJOR 28(1):337\u2013366","journal-title":"CEJOR"},{"key":"9837_CR21","volume-title":"Robust discrete optimization and its applications","author":"P Kouvelis","year":"2013","unstructured":"Kouvelis P, Yu G (2013) Robust discrete optimization and its applications, vol 14. Springer, Springer"},{"key":"9837_CR22","doi-asserted-by":"crossref","unstructured":"Lacomme P, Prins C, Sevaux M (2006) A genetic algorithm for a bi-objective capacitated arc routing problem. Comput Oper Res 33(12):3473\u20133493","DOI":"10.1016\/j.cor.2005.02.017"},{"issue":"22","key":"9837_CR23","doi-asserted-by":"publisher","first-page":"11557","DOI":"10.1007\/s00500-018-03697-3","volume":"23","author":"S Majumder","year":"2019","unstructured":"Majumder S, Kar S, Pal T (2019) Uncertain multi-objective Chinese postman problem. Soft Comput 23(22):11557\u201311572","journal-title":"Soft Comput"},{"key":"9837_CR24","doi-asserted-by":"publisher","first-page":"3279","DOI":"10.1007\/s00500-017-2987-7","volume":"23","author":"S Majumder","year":"2019","unstructured":"Majumder S, Kundu P, Kar S, Pal T (2019) Uncertain multi-objective multi-item fixed charge solid transportation problem with budget constraint. Soft Comput 23:3279\u20133301","journal-title":"Soft Comput"},{"key":"9837_CR25","doi-asserted-by":"publisher","first-page":"8975","DOI":"10.1007\/s00500-019-04423-3","volume":"24","author":"S Majumder","year":"2020","unstructured":"Majumder S, Kar MB, Kar S, Pal T (2020) Uncertain programming models for multi-objective shortest path problem with uncertain parameters. Soft Comput 24:8975\u20138996","journal-title":"Soft Comput"},{"issue":"1","key":"9837_CR26","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1109\/TCYB.2014.2317693","volume":"45","author":"K Nag","year":"2014","unstructured":"Nag K, Pal T, Pal NR (2014) Asmiga: an archive-based steady-state micro genetic algorithm. IEEE Trans Cybern 45(1):40\u201352","journal-title":"IEEE Trans Cybern"},{"key":"9837_CR27","doi-asserted-by":"crossref","unstructured":"Nebro AJ, Alba E, Molina G, Chicano F, Luna F, Durillo JJ (2007) Optimal antenna placement using a new multi-objective chc algorithm. In: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, pp. 876\u2013883","DOI":"10.1145\/1276958.1277128"},{"issue":"3","key":"9837_CR28","doi-asserted-by":"publisher","first-page":"1131","DOI":"10.1016\/j.ejor.2016.09.010","volume":"258","author":"J Nossack","year":"2017","unstructured":"Nossack J, Golden B, Pesch E, Zhang R (2017) The windy rural postman problem with a time-dependent zigzag option. Eur J Oper Res 258(3):1131\u20131142","journal-title":"Eur J Oper Res"},{"issue":"4","key":"9837_CR29","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1016\/0167-6377(94)90073-6","volume":"16","author":"WL Pearn","year":"1994","unstructured":"Pearn WL (1994) Solvable cases of the k-person Chinese postman problem. Oper Res Lett 16(4):241\u2013244","journal-title":"Oper Res Lett"},{"issue":"4","key":"9837_CR30","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1016\/S0305-0483(03)00051-3","volume":"31","author":"W Pearn","year":"2003","unstructured":"Pearn W, Wang K (2003) On the maximum benefit Chinese postman problem. Omega 31(4):269\u2013273","journal-title":"Omega"},{"key":"9837_CR31","doi-asserted-by":"publisher","DOI":"10.1002\/9781119454816","volume-title":"Engineering optimization: theory and practice","author":"SS Rao","year":"2019","unstructured":"Rao SS (2019) Engineering optimization: theory and practice. John Wiley & Sons, Hoboken"},{"key":"9837_CR32","unstructured":"Sokmen OC, Emec S, Yilmaz M, Akkaya G (2019) An overview of chinese postman problem. In: 3rd International Conference on Advanced Engineering Technologies, vol. 10"},{"issue":"5","key":"9837_CR33","doi-asserted-by":"publisher","first-page":"1154","DOI":"10.1287\/opre.21.5.1154","volume":"21","author":"AL Soyster","year":"1973","unstructured":"Soyster AL (1973) Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper Res 21(5):1154\u20131157","journal-title":"Oper Res"},{"key":"9837_CR34","doi-asserted-by":"crossref","unstructured":"Tan G, Cui X, Zhang Y (2005) Chinese postman problem in stochastic networks. In: Joint International Conference on Autonomic and Autonomous Systems and International Conference on Networking and Services-(icas-isns\u2019 05), pp. 78. IEEE","DOI":"10.1109\/ICAS-ICNS.2005.31"},{"issue":"3\u20134","key":"9837_CR35","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1016\/S0898-1221(02)00156-6","volume":"44","author":"H-F Wang","year":"2002","unstructured":"Wang H-F, Wen Y-P (2002) Time-constrained Chinese postman problems. Comput Math Appl 44(3\u20134):375\u2013387","journal-title":"Comput Math Appl"},{"key":"9837_CR36","doi-asserted-by":"crossref","unstructured":"Yamashita DS, Armentano VA, Laguna M (2007) Robust optimization models for project scheduling with resource availability cost. J Sched 10(1):67\u201376","DOI":"10.1007\/s10951-006-0326-4"},{"issue":"5","key":"9837_CR37","first-page":"87","volume":"18","author":"M Y\u0131lmaz","year":"2021","unstructured":"Y\u0131lmaz M et al (2021) Hierarchical Chinese postman problem with fuzzy travel times. Iran J Fuzzy Syst 18(5):87\u2013105","journal-title":"Iran J Fuzzy Syst"},{"issue":"1","key":"9837_CR38","first-page":"18","volume":"11","author":"B Zhang","year":"2012","unstructured":"Zhang B, Peng J (2012) Uncertain programming model for chinese postman problem with uncertain weights. Ind Eng Manag Syst 11(1):18\u201325","journal-title":"Ind Eng Manag Syst"},{"issue":"1","key":"9837_CR39","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/0165-0114(78)90031-3","volume":"1","author":"H-J Zimmermann","year":"1978","unstructured":"Zimmermann H-J (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1(1):45\u201355","journal-title":"Fuzzy Sets Syst"},{"key":"9837_CR40","doi-asserted-by":"crossref","unstructured":"Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans Evol Comput 3(4):257\u2013271","DOI":"10.1109\/4235.797969"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-024-09837-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-024-09837-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-024-09837-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T15:25:52Z","timestamp":1729178752000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-024-09837-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,31]]},"references-count":40,"journal-issue":{"issue":"17-18","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["9837"],"URL":"https:\/\/doi.org\/10.1007\/s00500-024-09837-2","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-1381785\/v1","asserted-by":"object"}]},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,31]]},"assertion":[{"value":"20 March 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 July 2024","order":2,"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 there is no conflict of interest regarding the publication of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"There is no need for ethical approval of the present research","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"We all took an interest in publishing our work in this journal.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}}]}}