{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T06:10:15Z","timestamp":1697868615543},"reference-count":12,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":7619,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1985,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The overall methodology developed in this paper can be organized into two major parts. The first part consists of a representation of the Multi\u2010Traveling Salesman Problem as a network circulation model. The second part is a subtour elimination procedure. The circulation\u2010network representation of the Multi\u2010Traveling Salesman Problem allows the generation of a starting solution which satisfies the optimality LP conditions of the network, but which may not be feasible in the context of the original problem due to the existence of subtours. The proposed network algorithm iteratively reduces the set of solutions with subtours by eliminating one link and then rerouting its flow, using the remaining arcs without violating their LP optimality conditions. Computational results based on a sample of 91 randomly generated problems are reported.<\/jats:p>","DOI":"10.1002\/net.3230150407","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T20:17:47Z","timestamp":1178914667000},"page":"455-467","source":"Crossref","is-referenced-by-count":2,"title":["A heuristic circulation\u2010network approach to solve the multi\u2010traveling salesman problem"],"prefix":"10.1002","volume":"15","author":[{"given":"Alberto","family":"Garcia\u2010Diaz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"A. I.Ali andJ. L.Kennington TheM\u2010traveling salesman problem: A duality based branch and bound algorithm. Technical Report OR 80018 Southern Methodist University Dallas (August 1980)."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585504"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.16.3.538"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1145\/321832.321847"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1057\/jors.1969.75"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1057\/jors.1972.79"},{"key":"e_1_2_1_8_2","first-page":"18","article-title":"The out\u2010of\u2010kilter method for minimal\u2010cost flow problems","volume":"9","author":"Fulkerson D. R.","year":"1961","journal-title":"J. Appl. Math."},{"key":"e_1_2_1_9_2","unstructured":"B.Gavish andK.Srikanth An optimal solution method for the multiple traveling salesman problem.Operations Res. in press."},{"key":"e_1_2_1_10_2","unstructured":"G.Laporte andY.Nobert A cutting plane algorithm for theM\u2010salesman problem. Raport De Recherche No. 79\u201008 Ecole Des H'autes Etudes Commerciales Montreal (June 1979)."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.11.6.972"},{"key":"e_1_2_1_12_2","volume-title":"Fundamentals of Network Analysis","author":"Phillips D. T.","year":"1981"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.19.7.790"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230150407","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230150407","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T20:06:44Z","timestamp":1697832404000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230150407"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,12]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1985,12]]}},"alternative-id":["10.1002\/net.3230150407"],"URL":"https:\/\/doi.org\/10.1002\/net.3230150407","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,12]]}}}