A new integer programming formulation of the graphical traveling salesman problem
In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost c ij of traveling from city i to city j , which is the same in either direction for the Symmetric TSP. The objective is to visit each city exactly once, minimizing total travel costs....
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| Veröffentlicht in: | Mathematical programming 2023-02, Vol.197 (2), p.877-902 |
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| container_title | Mathematical programming |
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| creator | Carr, Robert Ravi, R. Simonetti, Neil |
| description | In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost
c
ij
of traveling from city
i
to city
j
, which is the same in either direction for the Symmetric TSP. The objective is to visit each city exactly once, minimizing total travel costs. In the Graphical TSP, a city may be visited more than once, which may be necessary on a sparse graph. We present a new integer programming formulation for the Graphical TSP requiring only two classes of polynomial-sized constraints while addressing an open question proposed by Denis Naddef. We generalize one of these classes, and present promising preliminary computational results. |
| doi_str_mv | 10.1007/s10107-022-01849-w |
| format | Article |
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c
ij
of traveling from city
i
to city
j
, which is the same in either direction for the Symmetric TSP. The objective is to visit each city exactly once, minimizing total travel costs. In the Graphical TSP, a city may be visited more than once, which may be necessary on a sparse graph. We present a new integer programming formulation for the Graphical TSP requiring only two classes of polynomial-sized constraints while addressing an open question proposed by Denis Naddef. We generalize one of these classes, and present promising preliminary computational results.</description><identifier>ISSN: 0025-5610</identifier><identifier>EISSN: 1436-4646</identifier><identifier>DOI: 10.1007/s10107-022-01849-w</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Calculus of Variations and Optimal Control; Optimization ; Combinatorics ; Full Length Paper ; Integer programming ; Management science ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Mathematics of Computing ; Numerical Analysis ; Polynomials ; Theoretical ; Traveling salesman problem</subject><ispartof>Mathematical programming, 2023-02, Vol.197 (2), p.877-902</ispartof><rights>Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2022</rights><rights>COPYRIGHT 2023 Springer</rights><rights>Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c358t-717c00b6c7ee2ffcf8bd5865123a8317a916c2e6526ccaeef44a6d874a39321a3</citedby><cites>FETCH-LOGICAL-c358t-717c00b6c7ee2ffcf8bd5865123a8317a916c2e6526ccaeef44a6d874a39321a3</cites><orcidid>0000-0001-6128-712X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10107-022-01849-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10107-022-01849-w$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Carr, Robert</creatorcontrib><creatorcontrib>Ravi, R.</creatorcontrib><creatorcontrib>Simonetti, Neil</creatorcontrib><title>A new integer programming formulation of the graphical traveling salesman problem</title><title>Mathematical programming</title><addtitle>Math. Program</addtitle><description>In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost
c
ij
of traveling from city
i
to city
j
, which is the same in either direction for the Symmetric TSP. The objective is to visit each city exactly once, minimizing total travel costs. In the Graphical TSP, a city may be visited more than once, which may be necessary on a sparse graph. We present a new integer programming formulation for the Graphical TSP requiring only two classes of polynomial-sized constraints while addressing an open question proposed by Denis Naddef. We generalize one of these classes, and present promising preliminary computational results.</description><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Combinatorics</subject><subject>Full Length Paper</subject><subject>Integer programming</subject><subject>Management science</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics of Computing</subject><subject>Numerical Analysis</subject><subject>Polynomials</subject><subject>Theoretical</subject><subject>Traveling salesman problem</subject><issn>0025-5610</issn><issn>1436-4646</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LKzEUhoMoWD_-gKsB16PnJJkkXRbRqyCIoOuQpid1ZCZTk6nFf39TR3AnWQRy3ifn5WHsAuEKAfR1RkDQNXBeAxo5r3cHbIZSqFoqqQ7ZDIA3daMQjtlJzu8AgMKYGXteVJF2VRtHWlOqNmlYJ9f3bVxXYUj9tnNjO8RqCNX4RlWZbd5a77pqTO6Tun0su45y7-KeXXbUn7Gj4LpM5z_3KXu9u325ua8fn_493Cweay8aM9YatQdYKq-JeAg-mOWqMapBLpwRqN0cleekGq68d0RBSqdWRksn5oKjE6fscvq37P3YUh7t-7BNsay0XGthGjCoSupqSq1LTdvGMJTmvpwV9a0fIoW2vC-0UCilElgAPgE-DTknCnaT2t6lL4tg967t5NoW1_bbtd0VSExQLuFYRP52-YP6D6kQgoA</recordid><startdate>20230201</startdate><enddate>20230201</enddate><creator>Carr, Robert</creator><creator>Ravi, R.</creator><creator>Simonetti, Neil</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0001-6128-712X</orcidid></search><sort><creationdate>20230201</creationdate><title>A new integer programming formulation of the graphical traveling salesman problem</title><author>Carr, Robert ; Ravi, R. ; Simonetti, Neil</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c358t-717c00b6c7ee2ffcf8bd5865123a8317a916c2e6526ccaeef44a6d874a39321a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Combinatorics</topic><topic>Full Length Paper</topic><topic>Integer programming</topic><topic>Management science</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics of Computing</topic><topic>Numerical Analysis</topic><topic>Polynomials</topic><topic>Theoretical</topic><topic>Traveling salesman problem</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Carr, Robert</creatorcontrib><creatorcontrib>Ravi, R.</creatorcontrib><creatorcontrib>Simonetti, Neil</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Mathematical programming</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Carr, Robert</au><au>Ravi, R.</au><au>Simonetti, Neil</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A new integer programming formulation of the graphical traveling salesman problem</atitle><jtitle>Mathematical programming</jtitle><stitle>Math. Program</stitle><date>2023-02-01</date><risdate>2023</risdate><volume>197</volume><issue>2</issue><spage>877</spage><epage>902</epage><pages>877-902</pages><issn>0025-5610</issn><eissn>1436-4646</eissn><abstract>In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost
c
ij
of traveling from city
i
to city
j
, which is the same in either direction for the Symmetric TSP. The objective is to visit each city exactly once, minimizing total travel costs. In the Graphical TSP, a city may be visited more than once, which may be necessary on a sparse graph. We present a new integer programming formulation for the Graphical TSP requiring only two classes of polynomial-sized constraints while addressing an open question proposed by Denis Naddef. We generalize one of these classes, and present promising preliminary computational results.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s10107-022-01849-w</doi><tpages>26</tpages><orcidid>https://orcid.org/0000-0001-6128-712X</orcidid></addata></record> |
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| ispartof | Mathematical programming, 2023-02, Vol.197 (2), p.877-902 |
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| subjects | Calculus of Variations and Optimal Control Optimization Combinatorics Full Length Paper Integer programming Management science Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Polynomials Theoretical Traveling salesman problem |
| title | A new integer programming formulation of the graphical traveling salesman problem |
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