A compact transformation of arc routing problems into node routing problems
We describe a compact method to transform arc routing problem instances into node routing problem instances. Any node routing problem instance thus created must be solved by a branch-and-price process, such as the one described in this paper. The purpose is to make the number of nodes in the resulti...
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| Veröffentlicht in: | Annals of operations research 2015-03, Vol.226 (1), p.177-200 |
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| container_title | Annals of operations research |
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| creator | Foulds, Les Longo, Humberto Martins, Jean |
| description | We describe a compact method to transform arc routing problem instances into node routing problem instances. Any node routing problem instance thus created must be solved by a branch-and-price process, such as the one described in this paper. The purpose is to make the number of nodes in the resulting transformed graphs greater by only one unit than the number
r
of required arcs (arcs having demand) in the original graph, that is,
r
+
1
nodes. This low increase in the number of nodes represents an improvement compared to the methods previously presented by Pearn, Assad and Golden (
3
r
+
1
nodes) and by Longo, Poggi de Aragão and Uchoa and also by Baldacci and Maniezzo (
2
r
+
1
nodes). Using an adapted version of an existing branch-cut-and-price algorithm for a capacitated node routing problem on the transformed graph results in an effective approach for a capacitated arc routing problem. Computational experiments using this approach produced useful lower bounds in reasonable computational time for many challenging numerical instances from the literature. Additionally, some such previously open instances were solved to optimality for the first time. |
| doi_str_mv | 10.1007/s10479-014-1732-1 |
| format | Article |
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r
of required arcs (arcs having demand) in the original graph, that is,
r
+
1
nodes. This low increase in the number of nodes represents an improvement compared to the methods previously presented by Pearn, Assad and Golden (
3
r
+
1
nodes) and by Longo, Poggi de Aragão and Uchoa and also by Baldacci and Maniezzo (
2
r
+
1
nodes). Using an adapted version of an existing branch-cut-and-price algorithm for a capacitated node routing problem on the transformed graph results in an effective approach for a capacitated arc routing problem. Computational experiments using this approach produced useful lower bounds in reasonable computational time for many challenging numerical instances from the literature. Additionally, some such previously open instances were solved to optimality for the first time.</description><identifier>ISSN: 0254-5330</identifier><identifier>EISSN: 1572-9338</identifier><identifier>DOI: 10.1007/s10479-014-1732-1</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Algorithms ; Business and Management ; Combinatorics ; Computation ; Customers ; Graph theory ; Graphs ; Lower bounds ; Mathematical optimization ; Mathematical research ; Operations research ; Operations Research/Decision Theory ; Optimization ; Roads & highways ; Routing ; Shortest path algorithms ; Studies ; Texts ; Theory of Computation ; Transformations ; Transforms ; Transportation terminals ; Vehicles</subject><ispartof>Annals of operations research, 2015-03, Vol.226 (1), p.177-200</ispartof><rights>Springer Science+Business Media New York 2014</rights><rights>COPYRIGHT 2015 Springer</rights><rights>Springer Science+Business Media New York 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c523t-57656c015d9eb9b3ca54c82dd93511249c7651b30e44bcdd913cdebc6e9d3cc3</citedby><cites>FETCH-LOGICAL-c523t-57656c015d9eb9b3ca54c82dd93511249c7651b30e44bcdd913cdebc6e9d3cc3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10479-014-1732-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10479-014-1732-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Foulds, Les</creatorcontrib><creatorcontrib>Longo, Humberto</creatorcontrib><creatorcontrib>Martins, Jean</creatorcontrib><title>A compact transformation of arc routing problems into node routing problems</title><title>Annals of operations research</title><addtitle>Ann Oper Res</addtitle><description>We describe a compact method to transform arc routing problem instances into node routing problem instances. Any node routing problem instance thus created must be solved by a branch-and-price process, such as the one described in this paper. The purpose is to make the number of nodes in the resulting transformed graphs greater by only one unit than the number
r
of required arcs (arcs having demand) in the original graph, that is,
r
+
1
nodes. This low increase in the number of nodes represents an improvement compared to the methods previously presented by Pearn, Assad and Golden (
3
r
+
1
nodes) and by Longo, Poggi de Aragão and Uchoa and also by Baldacci and Maniezzo (
2
r
+
1
nodes). Using an adapted version of an existing branch-cut-and-price algorithm for a capacitated node routing problem on the transformed graph results in an effective approach for a capacitated arc routing problem. Computational experiments using this approach produced useful lower bounds in reasonable computational time for many challenging numerical instances from the literature. Additionally, some such previously open instances were solved to optimality for the first time.</description><subject>Algorithms</subject><subject>Business and Management</subject><subject>Combinatorics</subject><subject>Computation</subject><subject>Customers</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>Lower bounds</subject><subject>Mathematical optimization</subject><subject>Mathematical research</subject><subject>Operations research</subject><subject>Operations Research/Decision Theory</subject><subject>Optimization</subject><subject>Roads & highways</subject><subject>Routing</subject><subject>Shortest path algorithms</subject><subject>Studies</subject><subject>Texts</subject><subject>Theory of Computation</subject><subject>Transformations</subject><subject>Transforms</subject><subject>Transportation terminals</subject><subject>Vehicles</subject><issn>0254-5330</issn><issn>1572-9338</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>N95</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kU1r3DAQhkVpoNttfkBuhlx6qBONJfnjuITmgwR6yV3IY9lRsKWtxj7031eLA8kmLQIJZp53PvQydgb8AjivLgm4rJqcg8yhEkUOn9gGVFXkjRD1Z7bhhZK5EoJ_YV-JnjnnALXasPtdhmHaG5yzORpPfYiTmV3wWegzEzGLYZmdH7J9DO1oJ8qcn0PmQ2c_pL6xk96MZE9f3i17vP75eHWbP_y6ubvaPeSoCjHnqipViRxU19i2aQUaJbEuuq4RCqCQDSYAWsGtlC2mMAjsbIulbTqBKLbs-1o29f29WJr15AjtOBpvw0IayqpKmrLmCT1_hz6HJfo0XKKUkqpOLV-pwYxWO9-H9BV4KKp3klc1yFoWibr4B5VOZyeHwdvepfiR4McbQbuQ85bSRW54mmkwC9ExDiuOMRBF2-t9dJOJfzRwffBYrx7r5LE-eKwPkxerhhLrBxvf7Pdf0V-W36ds</recordid><startdate>20150301</startdate><enddate>20150301</enddate><creator>Foulds, Les</creator><creator>Longo, Humberto</creator><creator>Martins, Jean</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>N95</scope><scope>3V.</scope><scope>7TA</scope><scope>7TB</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AL</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JG9</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KR7</scope><scope>L.-</scope><scope>L6V</scope><scope>M0C</scope><scope>M0N</scope><scope>M2P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20150301</creationdate><title>A compact transformation of arc routing problems into node routing problems</title><author>Foulds, Les ; Longo, Humberto ; Martins, Jean</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c523t-57656c015d9eb9b3ca54c82dd93511249c7651b30e44bcdd913cdebc6e9d3cc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Algorithms</topic><topic>Business and Management</topic><topic>Combinatorics</topic><topic>Computation</topic><topic>Customers</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>Lower bounds</topic><topic>Mathematical optimization</topic><topic>Mathematical research</topic><topic>Operations research</topic><topic>Operations Research/Decision Theory</topic><topic>Optimization</topic><topic>Roads & highways</topic><topic>Routing</topic><topic>Shortest path algorithms</topic><topic>Studies</topic><topic>Texts</topic><topic>Theory of Computation</topic><topic>Transformations</topic><topic>Transforms</topic><topic>Transportation terminals</topic><topic>Vehicles</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Foulds, Les</creatorcontrib><creatorcontrib>Longo, Humberto</creatorcontrib><creatorcontrib>Martins, Jean</creatorcontrib><collection>CrossRef</collection><collection>Gale Business: Insights</collection><collection>ProQuest Central (Corporate)</collection><collection>Materials Business File</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Access via ABI/INFORM (ProQuest)</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Annals of operations research</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Foulds, Les</au><au>Longo, Humberto</au><au>Martins, Jean</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A compact transformation of arc routing problems into node routing problems</atitle><jtitle>Annals of operations research</jtitle><stitle>Ann Oper Res</stitle><date>2015-03-01</date><risdate>2015</risdate><volume>226</volume><issue>1</issue><spage>177</spage><epage>200</epage><pages>177-200</pages><issn>0254-5330</issn><eissn>1572-9338</eissn><abstract>We describe a compact method to transform arc routing problem instances into node routing problem instances. Any node routing problem instance thus created must be solved by a branch-and-price process, such as the one described in this paper. The purpose is to make the number of nodes in the resulting transformed graphs greater by only one unit than the number
r
of required arcs (arcs having demand) in the original graph, that is,
r
+
1
nodes. This low increase in the number of nodes represents an improvement compared to the methods previously presented by Pearn, Assad and Golden (
3
r
+
1
nodes) and by Longo, Poggi de Aragão and Uchoa and also by Baldacci and Maniezzo (
2
r
+
1
nodes). Using an adapted version of an existing branch-cut-and-price algorithm for a capacitated node routing problem on the transformed graph results in an effective approach for a capacitated arc routing problem. Computational experiments using this approach produced useful lower bounds in reasonable computational time for many challenging numerical instances from the literature. Additionally, some such previously open instances were solved to optimality for the first time.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s10479-014-1732-1</doi><tpages>24</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0254-5330 |
| ispartof | Annals of operations research, 2015-03, Vol.226 (1), p.177-200 |
| issn | 0254-5330 1572-9338 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1677913680 |
| source | EBSCOhost Business Source Complete; SpringerLink Journals - AutoHoldings |
| subjects | Algorithms Business and Management Combinatorics Computation Customers Graph theory Graphs Lower bounds Mathematical optimization Mathematical research Operations research Operations Research/Decision Theory Optimization Roads & highways Routing Shortest path algorithms Studies Texts Theory of Computation Transformations Transforms Transportation terminals Vehicles |
| title | A compact transformation of arc routing problems into node routing problems |
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