Robust optimal discrete arc sizing for tree-shaped potential networks
We consider the problem of discrete arc sizing for tree-shaped potential networks with respect to infinitely many demand scenarios. This means that the arc sizes need to be feasible for an infinite set of scenarios. The problem can be seen as a strictly robust counterpart of a single-scenario networ...
Gespeichert in:
| Veröffentlicht in: | Computational optimization and applications 2019-07, Vol.73 (3), p.791-819 |
|---|---|
| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 819 |
|---|---|
| container_issue | 3 |
| container_start_page | 791 |
| container_title | Computational optimization and applications |
| container_volume | 73 |
| creator | Robinius, Martin Schewe, Lars Schmidt, Martin Stolten, Detlef Thürauf, Johannes Welder, Lara |
| description | We consider the problem of discrete arc sizing for tree-shaped potential networks with respect to infinitely many demand scenarios. This means that the arc sizes need to be feasible for an infinite set of scenarios. The problem can be seen as a strictly robust counterpart of a single-scenario network design problem, which is shown to be NP-complete even on trees. In order to obtain a tractable problem, we introduce a method for generating a finite scenario set such that optimality of a sizing for this finite set implies the sizing’s optimality for the originally given infinite set of scenarios. We further prove that the size of the finite scenario set is quadratically bounded above in the number of nodes of the underlying tree and that it can be computed in polynomial time. The resulting problem can then be solved as a standard mixed-integer linear optimization problem. Finally, we show the applicability of our theoretical results by computing globally optimal arc sizes for a realistic hydrogen transport network of Eastern Germany. |
| doi_str_mv | 10.1007/s10589-019-00085-x |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2196100939</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2196100939</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-16ee82160e5cf8a66b044d62f7b163399ba560ea3504f819e7fc9b0ba0ad8fa43</originalsourceid><addsrcrecordid>eNp9kE1LxDAQhoMouH78AU8Bz9FJ0qbNUZb1AxYE0XNI28nadW1qksXVX2-0gjcPwxzmeWeYh5AzDhccoLqMHMpaM-C5AOqS7fbIjJeVZKLWxT6ZgRaKKQB5SI5iXGdIV1LMyOLBN9uYqB9T_2o3tOtjGzAhtaGlsf_shxV1PtAUEFl8tiN2dPQJh9RnesD07sNLPCEHzm4inv72Y_J0vXic37Ll_c3d_GrJWsl1Ylwh1oIrwLJ1tVWqgaLolHBVw5WUWje2zEMrSyhczTVWrtUNNBZsVztbyGNyPu0dg3_bYkxm7bdhyCeN4FplFVrqTImJaoOPMaAzY8jPhQ_DwXzrMpMuk3WZH11ml0NyCsUMDysMf6v_SX0Bcw9uZQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2196100939</pqid></control><display><type>article</type><title>Robust optimal discrete arc sizing for tree-shaped potential networks</title><source>SpringerLink (full text journal articles and electronic books)</source><source>EBSCO Business Source Complete</source><creator>Robinius, Martin ; Schewe, Lars ; Schmidt, Martin ; Stolten, Detlef ; Thürauf, Johannes ; Welder, Lara</creator><creatorcontrib>Robinius, Martin ; Schewe, Lars ; Schmidt, Martin ; Stolten, Detlef ; Thürauf, Johannes ; Welder, Lara</creatorcontrib><description>We consider the problem of discrete arc sizing for tree-shaped potential networks with respect to infinitely many demand scenarios. This means that the arc sizes need to be feasible for an infinite set of scenarios. The problem can be seen as a strictly robust counterpart of a single-scenario network design problem, which is shown to be NP-complete even on trees. In order to obtain a tractable problem, we introduce a method for generating a finite scenario set such that optimality of a sizing for this finite set implies the sizing’s optimality for the originally given infinite set of scenarios. We further prove that the size of the finite scenario set is quadratically bounded above in the number of nodes of the underlying tree and that it can be computed in polynomial time. The resulting problem can then be solved as a standard mixed-integer linear optimization problem. Finally, we show the applicability of our theoretical results by computing globally optimal arc sizes for a realistic hydrogen transport network of Eastern Germany.</description><identifier>ISSN: 0926-6003</identifier><identifier>EISSN: 1573-2894</identifier><identifier>DOI: 10.1007/s10589-019-00085-x</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Convex and Discrete Geometry ; Management Science ; Mathematics ; Mathematics and Statistics ; Operations Research ; Operations Research/Decision Theory ; Optimization ; Polynomials ; Sizing ; Statistics ; Transportation networks</subject><ispartof>Computational optimization and applications, 2019-07, Vol.73 (3), p.791-819</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2019</rights><rights>Computational Optimization and Applications is a copyright of Springer, (2019). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-16ee82160e5cf8a66b044d62f7b163399ba560ea3504f819e7fc9b0ba0ad8fa43</citedby><cites>FETCH-LOGICAL-c319t-16ee82160e5cf8a66b044d62f7b163399ba560ea3504f819e7fc9b0ba0ad8fa43</cites><orcidid>0000-0001-6208-5677 ; 0000-0002-3778-262X</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/s10589-019-00085-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10589-019-00085-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Robinius, Martin</creatorcontrib><creatorcontrib>Schewe, Lars</creatorcontrib><creatorcontrib>Schmidt, Martin</creatorcontrib><creatorcontrib>Stolten, Detlef</creatorcontrib><creatorcontrib>Thürauf, Johannes</creatorcontrib><creatorcontrib>Welder, Lara</creatorcontrib><title>Robust optimal discrete arc sizing for tree-shaped potential networks</title><title>Computational optimization and applications</title><addtitle>Comput Optim Appl</addtitle><description>We consider the problem of discrete arc sizing for tree-shaped potential networks with respect to infinitely many demand scenarios. This means that the arc sizes need to be feasible for an infinite set of scenarios. The problem can be seen as a strictly robust counterpart of a single-scenario network design problem, which is shown to be NP-complete even on trees. In order to obtain a tractable problem, we introduce a method for generating a finite scenario set such that optimality of a sizing for this finite set implies the sizing’s optimality for the originally given infinite set of scenarios. We further prove that the size of the finite scenario set is quadratically bounded above in the number of nodes of the underlying tree and that it can be computed in polynomial time. The resulting problem can then be solved as a standard mixed-integer linear optimization problem. Finally, we show the applicability of our theoretical results by computing globally optimal arc sizes for a realistic hydrogen transport network of Eastern Germany.</description><subject>Convex and Discrete Geometry</subject><subject>Management Science</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operations Research</subject><subject>Operations Research/Decision Theory</subject><subject>Optimization</subject><subject>Polynomials</subject><subject>Sizing</subject><subject>Statistics</subject><subject>Transportation networks</subject><issn>0926-6003</issn><issn>1573-2894</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp9kE1LxDAQhoMouH78AU8Bz9FJ0qbNUZb1AxYE0XNI28nadW1qksXVX2-0gjcPwxzmeWeYh5AzDhccoLqMHMpaM-C5AOqS7fbIjJeVZKLWxT6ZgRaKKQB5SI5iXGdIV1LMyOLBN9uYqB9T_2o3tOtjGzAhtaGlsf_shxV1PtAUEFl8tiN2dPQJh9RnesD07sNLPCEHzm4inv72Y_J0vXic37Ll_c3d_GrJWsl1Ylwh1oIrwLJ1tVWqgaLolHBVw5WUWje2zEMrSyhczTVWrtUNNBZsVztbyGNyPu0dg3_bYkxm7bdhyCeN4FplFVrqTImJaoOPMaAzY8jPhQ_DwXzrMpMuk3WZH11ml0NyCsUMDysMf6v_SX0Bcw9uZQ</recordid><startdate>20190701</startdate><enddate>20190701</enddate><creator>Robinius, Martin</creator><creator>Schewe, Lars</creator><creator>Schmidt, Martin</creator><creator>Stolten, Detlef</creator><creator>Thürauf, Johannes</creator><creator>Welder, Lara</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</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>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</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>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope><orcidid>https://orcid.org/0000-0001-6208-5677</orcidid><orcidid>https://orcid.org/0000-0002-3778-262X</orcidid></search><sort><creationdate>20190701</creationdate><title>Robust optimal discrete arc sizing for tree-shaped potential networks</title><author>Robinius, Martin ; Schewe, Lars ; Schmidt, Martin ; Stolten, Detlef ; Thürauf, Johannes ; Welder, Lara</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-16ee82160e5cf8a66b044d62f7b163399ba560ea3504f819e7fc9b0ba0ad8fa43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Convex and Discrete Geometry</topic><topic>Management Science</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operations Research</topic><topic>Operations Research/Decision Theory</topic><topic>Optimization</topic><topic>Polynomials</topic><topic>Sizing</topic><topic>Statistics</topic><topic>Transportation networks</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Robinius, Martin</creatorcontrib><creatorcontrib>Schewe, Lars</creatorcontrib><creatorcontrib>Schmidt, Martin</creatorcontrib><creatorcontrib>Stolten, Detlef</creatorcontrib><creatorcontrib>Thürauf, Johannes</creatorcontrib><creatorcontrib>Welder, Lara</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection</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)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>ProQuest Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection (Proquest) (PQ_SDU_P3)</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>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering 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><collection>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>ProQuest Science Journals</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>One Business (ProQuest)</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>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Computational optimization and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Robinius, Martin</au><au>Schewe, Lars</au><au>Schmidt, Martin</au><au>Stolten, Detlef</au><au>Thürauf, Johannes</au><au>Welder, Lara</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Robust optimal discrete arc sizing for tree-shaped potential networks</atitle><jtitle>Computational optimization and applications</jtitle><stitle>Comput Optim Appl</stitle><date>2019-07-01</date><risdate>2019</risdate><volume>73</volume><issue>3</issue><spage>791</spage><epage>819</epage><pages>791-819</pages><issn>0926-6003</issn><eissn>1573-2894</eissn><abstract>We consider the problem of discrete arc sizing for tree-shaped potential networks with respect to infinitely many demand scenarios. This means that the arc sizes need to be feasible for an infinite set of scenarios. The problem can be seen as a strictly robust counterpart of a single-scenario network design problem, which is shown to be NP-complete even on trees. In order to obtain a tractable problem, we introduce a method for generating a finite scenario set such that optimality of a sizing for this finite set implies the sizing’s optimality for the originally given infinite set of scenarios. We further prove that the size of the finite scenario set is quadratically bounded above in the number of nodes of the underlying tree and that it can be computed in polynomial time. The resulting problem can then be solved as a standard mixed-integer linear optimization problem. Finally, we show the applicability of our theoretical results by computing globally optimal arc sizes for a realistic hydrogen transport network of Eastern Germany.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10589-019-00085-x</doi><tpages>29</tpages><orcidid>https://orcid.org/0000-0001-6208-5677</orcidid><orcidid>https://orcid.org/0000-0002-3778-262X</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0926-6003 |
| ispartof | Computational optimization and applications, 2019-07, Vol.73 (3), p.791-819 |
| issn | 0926-6003 1573-2894 |
| language | eng |
| recordid | cdi_proquest_journals_2196100939 |
| source | SpringerLink (full text journal articles and electronic books); EBSCO Business Source Complete |
| subjects | Convex and Discrete Geometry Management Science Mathematics Mathematics and Statistics Operations Research Operations Research/Decision Theory Optimization Polynomials Sizing Statistics Transportation networks |
| title | Robust optimal discrete arc sizing for tree-shaped potential networks |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T19%3A23%3A56IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Robust%20optimal%20discrete%20arc%20sizing%20for%20tree-shaped%20potential%20networks&rft.jtitle=Computational%20optimization%20and%20applications&rft.au=Robinius,%20Martin&rft.date=2019-07-01&rft.volume=73&rft.issue=3&rft.spage=791&rft.epage=819&rft.pages=791-819&rft.issn=0926-6003&rft.eissn=1573-2894&rft_id=info:doi/10.1007/s10589-019-00085-x&rft_dat=%3Cproquest_cross%3E2196100939%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2196100939&rft_id=info:pmid/&rfr_iscdi=true |