{"id":"https://openalex.org/W2017709219","doi":"https://doi.org/10.1007/s10472-011-9261-y","title":"Combining probabilistic algorithms, Constraint Programming and Lagrangian Relaxation to solve the Vehicle Routing Problem","display_name":"Combining probabilistic algorithms, Constraint Programming and Lagrangian Relaxation to solve the Vehicle Routing Problem","publication_year":2011,"publication_date":"2011-07-01","ids":{"openalex":"https://openalex.org/W2017709219","doi":"https://doi.org/10.1007/s10472-011-9261-y","mag":"2017709219"},"language":"en","primary_location":{"id":"doi:10.1007/s10472-011-9261-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10472-011-9261-y","pdf_url":null,"source":{"id":"https://openalex.org/S90199469","display_name":"Annals of Mathematics and Artificial Intelligence","issn_l":"1012-2443","issn":["1012-2443","1573-7470"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Mathematics and Artificial Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10609/90886","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049437685","display_name":"Daniel Guimarans","orcid":"https://orcid.org/0000-0002-5268-7241"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Daniel Guimarans","raw_affiliation_strings":["Dpt. de Telecomunicaci\u00f3 i Enginyeria de Sistemes, Universitat Aut\u00f2noma de Barcelona (UAB), Cerdanyola del Vall\u00e8s, 08193, Barcelona, Spain","Dpt. de Telecomunicaci\u00f3 i Enginyeria de Sistemes, Universitat Aut\u00f2noma de Barcelona (UAB), Barcelona, Spain 08193#TAB#"],"affiliations":[{"raw_affiliation_string":"Dpt. de Telecomunicaci\u00f3 i Enginyeria de Sistemes, Universitat Aut\u00f2noma de Barcelona (UAB), Cerdanyola del Vall\u00e8s, 08193, Barcelona, Spain","institution_ids":["https://openalex.org/I123044942"]},{"raw_affiliation_string":"Dpt. de Telecomunicaci\u00f3 i Enginyeria de Sistemes, Universitat Aut\u00f2noma de Barcelona (UAB), Barcelona, Spain 08193#TAB#","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079302293","display_name":"Rosa Herrero","orcid":"https://orcid.org/0000-0003-3575-0963"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Rosa Herrero","raw_affiliation_strings":["Dpt. de Telecomunicaci\u00f3 i Enginyeria de Sistemes, Universitat Aut\u00f2noma de Barcelona (UAB), Cerdanyola del Vall\u00e8s, 08193, Barcelona, Spain","Dpt. de Telecomunicaci\u00f3 i Enginyeria de Sistemes, Universitat Aut\u00f2noma de Barcelona (UAB), Barcelona, Spain 08193#TAB#"],"affiliations":[{"raw_affiliation_string":"Dpt. de Telecomunicaci\u00f3 i Enginyeria de Sistemes, Universitat Aut\u00f2noma de Barcelona (UAB), Cerdanyola del Vall\u00e8s, 08193, Barcelona, Spain","institution_ids":["https://openalex.org/I123044942"]},{"raw_affiliation_string":"Dpt. de Telecomunicaci\u00f3 i Enginyeria de Sistemes, Universitat Aut\u00f2noma de Barcelona (UAB), Barcelona, Spain 08193#TAB#","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030514013","display_name":"Daniel Riera","orcid":"https://orcid.org/0000-0002-4718-7234"},"institutions":[{"id":"https://openalex.org/I138847295","display_name":"Universitat Oberta de Catalunya","ror":"https://ror.org/01f5wp925","country_code":"ES","type":"education","lineage":["https://openalex.org/I138847295"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Daniel Riera","raw_affiliation_strings":["Universitat Oberta de Catalunya (UOC), Barcelona, Spain","Universitat Oberta de Catalunya (UOC); Barcelona Spain"],"affiliations":[{"raw_affiliation_string":"Universitat Oberta de Catalunya (UOC), Barcelona, Spain","institution_ids":["https://openalex.org/I138847295"]},{"raw_affiliation_string":"Universitat Oberta de Catalunya (UOC); Barcelona Spain","institution_ids":["https://openalex.org/I138847295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080136207","display_name":"\u00c1ngel A. Juan","orcid":"https://orcid.org/0000-0003-1392-1776"},"institutions":[{"id":"https://openalex.org/I138847295","display_name":"Universitat Oberta de Catalunya","ror":"https://ror.org/01f5wp925","country_code":"ES","type":"education","lineage":["https://openalex.org/I138847295"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Angel A. Juan","raw_affiliation_strings":["Universitat Oberta de Catalunya (UOC), Barcelona, Spain","Universitat Oberta de Catalunya (UOC); Barcelona Spain"],"affiliations":[{"raw_affiliation_string":"Universitat Oberta de Catalunya (UOC), Barcelona, Spain","institution_ids":["https://openalex.org/I138847295"]},{"raw_affiliation_string":"Universitat Oberta de Catalunya (UOC); Barcelona Spain","institution_ids":["https://openalex.org/I138847295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010580236","display_name":"Juan Jos\u00e9 Ramos","orcid":"https://orcid.org/0000-0002-0881-7205"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Juan Jos\u00e9 Ramos","raw_affiliation_strings":["Dpt. de Telecomunicaci\u00f3 i Enginyeria de Sistemes, Universitat Aut\u00f2noma de Barcelona (UAB), Cerdanyola del Vall\u00e8s, 08193, Barcelona, Spain","Dpt. de Telecomunicaci\u00f3 i Enginyeria de Sistemes, Universitat Aut\u00f2noma de Barcelona (UAB), Barcelona, Spain 08193#TAB#"],"affiliations":[{"raw_affiliation_string":"Dpt. de Telecomunicaci\u00f3 i Enginyeria de Sistemes, Universitat Aut\u00f2noma de Barcelona (UAB), Cerdanyola del Vall\u00e8s, 08193, Barcelona, Spain","institution_ids":["https://openalex.org/I123044942"]},{"raw_affiliation_string":"Dpt. de Telecomunicaci\u00f3 i Enginyeria de Sistemes, Universitat Aut\u00f2noma de Barcelona (UAB), Barcelona, Spain 08193#TAB#","institution_ids":["https://openalex.org/I123044942"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5049437685"],"corresponding_institution_ids":["https://openalex.org/I123044942"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.0487,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.90869903,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"62","issue":"3-4","first_page":"299","last_page":"315"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11942","display_name":"Transportation and Mobility Innovations","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/vehicle-routing-problem","display_name":"Vehicle routing problem","score":0.845206618309021},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.688946008682251},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6362261772155762},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6003109812736511},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5984025001525879},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.5724672079086304},{"id":"https://openalex.org/keywords/flexibility","display_name":"Flexibility (engineering)","score":0.5097705721855164},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5081589221954346},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.48087790608406067},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.46753427386283875},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.46287041902542114},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.4550843834877014},{"id":"https://openalex.org/keywords/probabilistic-analysis-of-algorithms","display_name":"Probabilistic analysis of algorithms","score":0.43297770619392395},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41012445092201233},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.34648212790489197},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.327822744846344},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15973860025405884}],"concepts":[{"id":"https://openalex.org/C123784306","wikidata":"https://www.wikidata.org/wiki/Q944041","display_name":"Vehicle routing problem","level":3,"score":0.845206618309021},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.688946008682251},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6362261772155762},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6003109812736511},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5984025001525879},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.5724672079086304},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.5097705721855164},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5081589221954346},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.48087790608406067},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.46753427386283875},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.46287041902542114},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.4550843834877014},{"id":"https://openalex.org/C24404364","wikidata":"https://www.wikidata.org/wiki/Q7246846","display_name":"Probabilistic analysis of algorithms","level":3,"score":0.43297770619392395},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41012445092201233},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.34648212790489197},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.327822744846344},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15973860025405884},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10472-011-9261-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10472-011-9261-y","pdf_url":null,"source":{"id":"https://openalex.org/S90199469","display_name":"Annals of Mathematics and Artificial Intelligence","issn_l":"1012-2443","issn":["1012-2443","1573-7470"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Mathematics and Artificial Intelligence","raw_type":"journal-article"},{"id":"pmh:oai:dnet:orepositorio::b6657f18df39eed2e5d03895ff09b556","is_oa":true,"landing_page_url":"http://hdl.handle.net/10609/90886","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:upcommons.upc.edu:2117/17339","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/17339","pdf_url":null,"source":{"id":"https://openalex.org/S4210207057","display_name":"QRU Quaderns de Recerca en Urbanisme","issn_l":"2014-9689","issn":["2014-9689","2385-6777"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310322448","host_organization_name":"Q71272178","host_organization_lineage":["https://openalex.org/P4310322448"],"host_organization_lineage_names":["Q71272178"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:dnet:orepositorio::b6657f18df39eed2e5d03895ff09b556","is_oa":true,"landing_page_url":"http://hdl.handle.net/10609/90886","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.7400000095367432,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W47957325","https://openalex.org/W161389394","https://openalex.org/W161739349","https://openalex.org/W1481869366","https://openalex.org/W1488405589","https://openalex.org/W1509915115","https://openalex.org/W1571106608","https://openalex.org/W1588856286","https://openalex.org/W1601649239","https://openalex.org/W1717440967","https://openalex.org/W1966687122","https://openalex.org/W1966842536","https://openalex.org/W1967029759","https://openalex.org/W1968609670","https://openalex.org/W1971400038","https://openalex.org/W1972755385","https://openalex.org/W1983258309","https://openalex.org/W1992870153","https://openalex.org/W1995235889","https://openalex.org/W2005944398","https://openalex.org/W2010334716","https://openalex.org/W2027106651","https://openalex.org/W2037882067","https://openalex.org/W2039766013","https://openalex.org/W2041228906","https://openalex.org/W2046280257","https://openalex.org/W2048583876","https://openalex.org/W2052614107","https://openalex.org/W2058748455","https://openalex.org/W2061239862","https://openalex.org/W2069973745","https://openalex.org/W2083743924","https://openalex.org/W2084599642","https://openalex.org/W2090275183","https://openalex.org/W2108536179","https://openalex.org/W2111174053","https://openalex.org/W2111563176","https://openalex.org/W2111581650","https://openalex.org/W2125784747","https://openalex.org/W2132210624","https://openalex.org/W2134946882","https://openalex.org/W2148975235","https://openalex.org/W2150319243","https://openalex.org/W2154524377","https://openalex.org/W2163192379","https://openalex.org/W2192152020","https://openalex.org/W2337727499","https://openalex.org/W2489984537","https://openalex.org/W2791704884","https://openalex.org/W2997776631","https://openalex.org/W2999341115","https://openalex.org/W3023322615","https://openalex.org/W3140629188","https://openalex.org/W4236384091","https://openalex.org/W6601945944"],"related_works":["https://openalex.org/W2131718214","https://openalex.org/W2167308866","https://openalex.org/W1635517180","https://openalex.org/W2051181280","https://openalex.org/W4287147549","https://openalex.org/W2894610790","https://openalex.org/W195910675","https://openalex.org/W4386570139","https://openalex.org/W2176720246","https://openalex.org/W2800829962"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}