{"id":"https://openalex.org/W2157809688","doi":"https://doi.org/10.1016/s0165-4896(99)00056-6","title":"Characterizing properties of approximate solutions for optimization problems","display_name":"Characterizing properties of approximate solutions for optimization problems","publication_year":2000,"publication_date":"2000-11-01","ids":{"openalex":"https://openalex.org/W2157809688","doi":"https://doi.org/10.1016/s0165-4896(99)00056-6","mag":"2157809688"},"language":"en","primary_location":{"id":"doi:10.1016/s0165-4896(99)00056-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0165-4896(99)00056-6","pdf_url":null,"source":{"id":"https://openalex.org/S149064342","display_name":"Mathematical Social Sciences","issn_l":"0165-4896","issn":["0165-4896","1879-3118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Social Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040358774","display_name":"Henk Norde","orcid":"https://orcid.org/0000-0003-1541-8189"},"institutions":[{"id":"https://openalex.org/I193700539","display_name":"Tilburg University","ror":"https://ror.org/04b8v1s79","country_code":"NL","type":"education","lineage":["https://openalex.org/I193700539"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Henk Norde","raw_affiliation_strings":["Department of Econometrics and CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Econometrics and CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands","institution_ids":["https://openalex.org/I193700539"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033164576","display_name":"Fioravante Patrone","orcid":null},"institutions":[{"id":"https://openalex.org/I83816512","display_name":"University of Genoa","ror":"https://ror.org/0107c5v14","country_code":"IT","type":"education","lineage":["https://openalex.org/I83816512"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Fioravante Patrone","raw_affiliation_strings":["Department of Mathematics, Via Dodecaneso 35, University of Genoa, 16146 Genoa, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Via Dodecaneso 35, University of Genoa, 16146 Genoa, Italy","institution_ids":["https://openalex.org/I83816512"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110737580","display_name":"S.H. Tijs","orcid":null},"institutions":[{"id":"https://openalex.org/I193700539","display_name":"Tilburg University","ror":"https://ror.org/04b8v1s79","country_code":"NL","type":"education","lineage":["https://openalex.org/I193700539"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Stef Tijs","raw_affiliation_strings":["Department of Econometrics and CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Econometrics and CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands","institution_ids":["https://openalex.org/I193700539"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040358774"],"corresponding_institution_ids":["https://openalex.org/I193700539"],"apc_list":{"value":2720,"currency":"USD","value_usd":2720},"apc_paid":null,"fwci":1.1198,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.87785356,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"40","issue":"3","first_page":"297","last_page":"311"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11182","display_name":"Auction Theory and Applications","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/satisficing","display_name":"Satisficing","score":0.8653359413146973},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7641915082931519},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6855190992355347},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6764293313026428},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.548774778842926},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5372649431228638},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.527636706829071},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5218449831008911},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47008609771728516},{"id":"https://openalex.org/keywords/bounded-rationality","display_name":"Bounded rationality","score":0.46060851216316223},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.45733198523521423},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4362143874168396},{"id":"https://openalex.org/keywords/sort","display_name":"sort","score":0.43247273564338684},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.4189629554748535},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.4159996509552002},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3347039222717285},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.32051360607147217},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2647448778152466},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19876432418823242},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12368223071098328},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08395513892173767}],"concepts":[{"id":"https://openalex.org/C94822996","wikidata":"https://www.wikidata.org/wiki/Q1777902","display_name":"Satisficing","level":2,"score":0.8653359413146973},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7641915082931519},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6855190992355347},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6764293313026428},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.548774778842926},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5372649431228638},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.527636706829071},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5218449831008911},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47008609771728516},{"id":"https://openalex.org/C58694771","wikidata":"https://www.wikidata.org/wiki/Q814385","display_name":"Bounded rationality","level":2,"score":0.46060851216316223},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.45733198523521423},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4362143874168396},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.43247273564338684},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.4189629554748535},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4159996509552002},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3347039222717285},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.32051360607147217},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2647448778152466},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19876432418823242},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12368223071098328},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08395513892173767},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/s0165-4896(99)00056-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0165-4896(99)00056-6","pdf_url":null,"source":{"id":"https://openalex.org/S149064342","display_name":"Mathematical Social Sciences","issn_l":"0165-4896","issn":["0165-4896","1879-3118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Social Sciences","raw_type":"journal-article"},{"id":"pmh:oai:tilburguniversity.edu:publications/3dcd6016-ec6d-46fc-941d-2e39d3083630","is_oa":false,"landing_page_url":"https://research.tilburguniversity.edu/en/publications/3dcd6016-ec6d-46fc-941d-2e39d3083630","pdf_url":null,"source":{"id":"https://openalex.org/S4306401490","display_name":"Research portal (Tilburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193700539","host_organization_name":"Tilburg University","host_organization_lineage":["https://openalex.org/I193700539"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"},{"id":"https://openalex.org/F4320324594","display_name":"Universiteit van Tilburg","ror":"https://ror.org/04b8v1s79"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1486587973","https://openalex.org/W1503702085","https://openalex.org/W1540131774","https://openalex.org/W1554220717","https://openalex.org/W1996140050","https://openalex.org/W2006353636","https://openalex.org/W2011758327","https://openalex.org/W2015345803","https://openalex.org/W2034716068","https://openalex.org/W2110667918","https://openalex.org/W2122906957","https://openalex.org/W2148962857","https://openalex.org/W2335705189","https://openalex.org/W4206111119","https://openalex.org/W6629913385"],"related_works":["https://openalex.org/W2077638144","https://openalex.org/W2792598057","https://openalex.org/W4252791283","https://openalex.org/W4293230663","https://openalex.org/W2071697325","https://openalex.org/W3148966567","https://openalex.org/W1694674282","https://openalex.org/W2506356602","https://openalex.org/W4234968985","https://openalex.org/W4249305459"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}