{"id":"https://openalex.org/W2602220366","doi":null,"title":"Comparison of algorithms for solving a bi-level toll setting problem","display_name":"Comparison of algorithms for solving a bi-level toll setting problem","publication_year":2010,"publication_date":"2010-08-01","ids":{"openalex":"https://openalex.org/W2602220366","mag":"2602220366"},"language":"en","primary_location":{"id":"mag:2602220366","doi":null,"is_oa":false,"landing_page_url":"http://www.ijicic.org/09-0243-1.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S91105121","display_name":"International journal of innovative computing, information & control","issn_l":"1349-4198","issn":["1349-4198"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310313486","host_organization_name":"Kyushu Tokai University","host_organization_lineage":["https://openalex.org/P4310313486"],"host_organization_lineage_names":["Kyushu Tokai University"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"International journal of innovative computing, information & control","raw_type":null},"volume":null,"type":"article","indexed_in":[],"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/A5028634910","display_name":"Vyacheslav V. Kalashnikov","orcid":"https://orcid.org/0000-0001-6747-580X","observed_orcids":["https://orcid.org/0000-0001-6747-580X"]},"institutions":[{"id":"https://openalex.org/I98461037","display_name":"Tecnol\u00f3gico de Monterrey","ror":"https://ror.org/03ayjn504","country_code":"MX","type":"education","lineage":["https://openalex.org/I98461037"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Vyacheslav V. Kalashnikov","raw_affiliation_strings":["Instituto Tecnologico de Estudios Superiores de Monterrey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto Tecnologico de Estudios Superiores de Monterrey","institution_ids":["https://openalex.org/I98461037"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Fernando Camacho","orcid":"https://orcid.org/0000-0002-3077-5689","observed_orcids":["https://orcid.org/0000-0002-3077-5689"]},"institutions":[{"id":"https://openalex.org/I98461037","display_name":"Tecnol\u00f3gico de Monterrey","ror":"https://ror.org/03ayjn504","country_code":"MX","type":"education","lineage":["https://openalex.org/I98461037"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Fernando Camacho","raw_affiliation_strings":["Instituto Tecnologico de Estudios Superiores de Monterrey"],"raw_orcid":"https://orcid.org/0000-0002-3077-5689","affiliations":[{"raw_affiliation_string":"Instituto Tecnologico de Estudios Superiores de Monterrey","institution_ids":["https://openalex.org/I98461037"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011219336","display_name":"Ronald G. Askin","orcid":"https://orcid.org/0000-0002-8348-448X","observed_orcids":["https://orcid.org/0000-0002-8348-448X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ronald G. Askin","raw_affiliation_strings":["IAFSE-SCAI: Industrial, Systems and Operations Engineering"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IAFSE-SCAI: Industrial, Systems and Operations Engineering","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102762639","display_name":"Nataliya I. Kalashnykova","orcid":"https://orcid.org/0000-0002-3892-6605","observed_orcids":["https://orcid.org/0000-0002-3892-6605","https://orcid.org/0000-0002-2314-3106"]},"institutions":[{"id":"https://openalex.org/I169046204","display_name":"Universidad Aut\u00f3noma de Nuevo Le\u00f3n","ror":"https://ror.org/01fh86n78","country_code":"MX","type":"education","lineage":["https://openalex.org/I169046204"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Nataliya Kalashnykova","raw_affiliation_strings":["Universidad Aut\u00f3noma De Nuevo Le\u00f3n"],"raw_orcid":"https://orcid.org/0000-0002-2314-3106","affiliations":[{"raw_affiliation_string":"Universidad Aut\u00f3noma De Nuevo Le\u00f3n","institution_ids":["https://openalex.org/I169046204"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3331,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.91689444,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"6","issue":"8","first_page":"3529","last_page":"3549"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9125999808311462,"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"}},"topics":[{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9125999808311462,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.044199999421834946,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.010300000198185444,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/toll-setting","display_name":"toll setting","score":0.652999997138977},{"id":"https://openalex.org/keywords/bi-level-optimization","display_name":"bi-level optimization","score":0.8820000290870667},{"id":"https://openalex.org/keywords/traffic-equilibrium","display_name":"traffic equilibrium","score":0.4880000054836273},{"id":"https://openalex.org/keywords/penalty-function","display_name":"penalty method","score":0.5260000228881836},{"id":"https://openalex.org/keywords/quasi-newton-methods","display_name":"quasi-Newton methods","score":0.9649999737739563},{"id":"https://openalex.org/keywords/nelder-mead-simplex-search","display_name":"Nelder-Mead simplex search","score":0.8420000076293945},{"id":"https://openalex.org/keywords/gradient-approximation","display_name":"gradient approximation","score":0.6320000290870667},{"id":"https://openalex.org/keywords/algorithm-comparison","display_name":"algorithm comparison","score":0.45100000500679016},{"id":"https://openalex.org/keywords/travel-cost","display_name":"travel cost","score":0.38100001215934753}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8013208508491516},{"id":"https://openalex.org/C2778025104","wikidata":"https://www.wikidata.org/wiki/Q408004","display_name":"Toll","level":2,"score":0.6279057264328003},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6226370334625244},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.605766236782074},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5867593884468079},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.520144522190094},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.49150073528289795},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.4388086795806885},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.4128103256225586},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.3777303099632263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.13994058966636658},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2602220366","doi":null,"is_oa":false,"landing_page_url":"http://www.ijicic.org/09-0243-1.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S91105121","display_name":"International journal of innovative computing, information & control","issn_l":"1349-4198","issn":["1349-4198"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310313486","host_organization_name":"Kyushu Tokai University","host_organization_lineage":["https://openalex.org/P4310313486"],"host_organization_lineage_names":["Kyushu Tokai University"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"International journal of innovative computing, information & control","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.5378999710083008}],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1968531280","https://openalex.org/W1985348591","https://openalex.org/W2017040431","https://openalex.org/W2024975435","https://openalex.org/W2051247543","https://openalex.org/W2098679148","https://openalex.org/W2111240209","https://openalex.org/W2171074980","https://openalex.org/W2378023240","https://openalex.org/W2804405339","https://openalex.org/W2804857345","https://openalex.org/W3169384099"],"related_works":["https://openalex.org/W2035893651","https://openalex.org/W56282943","https://openalex.org/W107294591","https://openalex.org/W3007423803","https://openalex.org/W2561916901","https://openalex.org/W2103512375","https://openalex.org/W2912684174","https://openalex.org/W2139696051","https://openalex.org/W2063513976","https://openalex.org/W2138603670"],"abstract_inverted_index":{"In":[0,118],"this":[1,122],"paper,":[2],"we":[3,102,125],"consider":[4],"the":[5,12,29,46,49,62,92,98,114,169,177,181],"problem":[6,20,73,123],"of":[7,14,45,57,168,176],"assigning":[8],"optimal":[9],"tolls":[10,41,82,87],"to":[11,67,112,120],"arcs":[13,44],"a":[15,24,35,55,68,130,136,154,158,163],"multi-commodity":[16],"transportation":[17],"network.":[18],"The":[19,72,142,174],"is":[21,32,52,144,149],"formulated":[22],"as":[23,77,129],"bi-level":[25,93],"mathematical":[26,132],"program":[27,133],"where":[28],"upper":[30],"level":[31,51],"managed":[33],"by":[34,54],"firm":[36],"that":[37],"raises":[38],"revenues":[39,85],"from":[40],"set":[42],"on":[43,109],"network":[47],"and":[48,86,96,104,134,146,162],"lower":[50],"represented":[53],"group":[56],"car":[58],"users":[59],"traveling":[60],"along":[61],"cheapest":[63],"paths":[64],"with":[65],"respect":[66],"generalized":[69],"travel":[70],"cost.":[71],"can":[74],"be":[75],"interpreted":[76],"finding":[78],"an":[79],"equilibrium":[80],"among":[81],"generating":[83],"high":[84],"attracting":[88],"customers.":[89],"We":[90,151],"describe":[91,135],"programming":[94],"model":[95],"discuss":[97],"underlying":[99],"assumptions.":[100],"Next,":[101],"propose":[103],"evaluate":[105],"four":[106],"algorithms":[107],"based":[108],"different":[110],"principles":[111],"solve":[113,121],"toll":[115],"optimization":[116],"problem.":[117],"order":[119],"efficiently,":[124],"first":[126],"reformulate":[127],"it":[128],"standard":[131],"penalty-function":[137],"algorithm":[138,143],"for":[139],"its":[140,147],"solution.":[141],"well-founded":[145],"convergence":[148],"established.":[150],"then":[152],"detail":[153],"proposed":[155],"quasi-Newton-type":[156],"algorithm,":[157,161],"gradient":[159],"approximation-based":[160],"direct":[164],"method":[165],"making":[166],"use":[167],"Nelder-Mead":[170],"flexible":[171],"simplex":[172],"search.":[173],"results":[175],"numerical":[178],"experiments":[179],"support":[180],"algorithms\u2019":[182],"robustness.":[183]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-11-01T11:40:01.658920","created_date":"2017-04-07T00:00:00"}