{"id":"https://openalex.org/W4408017198","doi":"https://doi.org/10.1109/access.2025.3546320","title":"Linear Programming of the Loopwise Route Representation for the Shortest Path Problems by Introducing the Reference Link Flow","display_name":"Linear Programming of the Loopwise Route Representation for the Shortest Path Problems by Introducing the Reference Link Flow","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4408017198","doi":"https://doi.org/10.1109/access.2025.3546320"},"language":"en","primary_location":{"id":"doi:10.1109/access.2025.3546320","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3546320","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2025.3546320","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089653203","display_name":"Geunu Kim","orcid":"https://orcid.org/0000-0002-6253-2091"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Geunu Kim","raw_affiliation_strings":["Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology, Daejeon, South Korea"],"raw_orcid":"https://orcid.org/0000-0002-6253-2091","affiliations":[{"raw_affiliation_string":"Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology, Daejeon, South Korea","institution_ids":["https://openalex.org/I157485424"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058889039","display_name":"\uae40\ucc3d\uc601","orcid":null},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Changyeong Kim","raw_affiliation_strings":["Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology, Daejeon, South Korea"],"raw_orcid":"https://orcid.org/0009-0003-7873-3749","affiliations":[{"raw_affiliation_string":"Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology, Daejeon, South Korea","institution_ids":["https://openalex.org/I157485424"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Sanghoon Park","orcid":"https://orcid.org/0009-0005-9332-5350"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Sanghoon Park","raw_affiliation_strings":["Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology, Daejeon, South Korea"],"raw_orcid":"https://orcid.org/0009-0005-9332-5350","affiliations":[{"raw_affiliation_string":"Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology, Daejeon, South Korea","institution_ids":["https://openalex.org/I157485424"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jeonghun Kim","orcid":"https://orcid.org/0009-0006-1156-6415"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jeonghun Kim","raw_affiliation_strings":["Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology, Daejeon, South Korea"],"raw_orcid":"https://orcid.org/0009-0006-1156-6415","affiliations":[{"raw_affiliation_string":"Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology, Daejeon, South Korea","institution_ids":["https://openalex.org/I157485424"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010463699","display_name":"In Gwun Jang","orcid":"https://orcid.org/0000-0002-5250-1208"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"In Gwun Jang","raw_affiliation_strings":["Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology, Daejeon, South Korea"],"raw_orcid":"https://orcid.org/0000-0002-5250-1208","affiliations":[{"raw_affiliation_string":"Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology, Daejeon, South Korea","institution_ids":["https://openalex.org/I157485424"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5089653203"],"corresponding_institution_ids":["https://openalex.org/I157485424"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":1.0875,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.74682965,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"13","issue":null,"first_page":"38856","last_page":"38864"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10524","display_name":"Traffic control and management","score":0.9976000189781189,"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"}},{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/link","display_name":"Link (geometry)","score":0.7044650316238403},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6925497651100159},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.6674051284790039},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5812877416610718},{"id":"https://openalex.org/keywords/k-shortest-path-routing","display_name":"K shortest path routing","score":0.5521451830863953},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5118104815483093},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.4657175540924072},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.4644913971424103},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4557194411754608},{"id":"https://openalex.org/keywords/dijkstras-algorithm","display_name":"Dijkstra's algorithm","score":0.44344577193260193},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.43585461378097534},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4019466042518616},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3226397633552551},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.2472628653049469},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19678714871406555},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.09699386358261108}],"concepts":[{"id":"https://openalex.org/C2778753846","wikidata":"https://www.wikidata.org/wiki/Q6554239","display_name":"Link (geometry)","level":2,"score":0.7044650316238403},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6925497651100159},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.6674051284790039},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5812877416610718},{"id":"https://openalex.org/C70266271","wikidata":"https://www.wikidata.org/wiki/Q6343044","display_name":"K shortest path routing","level":4,"score":0.5521451830863953},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5118104815483093},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.4657175540924072},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4644913971424103},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4557194411754608},{"id":"https://openalex.org/C173870130","wikidata":"https://www.wikidata.org/wiki/Q8548","display_name":"Dijkstra's algorithm","level":4,"score":0.44344577193260193},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.43585461378097534},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4019466042518616},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3226397633552551},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.2472628653049469},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19678714871406555},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.09699386358261108},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2025.3546320","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3546320","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ea8c10330b3d4e2fa6983cef71686b23","is_oa":true,"landing_page_url":"https://doaj.org/article/ea8c10330b3d4e2fa6983cef71686b23","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 13, Pp 38856-38864 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2025.3546320","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3546320","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4399999976158142,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1571070457","https://openalex.org/W2022980325","https://openalex.org/W2100890245","https://openalex.org/W2104863367","https://openalex.org/W2134634502","https://openalex.org/W2169528473","https://openalex.org/W2227557434","https://openalex.org/W2233296499","https://openalex.org/W2522604845","https://openalex.org/W2601789150","https://openalex.org/W2625500717","https://openalex.org/W2793998795","https://openalex.org/W2803594690","https://openalex.org/W2927592310","https://openalex.org/W2929879061","https://openalex.org/W2982634526","https://openalex.org/W3039671113","https://openalex.org/W3090234698","https://openalex.org/W3099501324","https://openalex.org/W3101955277","https://openalex.org/W3106023117","https://openalex.org/W3112616303","https://openalex.org/W3134157502","https://openalex.org/W3165160234","https://openalex.org/W3195019475","https://openalex.org/W3196485901","https://openalex.org/W3208210813","https://openalex.org/W4285112699","https://openalex.org/W4301434930","https://openalex.org/W4308531274","https://openalex.org/W4312653892","https://openalex.org/W4376456824","https://openalex.org/W4385736039","https://openalex.org/W4389565663","https://openalex.org/W4399071399"],"related_works":["https://openalex.org/W2886722595","https://openalex.org/W2363342665","https://openalex.org/W2170980056","https://openalex.org/W4310124294","https://openalex.org/W2379804627","https://openalex.org/W2990531685","https://openalex.org/W2359532380","https://openalex.org/W4405632291","https://openalex.org/W4221129498","https://openalex.org/W78690942"],"abstract_inverted_index":{"Loopwise":[0],"route":[1,132],"representation":[2],"(LRR),":[3],"which":[4],"has":[5],"been":[6],"recently":[7],"proposed":[8,57,86,107,139,164,177,214],"as":[9,226],"an":[10],"alternative":[11],"network":[12],"representation,":[13],"can":[14],"determine":[15],"the":[16,20,48,52,64,81,85,95,99,103,106,129,138,163,176,201,213],"optimal":[17,185],"path":[18],"for":[19,47],"vehicle":[21,222],"routing":[22,223],"problems":[23,224],"with":[24,113],"a":[25,32,43,73,153,180,227,235],"simpler":[26],"optimization":[27,75],"formulation.":[28],"However,":[29],"it":[30],"requires":[31],"significant":[33],"computing":[34,147],"burden":[35],"due":[36],"to":[37,220,233],"nonlinear":[38,91],"optimization.":[39],"This":[40],"study":[41],"proposes":[42],"novel":[44],"linearization":[45,140,215],"approach":[46],"LRR":[49],"by":[50],"introducing":[51],"reference":[53,65],"link":[54,66],"flow.":[55],"The":[56],"method":[58,87,165,178],"consists":[59],"of":[60,98,105,117,146,193,204],"two":[61,83],"stages:":[62],"selecting":[63],"flow":[67],"in":[68,77,128,144,189,207,231],"Stage":[69,78],"1":[70],"and":[71,149,186],"formulating":[72],"linearized":[74],"problem":[76,230],"2.":[79],"Through":[80],"above":[82],"stages,":[84],"does":[88],"not":[89],"require":[90],"functions":[92],"while":[93],"maintaining":[94],"unique":[96],"advantages":[97],"LRR.":[100],"To":[101],"validate":[102],"performance":[104],"method,":[108],"numerical":[109],"experiments":[110],"are":[111],"designed":[112],"ideal":[114],"grid-type":[115,161],"networks":[116],"various":[118],"sizes.":[119],"For":[120,152],"comparison,":[121],"integer":[122],"linear":[123],"programming":[124],"(ILP)":[125],"is":[126],"conducted":[127],"corresponding":[130],"link-wise":[131],"representation.":[133],"Numerical":[134],"results":[135],"demonstrate":[136],"that":[137],"outperforms":[141],"conventional":[142,170,198],"ILP":[143,171,199],"terms":[145],"time":[148],"solution":[150],"accuracy.":[151],"<inline-formula":[154],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[155],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[156],"<tex-math":[157],"notation=\"LaTeX\">$100\\times":[158],"100$":[159],"</tex-math></inline-formula>":[160],"network,":[162],"takes":[166,172],"0.15":[167],"seconds,":[168],"whereas":[169,197],"1.39":[173],"seconds.":[174],"Furthermore,":[175],"provides":[179,200],"0-to-1%":[181],"relative":[182],"error":[183],"(i.e.,":[184],"near-optimal":[187],"solutions)":[188],"802":[190],"cases":[191],"out":[192],"total":[194],"1000":[195],"cases,":[196],"same":[202],"level":[203],"errors":[205],"only":[206],"406":[208],"cases.":[209],"With":[210],"further":[211],"work,":[212],"scheme":[216],"could":[217],"be":[218],"applied":[219],"other":[221],"such":[225],"traveling":[228],"salesman":[229],"order":[232],"enhance":[234],"computational":[236],"efficiency.":[237]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}