{"id":"https://openalex.org/W4362578051","doi":"https://doi.org/10.1007/s00500-023-08032-z","title":"Solving the hierarchical windy postman problem with variable service costs using a math-heuristic algorithm","display_name":"Solving the hierarchical windy postman problem with variable service costs using a math-heuristic algorithm","publication_year":2023,"publication_date":"2023-04-01","ids":{"openalex":"https://openalex.org/W4362578051","doi":"https://doi.org/10.1007/s00500-023-08032-z"},"language":"en","primary_location":{"id":"doi:10.1007/s00500-023-08032-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00500-023-08032-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00500-023-08032-z.pdf","source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00500-023-08032-z.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090866089","display_name":"Muhammed Emre Keskin","orcid":"https://orcid.org/0000-0001-9381-123X"},"institutions":[{"id":"https://openalex.org/I64134780","display_name":"Atat\u00fcrk University","ror":"https://ror.org/03je5c526","country_code":"TR","type":"education","lineage":["https://openalex.org/I64134780"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Muhammed Emre Keskin","raw_affiliation_strings":["Industrial Engineering Department, Atat\u00fcrk University, Erzurum, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Industrial Engineering Department, Atat\u00fcrk University, Erzurum, Turkey","institution_ids":["https://openalex.org/I64134780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100663045","display_name":"Mustafa Y\u0131lmaz","orcid":"https://orcid.org/0000-0002-2135-5762"},"institutions":[{"id":"https://openalex.org/I64134780","display_name":"Atat\u00fcrk University","ror":"https://ror.org/03je5c526","country_code":"TR","type":"education","lineage":["https://openalex.org/I64134780"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Mustafa Y\u0131lmaz","raw_affiliation_strings":["Industrial Engineering Department, Atat\u00fcrk University, Erzurum, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Industrial Engineering Department, Atat\u00fcrk University, Erzurum, Turkey","institution_ids":["https://openalex.org/I64134780"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039886917","display_name":"Chefi Triki","orcid":"https://orcid.org/0000-0002-8750-2470"},"institutions":[{"id":"https://openalex.org/I142910587","display_name":"University of Salento","ror":"https://ror.org/03fc1k060","country_code":"IT","type":"education","lineage":["https://openalex.org/I142910587"]},{"id":"https://openalex.org/I20581793","display_name":"University of Kent","ror":"https://ror.org/00xkeyj56","country_code":"GB","type":"education","lineage":["https://openalex.org/I20581793"]}],"countries":["GB","IT"],"is_corresponding":true,"raw_author_name":"Chefi Triki","raw_affiliation_strings":["Department of Engineering for Innovation, University of Salento, Lecce, Italy","Kent Business School, University of Kent, Canterbury, UK"],"raw_orcid":"https://orcid.org/0000-0002-8750-2470","affiliations":[{"raw_affiliation_string":"Department of Engineering for Innovation, University of Salento, Lecce, Italy","institution_ids":["https://openalex.org/I142910587"]},{"raw_affiliation_string":"Kent Business School, University of Kent, Canterbury, UK","institution_ids":["https://openalex.org/I20581793"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039886917"],"corresponding_institution_ids":["https://openalex.org/I142910587","https://openalex.org/I20581793"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.5926,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72033554,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"27","issue":"13","first_page":"8789","last_page":"8805"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9994999766349792,"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":0.9994999766349792,"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/T11502","display_name":"Facility Location and Emergency Management","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9873999953269958,"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/tree-traversal","display_name":"Tree traversal","score":0.6689412593841553},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5960715413093567},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5421295166015625},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5253628492355347},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5143888592720032},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.4645284116268158},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.4406013488769531},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4328751564025879},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4315509796142578},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4217425286769867},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3791058361530304},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22679835557937622}],"concepts":[{"id":"https://openalex.org/C140745168","wikidata":"https://www.wikidata.org/wiki/Q1210082","display_name":"Tree traversal","level":2,"score":0.6689412593841553},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5960715413093567},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5421295166015625},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5253628492355347},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5143888592720032},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.4645284116268158},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4406013488769531},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4328751564025879},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4315509796142578},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4217425286769867},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3791058361530304},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22679835557937622},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00500-023-08032-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00500-023-08032-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00500-023-08032-z.pdf","source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"},{"id":"pmh:oai:kar.kent.ac.uk:100835","is_oa":false,"landing_page_url":"https://kar.kent.ac.uk/100835/2/C.%20Triki%20-%20solving%20the%20hierarchical%20windy%20postman%20problem%20-%20AAM.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4377196264","display_name":"Kent Academic Repository (University of Kent)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20581793","host_organization_name":"University of Kent","host_organization_lineage":["https://openalex.org/I20581793"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":{"id":"doi:10.1007/s00500-023-08032-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00500-023-08032-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00500-023-08032-z.pdf","source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4362578051.pdf"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1512042978","https://openalex.org/W1985595965","https://openalex.org/W1999974188","https://openalex.org/W2029639072","https://openalex.org/W2035742741","https://openalex.org/W2039011874","https://openalex.org/W2050922218","https://openalex.org/W2055803317","https://openalex.org/W2063277077","https://openalex.org/W2070349606","https://openalex.org/W2075230927","https://openalex.org/W2080994240","https://openalex.org/W2085285568","https://openalex.org/W2090467917","https://openalex.org/W2112026633","https://openalex.org/W2123789618","https://openalex.org/W2169528473","https://openalex.org/W2233419640","https://openalex.org/W2320067374","https://openalex.org/W2477194186","https://openalex.org/W2484312656","https://openalex.org/W2556666261","https://openalex.org/W2565859681","https://openalex.org/W2663612361","https://openalex.org/W2746033960","https://openalex.org/W2756042703","https://openalex.org/W2845948618","https://openalex.org/W2886614777","https://openalex.org/W2905351216","https://openalex.org/W2998056665","https://openalex.org/W3040363661","https://openalex.org/W3128828969","https://openalex.org/W3133818392","https://openalex.org/W3172536095","https://openalex.org/W3209925360","https://openalex.org/W4233756358"],"related_works":["https://openalex.org/W2136735429","https://openalex.org/W170547082","https://openalex.org/W2587876411","https://openalex.org/W2358332176","https://openalex.org/W4229950834","https://openalex.org/W4301044568","https://openalex.org/W2128075414","https://openalex.org/W1587123803","https://openalex.org/W2571039174","https://openalex.org/W4377236495"],"abstract_inverted_index":{"Abstract":[0],"The":[1,43],"Hierarchical":[2],"Windy":[3],"Postman":[4],"Problem":[5],"(HWPP)":[6],"is":[7,17,56,81,105,124,130,174,218,266,307],"an":[8,14,148],"arc":[9],"routing":[10],"problem":[11,203,217],"in":[12,71,221],"which":[13,72,200,237],"order":[15,76,247],"relation":[16],"imposed":[18],"on":[19,176,242],"the":[20,23,39,54,59,62,69,74,78,92,100,136,157,162,167,170,177,180,193,208,222,243,250,259,262,269,298,303],"arcs/edges":[21],"of":[22,61,68,77,94,102,139,156,169,196,207,252,261,287],"graph,":[24],"and":[25,47,53,83,90,107,126,281,283,297,310],"one":[26],"has":[27],"to":[28,38,57,110,160,248,258],"pass":[29],"through":[30],"each":[31,86,96],"edge":[32,79,97],"at":[33,49],"least":[34,163],"once":[35],"while":[36,188],"adhering":[37],"hierarchical":[40],"priority":[41],"relations.":[42],"tour":[44],"starts":[45],"from":[46],"ends":[48],"a":[50,66,127,153,184,204],"specific":[51],"node":[52],"aim":[55],"minimize":[58],"length":[60],"tour.":[63],"We":[64],"consider":[65],"variant":[67,206],"HWPP":[70,113],"(i)":[73],"precedence":[75],"hierarchies":[80],"linear":[82,121],"edges":[84,236],"within":[85],"hierarchy":[87],"are":[88,226,235,276,292],"connected":[89],"(ii)":[91],"cost":[93,164,186,198],"serving":[95],"decreases":[98],"with":[99,114,192,230,256,284],"number":[101,286],"times":[103],"it":[104,111],"traversed,":[106],"we":[108,189],"refer":[109],"as":[112,152],"variable":[115],"service":[116],"costs.":[117],"An":[118],"integer":[119,149],"non-heuristic":[120],"mathematical":[122,150,263],"formulation":[123,151],"proposed,":[125],"solution":[128,133],"approach":[129],"designed.":[131],"Our":[132],"heuristic":[134,254,305],"adapts":[135],"layer":[137],"algorithm":[138,159,182,255],"Dror":[140],"et":[141],"al.":[142],"(Networks":[143],"17:283\u2013294,":[144],"1987)":[145],"but":[146,233],"employs":[147],"sub-procedure":[154],"instead":[155],"blossom":[158,181],"find":[161],"path":[165],"between":[166],"nodes":[168],"graph.":[171],"This":[172],"choice":[173],"based":[175],"fact":[178],"that":[179,215,224,265,302],"requires":[183],"symmetric":[185],"structure":[187],"deal":[190],"here":[191],"general":[194],"case":[195],"asymmetric":[197,220],"structure,":[199],"makes":[201],"our":[202,216,253],"windy":[205],"postman":[209],"problem.":[210],"It":[211],"should":[212],"be":[213],"noted":[214],"not":[219],"sense":[223],"there":[225,234],"no":[227],"opposite":[228],"arcs":[229],"different":[231,239,285],"costs":[232,240],"have":[238],"depending":[241],"traversal":[244],"direction.":[245],"In":[246],"compare":[249],"performance":[251,260],"respect":[257],"model":[264],"solved":[267,293],"by":[268,294],"commercial":[270],"solver":[271],"Gurobi,":[272],"84":[273],"test":[274,290],"instances":[275,291],"generated":[277,299],"having":[278],"varying":[279],"sizes":[280],"densities":[282],"hierarchies.":[288],"These":[289],"both":[295],"methods":[296],"results":[300],"show":[301],"proposed":[304],"method":[306],"much":[308],"faster":[309],"generates":[311],"better":[312],"quality":[313],"solutions.":[314]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-12-22T23:10:17.713674","created_date":"2025-10-10T00:00:00"}