{"id":"https://openalex.org/W2790914305","doi":"https://doi.org/10.3390/ijgi7030115","title":"Spatial Transformation of Equality \u2013 Generalized Travelling Salesman Problem to Travelling Salesman Problem","display_name":"Spatial Transformation of Equality \u2013 Generalized Travelling Salesman Problem to Travelling Salesman Problem","publication_year":2018,"publication_date":"2018-03-15","ids":{"openalex":"https://openalex.org/W2790914305","doi":"https://doi.org/10.3390/ijgi7030115","mag":"2790914305"},"language":"en","primary_location":{"id":"doi:10.3390/ijgi7030115","is_oa":true,"landing_page_url":"https://doi.org/10.3390/ijgi7030115","pdf_url":null,"source":{"id":"https://openalex.org/S2764431341","display_name":"ISPRS International Journal of Geo-Information","issn_l":"2220-9964","issn":["2220-9964"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISPRS International Journal of Geo-Information","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/ijgi7030115","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049077743","display_name":"Mohammed Zia","orcid":"https://orcid.org/0000-0001-7708-8352"},"institutions":[{"id":"https://openalex.org/I48912391","display_name":"Istanbul Technical University","ror":"https://ror.org/059636586","country_code":"TR","type":"education","lineage":["https://openalex.org/I48912391"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Mohammed Zia","raw_affiliation_strings":["Geomatics Engineering Department, Istanbul Technical University, Maslak, Istanbul 34469, Turkey","National Innovation and Research Center for Geographical Information Technologies, Maslak, Istanbul 34469, Turkey"],"raw_orcid":"https://orcid.org/0000-0001-7708-8352","affiliations":[{"raw_affiliation_string":"Geomatics Engineering Department, Istanbul Technical University, Maslak, Istanbul 34469, Turkey","institution_ids":["https://openalex.org/I48912391"]},{"raw_affiliation_string":"National Innovation and Research Center for Geographical Information Technologies, Maslak, Istanbul 34469, Turkey","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036446001","display_name":"Ziyadin \u00c7ak\u0131r","orcid":"https://orcid.org/0000-0003-3050-5619"},"institutions":[{"id":"https://openalex.org/I48912391","display_name":"Istanbul Technical University","ror":"https://ror.org/059636586","country_code":"TR","type":"education","lineage":["https://openalex.org/I48912391"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Ziyadin Cakir","raw_affiliation_strings":["Department of Geology, Faculty of Mines, Istanbul Technical University, Maslak, Istanbul 34469, Turkey","National Innovation and Research Center for Geographical Information Technologies, Maslak, Istanbul 34469, Turkey"],"raw_orcid":"https://orcid.org/0000-0003-3050-5619","affiliations":[{"raw_affiliation_string":"Department of Geology, Faculty of Mines, Istanbul Technical University, Maslak, Istanbul 34469, Turkey","institution_ids":["https://openalex.org/I48912391"]},{"raw_affiliation_string":"National Innovation and Research Center for Geographical Information Technologies, Maslak, Istanbul 34469, Turkey","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024707647","display_name":"Dursun Zafer \u015eeker","orcid":"https://orcid.org/0000-0001-7498-1540"},"institutions":[{"id":"https://openalex.org/I48912391","display_name":"Istanbul Technical University","ror":"https://ror.org/059636586","country_code":"TR","type":"education","lineage":["https://openalex.org/I48912391"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Dursun Seker","raw_affiliation_strings":["Geomatics Engineering Department, Istanbul Technical University, Maslak, Istanbul 34469, Turkey"],"raw_orcid":"https://orcid.org/0000-0001-7498-1540","affiliations":[{"raw_affiliation_string":"Geomatics Engineering Department, Istanbul Technical University, Maslak, Istanbul 34469, Turkey","institution_ids":["https://openalex.org/I48912391"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5049077743"],"corresponding_institution_ids":["https://openalex.org/I48912391"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.1389,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.88359502,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"7","issue":"3","first_page":"115","last_page":"115"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9983000159263611,"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":0.9983000159263611,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9977999925613403,"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/T11106","display_name":"Data Management and Algorithms","score":0.996999979019165,"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/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.965239405632019},{"id":"https://openalex.org/keywords/traveling-purchaser-problem","display_name":"Traveling purchaser problem","score":0.7460589408874512},{"id":"https://openalex.org/keywords/2-opt","display_name":"2-opt","score":0.6599408388137817},{"id":"https://openalex.org/keywords/bottleneck-traveling-salesman-problem","display_name":"Bottleneck traveling salesman problem","score":0.6500263214111328},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.6086078882217407},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5795956254005432},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5407453179359436},{"id":"https://openalex.org/keywords/cross-entropy-method","display_name":"Cross-entropy method","score":0.5292607545852661},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5194010734558105},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4757896661758423},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"Combinatorial optimization","score":0.4550626277923584},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4028290808200836},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2743532657623291},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.16142842173576355},{"id":"https://openalex.org/keywords/quadratic-assignment-problem","display_name":"Quadratic assignment problem","score":0.11474183201789856}],"concepts":[{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.965239405632019},{"id":"https://openalex.org/C4331618","wikidata":"https://www.wikidata.org/wiki/Q7836034","display_name":"Traveling purchaser problem","level":4,"score":0.7460589408874512},{"id":"https://openalex.org/C106472803","wikidata":"https://www.wikidata.org/wiki/Q291440","display_name":"2-opt","level":3,"score":0.6599408388137817},{"id":"https://openalex.org/C7668213","wikidata":"https://www.wikidata.org/wiki/Q4949085","display_name":"Bottleneck traveling salesman problem","level":3,"score":0.6500263214111328},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.6086078882217407},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5795956254005432},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5407453179359436},{"id":"https://openalex.org/C75782508","wikidata":"https://www.wikidata.org/wiki/Q3333633","display_name":"Cross-entropy method","level":4,"score":0.5292607545852661},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5194010734558105},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4757896661758423},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.4550626277923584},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4028290808200836},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2743532657623291},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.16142842173576355},{"id":"https://openalex.org/C98036226","wikidata":"https://www.wikidata.org/wiki/Q7268356","display_name":"Quadratic assignment problem","level":3,"score":0.11474183201789856},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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":4,"locations":[{"id":"doi:10.3390/ijgi7030115","is_oa":true,"landing_page_url":"https://doi.org/10.3390/ijgi7030115","pdf_url":null,"source":{"id":"https://openalex.org/S2764431341","display_name":"ISPRS International Journal of Geo-Information","issn_l":"2220-9964","issn":["2220-9964"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISPRS International Journal of Geo-Information","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4ed668dd92f84eeaac83d7346d07b01e","is_oa":true,"landing_page_url":"https://doaj.org/article/4ed668dd92f84eeaac83d7346d07b01e","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":"ISPRS International Journal of Geo-Information, Vol 7, Iss 3, p 115 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2220-9964/7/3/115/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/ijgi7030115","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISPRS International Journal of Geo-Information; Volume 7; Issue 3; Pages: 115","raw_type":"Text"},{"id":"pmh:oai:polen.itu.edu.tr:11527/37125","is_oa":false,"landing_page_url":"https://hdl.handle.net/11527/37125","pdf_url":null,"source":{"id":"https://openalex.org/S4306400460","display_name":"Istanbul Technical University Academic Open Archive (Istanbul Technical University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I48912391","host_organization_name":"Istanbul Technical University","host_organization_lineage":["https://openalex.org/I48912391"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.3390/ijgi7030115","is_oa":true,"landing_page_url":"https://doi.org/10.3390/ijgi7030115","pdf_url":null,"source":{"id":"https://openalex.org/S2764431341","display_name":"ISPRS International Journal of Geo-Information","issn_l":"2220-9964","issn":["2220-9964"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISPRS International Journal of Geo-Information","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.8299999833106995}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322626","display_name":"T\u00fcrkiye Bilimsel ve Teknolojik Ara\u015ft\u0131rma Kurumu","ror":"https://ror.org/04w9kkr77"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W108694910","https://openalex.org/W1517470327","https://openalex.org/W1571087346","https://openalex.org/W1971483538","https://openalex.org/W1975442866","https://openalex.org/W2018269848","https://openalex.org/W2019741214","https://openalex.org/W2024060531","https://openalex.org/W2047630421","https://openalex.org/W2048296377","https://openalex.org/W2054630393","https://openalex.org/W2067061580","https://openalex.org/W2083974195","https://openalex.org/W2086987885","https://openalex.org/W2098104518","https://openalex.org/W2112686410","https://openalex.org/W2120988215","https://openalex.org/W2139059344","https://openalex.org/W2163557644","https://openalex.org/W2405668439","https://openalex.org/W2755875052","https://openalex.org/W4294358747","https://openalex.org/W6604433457","https://openalex.org/W6630947020","https://openalex.org/W6633936085","https://openalex.org/W6667013628","https://openalex.org/W6713668260","https://openalex.org/W6744296097"],"related_works":["https://openalex.org/W4389782626","https://openalex.org/W4376138746","https://openalex.org/W2259723333","https://openalex.org/W1987671593","https://openalex.org/W4200179302","https://openalex.org/W2790914305","https://openalex.org/W2189435634","https://openalex.org/W2156273071","https://openalex.org/W2123233098","https://openalex.org/W2081878758"],"abstract_inverted_index":{"The":[0],"Equality-Generalized":[1],"Travelling":[2,12],"Salesman":[3,13],"Problem":[4,14],"(E-GTSP),":[5],"which":[6,101],"is":[7,16,119],"an":[8],"extension":[9],"of":[10,22,65,74],"the":[11,71,98,103,116,120],"(TSP),":[15],"stated":[17],"as":[18],"follows:":[19],"given":[20,78],"groups":[21],"points":[23,75,104],"within":[24],"a":[25,32,77,132],"city,":[26],"like":[27],"banks,":[28],"supermarkets,":[29],"etc.,":[30],"find":[31],"minimum":[33],"cost":[34],"Hamiltonian":[35],"cycle":[36],"that":[37,97],"visits":[38],"each":[39,106],"group":[40,107],"exactly":[41],"once.":[42],"It":[43],"can":[44],"model":[45],"many":[46],"real-life":[47],"combinatorial":[48],"optimization":[49],"scenarios":[50],"more":[51],"efficiently":[52],"than":[53],"TSP.":[54],"This":[55],"study":[56],"presents":[57],"five":[58],"spatially":[59],"driven":[60],"search-algorithms":[61],"for":[62,124,131,143],"possible":[63],"transformation":[64],"E-GTSP":[66,126],"to":[67,115,127],"TSP":[68,128],"by":[69,90],"considering":[70],"spatial":[72],"spread":[73],"in":[76],"urban":[79],"city.":[80],"Presented":[81],"algorithms":[82],"are":[83],"tested":[84],"over":[85],"15":[86],"different":[87],"cities,":[88],"classified":[89],"their":[91,110],"street-network\u2019s":[92],"fractal-dimension.":[93],"Obtained":[94],"results":[95],"denote":[96],"R-Search":[99],"algorithm,":[100],"selects":[102],"from":[105],"based":[108],"on":[109],"radial":[111],"separation":[112],"with":[113],"respect":[114],"start\u2013end":[117],"point,":[118],"best":[121],"search":[122],"criterion":[123],"any":[125],"conversion":[129],"modelled":[130],"city":[133],"street":[134],"network.":[135],"An":[136],"8.8%":[137],"length":[138],"error":[139],"has":[140],"been":[141],"reported":[142],"this":[144],"algorithm.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2018-03-29T00:00:00"}