{"id":"https://openalex.org/W1608467940","doi":"https://doi.org/10.1155/2015/569248","title":"Application of Fuzzy Optimization to the Orienteering Problem","display_name":"Application of Fuzzy Optimization to the Orienteering Problem","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1608467940","doi":"https://doi.org/10.1155/2015/569248","mag":"1608467940"},"language":"en","primary_location":{"id":"doi:10.1155/2015/569248","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2015/569248","pdf_url":"https://downloads.hindawi.com/journals/afs/2015/569248.pdf","source":{"id":"https://openalex.org/S117816480","display_name":"Advances in Fuzzy Systems","issn_l":"1687-7101","issn":["1687-7101","1687-711X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Fuzzy Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/afs/2015/569248.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020275503","display_name":"Madhushi Verma","orcid":"https://orcid.org/0000-0003-1996-2077"},"institutions":[{"id":"https://openalex.org/I56404289","display_name":"Indian Institute of Technology BHU","ror":"https://ror.org/01kh5gc44","country_code":"IN","type":"education","lineage":["https://openalex.org/I56404289","https://openalex.org/I91357014"]},{"id":"https://openalex.org/I91357014","display_name":"Banaras Hindu University","ror":"https://ror.org/04cdn2797","country_code":"IN","type":"education","lineage":["https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Madhushi Verma","raw_affiliation_strings":["Department of Computer Science and Engineering, IIT (BHU), Varanasi 221005, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, IIT (BHU), Varanasi 221005, India","institution_ids":["https://openalex.org/I56404289","https://openalex.org/I91357014"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046454544","display_name":"K.K. Shukla","orcid":"https://orcid.org/0000-0002-8756-6474"},"institutions":[{"id":"https://openalex.org/I56404289","display_name":"Indian Institute of Technology BHU","ror":"https://ror.org/01kh5gc44","country_code":"IN","type":"education","lineage":["https://openalex.org/I56404289","https://openalex.org/I91357014"]},{"id":"https://openalex.org/I91357014","display_name":"Banaras Hindu University","ror":"https://ror.org/04cdn2797","country_code":"IN","type":"education","lineage":["https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"K. K. Shukla","raw_affiliation_strings":["Department of Computer Science and Engineering, IIT (BHU), Varanasi 221005, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, IIT (BHU), Varanasi 221005, India","institution_ids":["https://openalex.org/I56404289","https://openalex.org/I91357014"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5020275503"],"corresponding_institution_ids":["https://openalex.org/I56404289","https://openalex.org/I91357014"],"apc_list":{"value":925,"currency":"USD","value_usd":925},"apc_paid":{"value":925,"currency":"USD","value_usd":925},"fwci":2.0779,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.87477511,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2015","issue":null,"first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9886000156402588,"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"}},"topics":[{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9886000156402588,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9711999893188477,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9103000164031982,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/orienteering","display_name":"Orienteering","score":0.7508751153945923},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6324650645256042},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5959457159042358},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5232276320457458},{"id":"https://openalex.org/keywords/knapsack-problem","display_name":"Knapsack problem","score":0.48874878883361816},{"id":"https://openalex.org/keywords/travelling-salesman-problem","display_name":"Travelling salesman problem","score":0.45531970262527466},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3633688688278198},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3330079913139343},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.33272677659988403},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3177991509437561}],"concepts":[{"id":"https://openalex.org/C513932644","wikidata":"https://www.wikidata.org/wiki/Q29358","display_name":"Orienteering","level":2,"score":0.7508751153945923},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6324650645256042},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5959457159042358},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5232276320457458},{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.48874878883361816},{"id":"https://openalex.org/C175859090","wikidata":"https://www.wikidata.org/wiki/Q322212","display_name":"Travelling salesman problem","level":2,"score":0.45531970262527466},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3633688688278198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3330079913139343},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.33272677659988403},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3177991509437561}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2015/569248","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2015/569248","pdf_url":"https://downloads.hindawi.com/journals/afs/2015/569248.pdf","source":{"id":"https://openalex.org/S117816480","display_name":"Advances in Fuzzy Systems","issn_l":"1687-7101","issn":["1687-7101","1687-711X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Fuzzy Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c00e19a0d6e94344844e9627f273592c","is_oa":true,"landing_page_url":"https://doaj.org/article/c00e19a0d6e94344844e9627f273592c","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":"Advances in Fuzzy Systems, Vol 2015 (2015)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2015/569248","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2015/569248","pdf_url":"https://downloads.hindawi.com/journals/afs/2015/569248.pdf","source":{"id":"https://openalex.org/S117816480","display_name":"Advances in Fuzzy Systems","issn_l":"1687-7101","issn":["1687-7101","1687-711X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Fuzzy Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7400000095367432,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320330011","display_name":"Indian Institute of Technology (BHU) Varanasi","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1608467940.pdf","grobid_xml":"https://content.openalex.org/works/W1608467940.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1583868557","https://openalex.org/W1728397794","https://openalex.org/W1829903004","https://openalex.org/W1968091565","https://openalex.org/W1973834849","https://openalex.org/W1978352585","https://openalex.org/W1990123366","https://openalex.org/W1998678640","https://openalex.org/W1999883971","https://openalex.org/W2003281104","https://openalex.org/W2014979043","https://openalex.org/W2022487853","https://openalex.org/W2043905543","https://openalex.org/W2071796503","https://openalex.org/W2071844871","https://openalex.org/W2076556084","https://openalex.org/W2084008847","https://openalex.org/W2086467817","https://openalex.org/W2088812877","https://openalex.org/W2105450752","https://openalex.org/W2113873983","https://openalex.org/W2135475768","https://openalex.org/W2140596151","https://openalex.org/W2144101552","https://openalex.org/W2148026779","https://openalex.org/W2165019776","https://openalex.org/W2189494213","https://openalex.org/W2293737317","https://openalex.org/W2295774037","https://openalex.org/W2914206936","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4249387127","https://openalex.org/W327165017","https://openalex.org/W241127407","https://openalex.org/W2356214734","https://openalex.org/W2394169628","https://openalex.org/W4254102998","https://openalex.org/W2381035939","https://openalex.org/W2468477307","https://openalex.org/W2381702286","https://openalex.org/W3083042533"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3,63,79,173],"the":[4,21,39,57,80,86,101,109,115,123,131,139,143,148,153,164,168,174],"orienteering":[5,88],"problem":[6,19,28,89],"(OP)":[7],"which":[8,69,177],"is":[9,25,30,54],"a":[10,74,93,120,191],"combination":[11],"of":[12,67,105,107,142,186],"two":[13,82,102],"well-known":[14],"problems":[15],"(i.e.,":[16],"travelling":[17],"salesman":[18],"and":[20,29,91,113,130,167],"knapsack":[22],"problem).":[23],"OP":[24,106],"an":[26],"NP-hard":[27],"useful":[31],"in":[32,42],"appropriately":[33],"modeling":[34],"several":[35],"challenging":[36],"applications.":[37],"As":[38],"parameters":[40],"involved":[41],"these":[43],"applications":[44],"cannot":[45,70],"be":[46,61,71],"measured":[47],"precisely,":[48],"depicting":[49],"them":[50],"using":[51,73],"crisp":[52,75,136],"numbers":[53],"unrealistic.":[55],"Further,":[56],"decision":[58,155],"maker":[59],"may":[60],"satisfied":[62],"graded":[64],"satisfaction":[65],"levels":[66],"solutions,":[68],"formulated":[72],"program.":[76],"To":[77,181],"deal":[78],"above-stated":[81],"issues,":[83],"we":[84,99,151,188],"formulate":[85],"fuzzy":[87,128,144,149,154],"(FOP)":[90],"provide":[92],"method":[94],"to":[95,118,176],"solve":[96,183],"it.":[97],"Here":[98],"state":[100],"necessary":[103,133],"conditions":[104,134],"maximizing":[108],"total":[110],"collected":[111],"score":[112],"minimizing":[114],"time":[116,125],"taken":[117],"traverse":[119],"path":[121],"(within":[122],"specified":[124],"bound)":[126],"as":[127,135],"goals":[129],"remaining":[132],"constraints.":[137],"Using":[138],"max-min":[140],"formulation":[141],"sets":[145,156],"obtained":[146],"from":[147],"goals,":[150],"calculate":[152],"(<mml:math":[157],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[158,160],"id=\"M1\"><mml:mrow><mml:mi>Z</mml:mi></mml:mrow></mml:math>and<mml:math":[159],"id=\"M2\"><mml:mrow><mml:msup><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mrow><mml:mi>\u2217</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>)":[161],"that":[162],"contain":[163],"feasible":[165],"paths":[166],"desirable":[169],"paths,":[170],"respectively,":[171],"along":[172],"degrees":[175],"they":[178],"are":[179],"acceptable.":[180],"efficiently":[182],"large":[184],"instances":[185],"FOP,":[187],"also":[189],"present":[190],"parallel":[192],"algorithm":[193],"on":[194],"CREW":[195],"PRAM":[196],"model.":[197]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}