{"id":"https://openalex.org/W4391846585","doi":"https://doi.org/10.1007/s10898-024-01364-6","title":"A K-means Supported Reinforcement Learning Framework to Multi-dimensional Knapsack","display_name":"A K-means Supported Reinforcement Learning Framework to Multi-dimensional Knapsack","publication_year":2024,"publication_date":"2024-02-15","ids":{"openalex":"https://openalex.org/W4391846585","doi":"https://doi.org/10.1007/s10898-024-01364-6"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-024-01364-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-024-01364-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-024-01364-6.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"Journal of Global Optimization","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/s10898-024-01364-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062072859","display_name":"Sabah Bushaj","orcid":"https://orcid.org/0000-0003-0433-692X"},"institutions":[{"id":"https://openalex.org/I63475719","display_name":"SUNY Plattsburgh","ror":"https://ror.org/033zmj163","country_code":"US","type":"education","lineage":["https://openalex.org/I63475719"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sabah Bushaj","raw_affiliation_strings":["Department of Management Information Systems and Analytics, SUNY Plattsburgh, New York, USA"],"raw_orcid":"https://orcid.org/0000-0003-0433-692X","affiliations":[{"raw_affiliation_string":"Department of Management Information Systems and Analytics, SUNY Plattsburgh, New York, USA","institution_ids":["https://openalex.org/I63475719"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025665669","display_name":"\u0130. Esra B\u00fcy\u00fcktahtak\u0131n","orcid":"https://orcid.org/0000-0001-8928-2638"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"\u0130. Esra B\u00fcy\u00fcktahtak\u0131n","raw_affiliation_strings":["Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, USA"],"raw_orcid":"https://orcid.org/0000-0001-8928-2638","affiliations":[{"raw_affiliation_string":"Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, USA","institution_ids":["https://openalex.org/I859038795"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025665669"],"corresponding_institution_ids":["https://openalex.org/I859038795"],"apc_list":{"value":2780,"currency":"USD","value_usd":2780},"apc_paid":{"value":2780,"currency":"USD","value_usd":2780},"fwci":1.1247,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.79746048,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"89","issue":"3","first_page":"655","last_page":"685"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11574","display_name":"Artificial Intelligence in Games","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12288","display_name":"Optimization and Search Problems","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9939000010490417,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/knapsack-problem","display_name":"Knapsack problem","score":0.8928378820419312},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8538528084754944},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.7754467725753784},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5565038323402405},{"id":"https://openalex.org/keywords/reinforcement","display_name":"Reinforcement","score":0.5305212736129761},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2575688362121582},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0997944176197052}],"concepts":[{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.8928378820419312},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8538528084754944},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.7754467725753784},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5565038323402405},{"id":"https://openalex.org/C67203356","wikidata":"https://www.wikidata.org/wiki/Q1321905","display_name":"Reinforcement","level":2,"score":0.5305212736129761},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2575688362121582},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0997944176197052},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10898-024-01364-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-024-01364-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-024-01364-6.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:vtechworks.lib.vt.edu:10919/124864","is_oa":true,"landing_page_url":"https://hdl.handle.net/10919/124864","pdf_url":"https://vtechworks.lib.vt.edu/bitstreams/3e5a59ff-5b6b-43a3-92c8-12e910e98589/download","source":{"id":"https://openalex.org/S4306400248","display_name":"VTechWorks (Virginia Tech)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I859038795","host_organization_name":"Virginia Tech","host_organization_lineage":["https://openalex.org/I859038795"],"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":null,"raw_type":"Article - Refereed"},{"id":"pmh:oai:RePEc:spr:jglopt:v:89:y:2024:i:3:d:10.1007_s10898-024-01364-6","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-024-01364-6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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:10.1007/s10898-024-01364-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-024-01364-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-024-01364-6.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"Journal of Global Optimization","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5099999904632568,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G3637526932","display_name":null,"funder_award_id":"CBET-1554018","funder_id":"https://openalex.org/F4320332170","funder_display_name":"Directorate for Engineering"},{"id":"https://openalex.org/G6155089174","display_name":"CAREER: Dynamic Invasive Species Control Optimization Via Integrated Education and Research (DISCOVER)","funder_award_id":"1554018","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332170","display_name":"Directorate for Engineering","ror":"https://ror.org/00b6sbb32"},{"id":"https://openalex.org/F4320337390","display_name":"Division of Chemical, Bioengineering, Environmental, and Transport Systems","ror":"https://ror.org/0471zv972"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4391846585.pdf","grobid_xml":"https://content.openalex.org/works/W4391846585.grobid-xml"},"referenced_works_count":64,"referenced_works":["https://openalex.org/W159308319","https://openalex.org/W1549861824","https://openalex.org/W1586409345","https://openalex.org/W1593916827","https://openalex.org/W1694216773","https://openalex.org/W1884730587","https://openalex.org/W1966693694","https://openalex.org/W1972314001","https://openalex.org/W1982719520","https://openalex.org/W1986013254","https://openalex.org/W1990995139","https://openalex.org/W2003709487","https://openalex.org/W2022338859","https://openalex.org/W2026106837","https://openalex.org/W2031666601","https://openalex.org/W2032107708","https://openalex.org/W2033971020","https://openalex.org/W2055037276","https://openalex.org/W2056802862","https://openalex.org/W2073127061","https://openalex.org/W2081751877","https://openalex.org/W2084974704","https://openalex.org/W2088888085","https://openalex.org/W2094232889","https://openalex.org/W2095018715","https://openalex.org/W2102428370","https://openalex.org/W2102543230","https://openalex.org/W2105339579","https://openalex.org/W2106433410","https://openalex.org/W2113868012","https://openalex.org/W2123402141","https://openalex.org/W2150593711","https://openalex.org/W2150827977","https://openalex.org/W2171682893","https://openalex.org/W2902907165","https://openalex.org/W2946660909","https://openalex.org/W2958071912","https://openalex.org/W2979093209","https://openalex.org/W2998327136","https://openalex.org/W3004718980","https://openalex.org/W3012428206","https://openalex.org/W3027979199","https://openalex.org/W3090460193","https://openalex.org/W3112138007","https://openalex.org/W3166014900","https://openalex.org/W3198266396","https://openalex.org/W3215162927","https://openalex.org/W3215990786","https://openalex.org/W4244216326","https://openalex.org/W4256012320","https://openalex.org/W4297218033","https://openalex.org/W4300076045","https://openalex.org/W4316654941","https://openalex.org/W4378802168","https://openalex.org/W4379516004","https://openalex.org/W4388116499","https://openalex.org/W6600075759","https://openalex.org/W6600135713","https://openalex.org/W6600175266","https://openalex.org/W6600341180","https://openalex.org/W6600922481","https://openalex.org/W6601132913","https://openalex.org/W6814003322","https://openalex.org/W6819198756"],"related_works":["https://openalex.org/W241127407","https://openalex.org/W2381035939","https://openalex.org/W2468477307","https://openalex.org/W2910645127","https://openalex.org/W162895179","https://openalex.org/W1521824362","https://openalex.org/W3177799343","https://openalex.org/W3119198325","https://openalex.org/W623642078","https://openalex.org/W3125085490"],"abstract_inverted_index":{"Abstract":[0],"In":[1,23],"this":[2,24,85],"paper,":[3],"we":[4,27],"address":[5],"the":[6,47,53,58,62,77,80,87,105,113,144,157,164,222,231,238],"difficulty":[7],"of":[8,46,70,76,82,91,104,112,123,161,218,224,230],"solving":[9],"large-scale":[10],"multi-dimensional":[11],"knapsack":[12],"instances":[13,122,179,194],"(MKP),":[14],"presenting":[15],"a":[16,33,68,96,130,214,246],"novel":[17,50],"deep":[18],"reinforcement":[19],"learning":[20],"(DRL)":[21],"framework.":[22],"DRL":[25,60,89,106,145,186,243],"framework,":[26],"train":[28,143,148],"different":[29,124,150,181],"agents":[30,151,173],"compatible":[31],"with":[32,163,180,213,237,242,250],"discrete":[34],"action":[35],"space":[36],"for":[37,66,210],"sequential":[38],"decision-making":[39],"while":[40],"still":[41],"satisfying":[42],"any":[43],"resource":[44],"constraint":[45],"MKP.":[48,114],"This":[49],"framework":[51,116,154,187],"incorporates":[52],"decision":[54],"variable":[55],"values":[56],"in":[57,94,152,200,235],"2D":[59,97],"where":[61],"agent":[63],"is":[64,86,99,117,140],"responsible":[65],"assigning":[67],"value":[69],"1":[71],"or":[72],"0":[73],"to":[74,119,133,142,221,252],"each":[75,160],"variables.":[78],"To":[79],"best":[81],"our":[83,153,172],"knowledge,":[84],"first":[88],"model":[90],"its":[92],"kind":[93],"which":[95],"environment":[98],"formulated,":[100],"and":[101,126,155,176,183,204],"an":[102,110,135],"element":[103],"solution":[107,138,202,216],"matrix":[108],"represents":[109],"item":[111],"Our":[115,185],"configured":[118],"solve":[120,192],"MKP":[121],"dimensions":[125],"distributions.":[127,184],"We":[128,147],"propose":[129],"K-means":[131],"approach":[132],"obtain":[134],"initial":[136],"feasible":[137],"that":[139,171,189],"used":[141],"agent.":[146],"four":[149],"present":[156],"results":[158,169],"comparing":[159],"them":[162],"CPLEX":[165,239],"commercial":[166],"solver.":[167],"The":[168],"show":[170],"can":[174,191],"learn":[175],"generalize":[177],"over":[178],"sizes":[182],"shows":[188],"it":[190],"medium-sized":[193],"at":[195,205,227],"least":[196,206,228],"45":[197],"times":[198,208],"faster":[199,209],"CPU":[201],"time":[203],"10":[207],"large":[211],"instances,":[212],"maximum":[215],"gap":[217,249],"0.28%":[219],"compared":[220],"performance":[223],"CPLEX.":[225],"Furthermore,":[226],"95%":[229],"items":[232],"are":[233],"predicted":[234],"line":[236],"solution.":[240],"Computations":[241],"also":[244],"provide":[245],"better":[247],"optimality":[248],"respect":[251],"state-of-the-art":[253],"approaches.":[254]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}