{"id":"https://openalex.org/W2136822103","doi":"https://doi.org/10.1109/jsac.2015.2435351","title":"Resource Allocation for Energy Efficiency Optimization in Heterogeneous Networks","display_name":"Resource Allocation for Energy Efficiency Optimization in Heterogeneous Networks","publication_year":2015,"publication_date":"2015-05-20","ids":{"openalex":"https://openalex.org/W2136822103","doi":"https://doi.org/10.1109/jsac.2015.2435351","mag":"2136822103"},"language":"en","primary_location":{"id":"doi:10.1109/jsac.2015.2435351","is_oa":true,"landing_page_url":"https://doi.org/10.1109/jsac.2015.2435351","pdf_url":"https://ieeexplore.ieee.org/ielx7/49/7265116/07110517.pdf","source":{"id":"https://openalex.org/S90422530","display_name":"IEEE Journal on Selected Areas in Communications","issn_l":"0733-8716","issn":["0733-8716","1558-0008"],"is_oa":false,"is_in_doaj":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Journal on Selected Areas in Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://ieeexplore.ieee.org/ielx7/49/7265116/07110517.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089631680","display_name":"Jie Tang","orcid":"https://orcid.org/0000-0003-0619-0338"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jie Tang","raw_affiliation_strings":["School of Electrical and Electronics Engineering, The University of Manchester, Manchester, U.K","Sch. of Electr. & Electron. Eng., Univ. of Manchester, Manchester, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronics Engineering, The University of Manchester, Manchester, U.K","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Sch. of Electr. & Electron. Eng., Univ. of Manchester, Manchester, UK#TAB#","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036412443","display_name":"Daniel K. C. So","orcid":"https://orcid.org/0000-0002-7642-1755"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Daniel K. C. So","raw_affiliation_strings":["School of Electrical and Electronics Engineering, The University of Manchester, Manchester, U.K","Sch. of Electr. & Electron. Eng., Univ. of Manchester, Manchester, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronics Engineering, The University of Manchester, Manchester, U.K","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Sch. of Electr. & Electron. Eng., Univ. of Manchester, Manchester, UK#TAB#","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002248410","display_name":"Emad Alsusa","orcid":"https://orcid.org/0000-0002-7724-2636"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Emad Alsusa","raw_affiliation_strings":["School of Electrical and Electronics Engineering, The University of Manchester, Manchester, U.K","Sch. of Electr. & Electron. Eng., Univ. of Manchester, Manchester, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronics Engineering, The University of Manchester, Manchester, U.K","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Sch. of Electr. & Electron. Eng., Univ. of Manchester, Manchester, UK#TAB#","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054743342","display_name":"Khairi Ashour Hamdi","orcid":"https://orcid.org/0000-0002-8060-5573"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Khairi Ashour Hamdi","raw_affiliation_strings":["School of Electrical and Electronics Engineering, The University of Manchester, Manchester, U.K","Sch. of Electr. & Electron. Eng., Univ. of Manchester, Manchester, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronics Engineering, The University of Manchester, Manchester, U.K","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Sch. of Electr. & Electron. Eng., Univ. of Manchester, Manchester, UK#TAB#","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001019738","display_name":"Arman Shojaeifard","orcid":"https://orcid.org/0000-0003-0826-1996"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Arman Shojaeifard","raw_affiliation_strings":["School of Electrical and Electronics Engineering, The University of Manchester, Manchester, U.K","Sch. of Electr. & Electron. Eng., Univ. of Manchester, Manchester, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronics Engineering, The University of Manchester, Manchester, U.K","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Sch. of Electr. & Electron. Eng., Univ. of Manchester, Manchester, UK#TAB#","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":null,"apc_paid":null,"fwci":10.5839,"has_fulltext":true,"cited_by_count":115,"citation_normalized_percentile":{"value":0.98693024,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"33","issue":"10","first_page":"2104","last_page":"2117"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10148","display_name":"Advanced MIMO Systems Optimization","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9994000196456909,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.8091365098953247},{"id":"https://openalex.org/keywords/heterogeneous-network","display_name":"Heterogeneous network","score":0.6765795946121216},{"id":"https://openalex.org/keywords/resource-allocation","display_name":"Resource allocation","score":0.6565150618553162},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6160293817520142},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5729131698608398},{"id":"https://openalex.org/keywords/transmitter-power-output","display_name":"Transmitter power output","score":0.5146316289901733},{"id":"https://openalex.org/keywords/efficient-energy-use","display_name":"Efficient energy use","score":0.5077870488166809},{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.4364203214645386},{"id":"https://openalex.org/keywords/telecommunications-link","display_name":"Telecommunications link","score":0.41740530729293823},{"id":"https://openalex.org/keywords/cellular-network","display_name":"Cellular network","score":0.4136950373649597},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.406648188829422},{"id":"https://openalex.org/keywords/wireless-network","display_name":"Wireless network","score":0.3904613256454468},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.3623013496398926},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.2720848023891449},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10923293232917786},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.09439945220947266},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.09158673882484436},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.07707828283309937}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8091365098953247},{"id":"https://openalex.org/C158207573","wikidata":"https://www.wikidata.org/wiki/Q5747224","display_name":"Heterogeneous network","level":4,"score":0.6765795946121216},{"id":"https://openalex.org/C29202148","wikidata":"https://www.wikidata.org/wiki/Q287260","display_name":"Resource allocation","level":2,"score":0.6565150618553162},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6160293817520142},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5729131698608398},{"id":"https://openalex.org/C65422117","wikidata":"https://www.wikidata.org/wiki/Q358527","display_name":"Transmitter power output","level":4,"score":0.5146316289901733},{"id":"https://openalex.org/C2742236","wikidata":"https://www.wikidata.org/wiki/Q924713","display_name":"Efficient energy use","level":2,"score":0.5077870488166809},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.4364203214645386},{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.41740530729293823},{"id":"https://openalex.org/C153646914","wikidata":"https://www.wikidata.org/wiki/Q535695","display_name":"Cellular network","level":2,"score":0.4136950373649597},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.406648188829422},{"id":"https://openalex.org/C108037233","wikidata":"https://www.wikidata.org/wiki/Q11375","display_name":"Wireless network","level":3,"score":0.3904613256454468},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.3623013496398926},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.2720848023891449},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10923293232917786},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.09439945220947266},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.09158673882484436},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.07707828283309937},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/jsac.2015.2435351","is_oa":true,"landing_page_url":"https://doi.org/10.1109/jsac.2015.2435351","pdf_url":"https://ieeexplore.ieee.org/ielx7/49/7265116/07110517.pdf","source":{"id":"https://openalex.org/S90422530","display_name":"IEEE Journal on Selected Areas in Communications","issn_l":"0733-8716","issn":["0733-8716","1558-0008"],"is_oa":false,"is_in_doaj":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Journal on Selected Areas in Communications","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/9707c441-9b04-4fc7-a0b5-7c152ff8228a","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/9707c441-9b04-4fc7-a0b5-7c152ff8228a","pdf_url":"https://pure.manchester.ac.uk/ws/files/22164065/POST-PEER-REVIEW-NON-PUBLISHERS.PDF","source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Tang, J, So, D K C, Alsusa, E, Hamdi, K & Shojaeifard, A 2015, 'Resource Allocation for Energy Efficiency Optimization in Heterogeneous Networks', I E E E Journal on Selected Areas in Communications, vol. 33, no. 10, pp. 2104-2117. https://doi.org/10.1109/JSAC.2015.2435351","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:1524057","is_oa":false,"landing_page_url":"http://discovery.ucl.ac.uk/1524057/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Journal on Selected Areas in Communications , 33 (10) pp. 2104-2117. (2015)","raw_type":"Article"},{"id":"pmh:oai:pure.atira.dk:publications/9707c441-9b04-4fc7-a0b5-7c152ff8228a","is_oa":true,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/resource-allocation-for-energy-efficiency-optimization-in-heterogeneous-networks(9707c441-9b04-4fc7-a0b5-7c152ff8228a).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"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":"","raw_type":""}],"best_oa_location":{"id":"doi:10.1109/jsac.2015.2435351","is_oa":true,"landing_page_url":"https://doi.org/10.1109/jsac.2015.2435351","pdf_url":"https://ieeexplore.ieee.org/ielx7/49/7265116/07110517.pdf","source":{"id":"https://openalex.org/S90422530","display_name":"IEEE Journal on Selected Areas in Communications","issn_l":"0733-8716","issn":["0733-8716","1558-0008"],"is_oa":false,"is_in_doaj":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Journal on Selected Areas in Communications","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.8700000047683716,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G4543044672","display_name":"Green Heterogeneous Networks","funder_award_id":"EP/J021768/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7985805409","display_name":null,"funder_award_id":"EP/J021768/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2136822103.pdf","grobid_xml":"https://content.openalex.org/works/W2136822103.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W1642407538","https://openalex.org/W1943205692","https://openalex.org/W1975574042","https://openalex.org/W1994080576","https://openalex.org/W1994534328","https://openalex.org/W2003806850","https://openalex.org/W2005450092","https://openalex.org/W2014060493","https://openalex.org/W2015870568","https://openalex.org/W2025453432","https://openalex.org/W2034490776","https://openalex.org/W2045202701","https://openalex.org/W2069119628","https://openalex.org/W2085080593","https://openalex.org/W2086476536","https://openalex.org/W2089126307","https://openalex.org/W2099837461","https://openalex.org/W2102157096","https://openalex.org/W2105358352","https://openalex.org/W2109872058","https://openalex.org/W2110519532","https://openalex.org/W2118343376","https://openalex.org/W2119952207","https://openalex.org/W2121171713","https://openalex.org/W2126106755","https://openalex.org/W2130891087","https://openalex.org/W2139057214","https://openalex.org/W2150415860","https://openalex.org/W2152481521","https://openalex.org/W2153008620","https://openalex.org/W2160998689","https://openalex.org/W2161473225","https://openalex.org/W2164631123","https://openalex.org/W2296319761","https://openalex.org/W4250589301","https://openalex.org/W6610930706","https://openalex.org/W6640900261","https://openalex.org/W6678165635"],"related_works":["https://openalex.org/W790449367","https://openalex.org/W3087844490","https://openalex.org/W2962922943","https://openalex.org/W2613807087","https://openalex.org/W3090699061","https://openalex.org/W2921549278","https://openalex.org/W4387546583","https://openalex.org/W3046102531","https://openalex.org/W1482197907","https://openalex.org/W2038093983"],"abstract_inverted_index":{"Heterogeneous":[0],"network":[1],"(HetNet)":[2],"deployment":[3],"is":[4,25,42,105,114,152],"considered":[5,89],"a":[6,26,67,74,106,147],"de":[7],"facto":[8],"solution":[9],"for":[10,30,45,61],"meeting":[11],"the":[12,34,46,57,94,123,128,144,156,164,170,178],"ever":[13],"increasing":[14],"mobile":[15,31],"traffic":[16],"demand.":[17],"However,":[18],"excessive":[19],"power":[20,84],"usage":[21],"in":[22,90],"such":[23],"networks":[24],"critical":[27],"issue,":[28],"particularly":[29],"operators.":[32],"Characterizing":[33],"fundamental":[35],"energy":[36,96],"efficiency":[37],"(EE)":[38],"performance":[39],"of":[40,48,66,159],"HetNets":[41,64],"therefore":[43],"important":[44],"design":[47,82],"green":[49],"wireless":[50],"systems.":[51],"In":[52,119],"this":[53],"paper,":[54],"we":[55,126],"address":[56],"EE":[58,99],"optimization":[59,111,137],"problem":[60,102,130],"downlink":[62],"two-tier":[63],"comprised":[65],"single":[68,140],"macro-cell":[69],"and":[70,77,83,109,167],"multiple":[71,132,136],"pico-cells.":[72],"Considering":[73],"heterogeneous":[75],"real-time":[76],"non-real-time":[78],"traffic,":[79],"transmit":[80],"beamforming":[81],"allocation":[85,101,150,173],"policies":[86],"are":[87],"jointly":[88],"order":[91,120],"to":[92,117,121],"optimize":[93],"system":[95],"efficiency.":[97],"The":[98],"resource":[100,149,172],"under":[103],"consideration":[104],"mixed":[107],"combinatorial":[108],"non-convex":[110],"problem,":[112,146],"which":[113],"extremely":[115],"difficult":[116],"solve.":[118],"reduce":[122],"computational":[124],"complexity,":[125],"decompose":[127],"original":[129],"with":[131,139],"inequality":[133,141],"constraints":[134],"into":[135],"problems":[138],"constraint.":[142],"For":[143],"latter":[145],"two-layer":[148],"algorithm":[151,174],"proposed":[153,171],"based":[154],"on":[155],"quasiconcavity":[157],"property":[158],"EE.":[160,180],"Simulation":[161],"results":[162],"confirm":[163],"theoretical":[165],"findings":[166],"demonstrate":[168],"that":[169],"can":[175],"efficiently":[176],"approach":[177],"optimal":[179]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":20},{"year":2017,"cited_by_count":27},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":6}],"updated_date":"2026-07-19T07:52:34.831488","created_date":"2025-10-10T00:00:00"}