{"id":"https://openalex.org/W2799349785","doi":"https://doi.org/10.1109/tcomm.2018.2834920","title":"Robust Multi-Objective Optimization for EE-SE Tradeoff in D2D Communications Underlaying Heterogeneous Networks","display_name":"Robust Multi-Objective Optimization for EE-SE Tradeoff in D2D Communications Underlaying Heterogeneous Networks","publication_year":2018,"publication_date":"2018-05-10","ids":{"openalex":"https://openalex.org/W2799349785","doi":"https://doi.org/10.1109/tcomm.2018.2834920","mag":"2799349785"},"language":"en","primary_location":{"id":"doi:10.1109/tcomm.2018.2834920","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tcomm.2018.2834920","pdf_url":"https://ieeexplore.ieee.org/ielx7/26/8493372/08357581.pdf","source":{"id":"https://openalex.org/S196647941","display_name":"IEEE Transactions on Communications","issn_l":"0090-6778","issn":["0090-6778","1558-0857"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","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 Transactions on Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://ieeexplore.ieee.org/ielx7/26/8493372/08357581.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087983554","display_name":"Yuanyuan Hao","orcid":"https://orcid.org/0000-0001-9841-0814"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuanyuan Hao","raw_affiliation_strings":["School of Information and Electronics, Beijing Institute of Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Information and Electronics, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069951778","display_name":"Qiang Ni","orcid":"https://orcid.org/0000-0002-4593-1656"},"institutions":[{"id":"https://openalex.org/I67415387","display_name":"Lancaster University","ror":"https://ror.org/04f2nsd36","country_code":"GB","type":"education","lineage":["https://openalex.org/I67415387"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Qiang Ni","raw_affiliation_strings":["School of Computing and Communications, Lancaster University, Lancaster, U.K"],"affiliations":[{"raw_affiliation_string":"School of Computing and Communications, Lancaster University, Lancaster, U.K","institution_ids":["https://openalex.org/I67415387"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100600583","display_name":"Li Hai","orcid":"https://orcid.org/0000-0002-6240-7688"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hai Li","raw_affiliation_strings":["School of Information and Electronics, Beijing Institute of Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Information and Electronics, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041410734","display_name":"Shujuan Hou","orcid":"https://orcid.org/0000-0003-1975-5254"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shujuan Hou","raw_affiliation_strings":["School of Information and Electronics, Beijing Institute of Technology, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Information and Electronics, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5087983554"],"corresponding_institution_ids":["https://openalex.org/I125839683"],"apc_list":null,"apc_paid":null,"fwci":5.3645,"has_fulltext":true,"cited_by_count":66,"citation_normalized_percentile":{"value":0.96163274,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"66","issue":"10","first_page":"4936","last_page":"4949"},"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.996999979019165,"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/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9969000220298767,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7186001539230347},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6945319771766663},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6592706441879272},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.6351903676986694},{"id":"https://openalex.org/keywords/spectral-efficiency","display_name":"Spectral efficiency","score":0.5030602812767029},{"id":"https://openalex.org/keywords/heterogeneous-network","display_name":"Heterogeneous network","score":0.4810902774333954},{"id":"https://openalex.org/keywords/cellular-network","display_name":"Cellular network","score":0.4601038694381714},{"id":"https://openalex.org/keywords/resource-allocation","display_name":"Resource allocation","score":0.4459121823310852},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4418613910675049},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4307669401168823},{"id":"https://openalex.org/keywords/quality-of-service","display_name":"Quality of service","score":0.43005266785621643},{"id":"https://openalex.org/keywords/interference","display_name":"Interference (communication)","score":0.42176368832588196},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.2983230650424957},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.2818443775177002},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.22322538495063782},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.2115873098373413},{"id":"https://openalex.org/keywords/wireless-network","display_name":"Wireless network","score":0.19622144103050232},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19499564170837402},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1748264729976654}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7186001539230347},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6945319771766663},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6592706441879272},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.6351903676986694},{"id":"https://openalex.org/C137246740","wikidata":"https://www.wikidata.org/wiki/Q583970","display_name":"Spectral efficiency","level":3,"score":0.5030602812767029},{"id":"https://openalex.org/C158207573","wikidata":"https://www.wikidata.org/wiki/Q5747224","display_name":"Heterogeneous network","level":4,"score":0.4810902774333954},{"id":"https://openalex.org/C153646914","wikidata":"https://www.wikidata.org/wiki/Q535695","display_name":"Cellular network","level":2,"score":0.4601038694381714},{"id":"https://openalex.org/C29202148","wikidata":"https://www.wikidata.org/wiki/Q287260","display_name":"Resource allocation","level":2,"score":0.4459121823310852},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4418613910675049},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4307669401168823},{"id":"https://openalex.org/C5119721","wikidata":"https://www.wikidata.org/wiki/Q220501","display_name":"Quality of service","level":2,"score":0.43005266785621643},{"id":"https://openalex.org/C32022120","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference (communication)","level":3,"score":0.42176368832588196},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.2983230650424957},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.2818443775177002},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.22322538495063782},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.2115873098373413},{"id":"https://openalex.org/C108037233","wikidata":"https://www.wikidata.org/wiki/Q11375","display_name":"Wireless network","level":3,"score":0.19622144103050232},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19499564170837402},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1748264729976654},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcomm.2018.2834920","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tcomm.2018.2834920","pdf_url":"https://ieeexplore.ieee.org/ielx7/26/8493372/08357581.pdf","source":{"id":"https://openalex.org/S196647941","display_name":"IEEE Transactions on Communications","issn_l":"0090-6778","issn":["0090-6778","1558-0857"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","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 Transactions on Communications","raw_type":"journal-article"},{"id":"pmh:oai:eprints.lancs.ac.uk:126859","is_oa":true,"landing_page_url":null,"pdf_url":"https://eprints.lancs.ac.uk/id/eprint/126859/1/FINAL_VERSION_updated.pdf","source":{"id":"https://openalex.org/S4306401916","display_name":"Lancaster EPrints (Lancaster University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67415387","host_organization_name":"Lancaster University","host_organization_lineage":["https://openalex.org/I67415387"],"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:10.1109/tcomm.2018.2834920","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tcomm.2018.2834920","pdf_url":"https://ieeexplore.ieee.org/ielx7/26/8493372/08357581.pdf","source":{"id":"https://openalex.org/S196647941","display_name":"IEEE Transactions on Communications","issn_l":"0090-6778","issn":["0090-6778","1558-0857"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","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 Transactions on Communications","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8199999928474426}],"awards":[{"id":"https://openalex.org/G2335177755","display_name":"Cognitive Resource Scheduling Designs Towards Green Wireless Systems","funder_award_id":"EP/K011693/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4041996909","display_name":null,"funder_award_id":"EP/K011693/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5068943091","display_name":null,"funder_award_id":"PIRSES-GA-2013-610524","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5303011379","display_name":null,"funder_award_id":"EP/R00692X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8983653019","display_name":null,"funder_award_id":"CSA7114","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2799349785.pdf","grobid_xml":"https://content.openalex.org/works/W2799349785.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W1969648546","https://openalex.org/W1973858398","https://openalex.org/W1992942660","https://openalex.org/W2066101774","https://openalex.org/W2073678698","https://openalex.org/W2082440976","https://openalex.org/W2121798960","https://openalex.org/W2126137945","https://openalex.org/W2149726897","https://openalex.org/W2160944442","https://openalex.org/W2191948661","https://openalex.org/W2211148590","https://openalex.org/W2220657415","https://openalex.org/W2255703988","https://openalex.org/W2261342007","https://openalex.org/W2296319761","https://openalex.org/W2339860134","https://openalex.org/W2384087374","https://openalex.org/W2387019571","https://openalex.org/W2395502954","https://openalex.org/W2470447231","https://openalex.org/W2481565790","https://openalex.org/W2483325812","https://openalex.org/W2507276032","https://openalex.org/W2513356504","https://openalex.org/W2518686865","https://openalex.org/W2546759705","https://openalex.org/W2565767594","https://openalex.org/W2566472168","https://openalex.org/W2581032613","https://openalex.org/W2589615107","https://openalex.org/W2593489945","https://openalex.org/W2615258659","https://openalex.org/W2648066211","https://openalex.org/W2738113351","https://openalex.org/W2738591571","https://openalex.org/W2749039782","https://openalex.org/W2962679604","https://openalex.org/W3098915991","https://openalex.org/W3102703331","https://openalex.org/W4250589301","https://openalex.org/W4251616545","https://openalex.org/W4293229790","https://openalex.org/W4302557773","https://openalex.org/W4361867455"],"related_works":["https://openalex.org/W2786534237","https://openalex.org/W2583418925","https://openalex.org/W3125936868","https://openalex.org/W2980078855","https://openalex.org/W2982073957","https://openalex.org/W2584407738","https://openalex.org/W2805060255","https://openalex.org/W2189050590","https://openalex.org/W2573375498","https://openalex.org/W2962706271"],"abstract_inverted_index":{"In":[0],"this":[1,126],"paper,":[2],"we":[3,35,101],"concentrate":[4],"on":[5,37],"the":[6,12,55,82,93,108,130,134,163,169,174],"robust":[7,39,156],"multi-objective":[8],"optimization":[9,116],"(MOO)":[10],"for":[11,43],"tradeoff":[13,172],"between":[14],"energy":[15],"efficiency":[16,20],"(EE)":[17],"and":[18,46,73,89,98,133,141,160,173],"spectral":[19],"(SE)":[21],"in":[22,49,166],"device-to-device":[23],"(D2D)":[24],"communications":[25,51],"underlaying":[26,52],"heterogeneous":[27],"networks":[28],"(HetNets).":[29],"Different":[30],"from":[31],"traditional":[32],"resource":[33],"optimization,":[34],"focus":[36],"finding":[38],"Pareto":[40],"optimal":[41],"solutions":[42],"spectrum":[44,135],"allocation":[45,136],"power":[47,131],"coordination":[48,132],"D2D":[50,90,181],"HetNets":[53],"with":[54],"consideration":[56],"of":[57,75,86,95,168,176,180],"interference":[58],"channel":[59],"uncertainties.":[60],"The":[61],"problem":[62,69,111],"is":[63,122,147],"formulated":[64],"as":[65],"an":[66,142],"uncertain":[67,109],"MOO":[68,110],"to":[70,106,124],"maximize":[71],"EE":[72],"SE":[74],"cellular":[76],"users":[77],"(CUs)":[78],"simultaneously":[79],"while":[80],"guaranteeing":[81],"minimum":[83],"rate":[84],"requirements":[85],"both":[87],"CUs":[88],"pairs.":[91,182],"With":[92],"aid":[94],"\u03b5-constraint":[96],"method":[97],"strict":[99],"robustness,":[100],"propose":[102],"a":[103,113],"general":[104],"framework":[105],"transform":[107],"into":[112],"deterministic":[114],"single-objective":[115],"problem.":[117],"As":[118],"exponential":[119],"computational":[120],"complexity":[121],"required":[123],"solve":[125],"highly":[127],"non-convex":[128],"problem,":[129],"problems":[137],"are":[138],"solved":[139],"separately,":[140],"effective":[143,170],"two-stage":[144],"iterative":[145],"algorithm":[146],"developed.":[148],"Finally,":[149],"simulation":[150],"results":[151],"validate":[152],"that":[153],"our":[154],"proposed":[155],"scheme":[157,165],"converges":[158],"fast":[159],"significantly":[161],"outperforms":[162],"non-robust":[164],"terms":[167],"EE-SE":[171],"quality":[175],"service":[177],"satisfying":[178],"probability":[179]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}