{"id":"https://openalex.org/W2084303984","doi":"https://doi.org/10.1080/00207160903045436","title":"Constrained circles packing test problems: all the optimal solutions known","display_name":"Constrained circles packing test problems: all the optimal solutions known","publication_year":2010,"publication_date":"2010-09-14","ids":{"openalex":"https://openalex.org/W2084303984","doi":"https://doi.org/10.1080/00207160903045436","mag":"2084303984"},"language":"en","primary_location":{"id":"doi:10.1080/00207160903045436","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160903045436","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008461757","display_name":"Chao Che","orcid":"https://orcid.org/0000-0003-2978-5430"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"C. Che","raw_affiliation_strings":["School of Computer Science and Technology, Dalian University of Technology , Dalian, 116024, China","School of Computer Science and Technology, Dalian University of Technology\n\t\t\t\t\t, Dalian, 116024, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Dalian University of Technology , Dalian, 116024, China","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"School of Computer Science and Technology, Dalian University of Technology\n\t\t\t\t\t, Dalian, 116024, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071708918","display_name":"Hong\u2010Fei Teng","orcid":"https://orcid.org/0000-0003-4946-0473"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]},{"id":"https://openalex.org/I4210092944","display_name":"Dalian University","ror":"https://ror.org/00g2ypp58","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210092944"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"H. F. Teng","raw_affiliation_strings":["School of Computer Science and Technology, Dalian University of Technology , Dalian, 116024, China","School of Mechanical Engineering, Dalian, University of Technology , Dalian, 116024, China","School of Mechanical Engineering, Dalian, University of Technology\n\t\t\t\t\t, Dalian, 116024, China","School of Computer Science and Technology, Dalian University of Technology\n\t\t\t\t\t, Dalian, 116024, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Dalian University of Technology , Dalian, 116024, China","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"School of Mechanical Engineering, Dalian, University of Technology , Dalian, 116024, China","institution_ids":["https://openalex.org/I27357992","https://openalex.org/I4210092944"]},{"raw_affiliation_string":"School of Mechanical Engineering, Dalian, University of Technology\n\t\t\t\t\t, Dalian, 116024, China","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"School of Computer Science and Technology, Dalian University of Technology\n\t\t\t\t\t, Dalian, 116024, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054090360","display_name":"Y. S. Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]},{"id":"https://openalex.org/I4210092944","display_name":"Dalian University","ror":"https://ror.org/00g2ypp58","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210092944"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Y. S. Wang","raw_affiliation_strings":["School of Aeronautics and Astronautics, Dalian University of Technology , Dalian, 116024, China","School of Aeronautics and Astronautics, Dalian University of Technology\n\t\t\t\t\t, Dalian, 116024, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aeronautics and Astronautics, Dalian University of Technology , Dalian, 116024, China","institution_ids":["https://openalex.org/I4210092944","https://openalex.org/I27357992"]},{"raw_affiliation_string":"School of Aeronautics and Astronautics, Dalian University of Technology\n\t\t\t\t\t, Dalian, 116024, China","institution_ids":["https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.20149709,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"87","issue":"13","first_page":"2887","last_page":"2902"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9998000264167786,"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/T11814","display_name":"Advanced Manufacturing and Logistics Optimization","score":0.9951000213623047,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9764999747276306,"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/mathematics","display_name":"Mathematics","score":0.7552204728126526},{"id":"https://openalex.org/keywords/circle-packing","display_name":"Circle packing","score":0.7369247078895569},{"id":"https://openalex.org/keywords/packing-problems","display_name":"Packing problems","score":0.6810917854309082},{"id":"https://openalex.org/keywords/test","display_name":"Test (biology)","score":0.5958682894706726},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5826394557952881},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.5753955841064453},{"id":"https://openalex.org/keywords/centroid","display_name":"Centroid","score":0.5400996208190918},{"id":"https://openalex.org/keywords/container","display_name":"Container (type theory)","score":0.4960871636867523},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4611767530441284},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.4534861445426941},{"id":"https://openalex.org/keywords/turning-radius","display_name":"Turning radius","score":0.4478128254413605},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4125860929489136},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.368941992521286},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25857841968536377},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2249317765235901},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21541699767112732},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08503609895706177}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7552204728126526},{"id":"https://openalex.org/C123115066","wikidata":"https://www.wikidata.org/wiki/Q5121501","display_name":"Circle packing","level":2,"score":0.7369247078895569},{"id":"https://openalex.org/C130253271","wikidata":"https://www.wikidata.org/wiki/Q3851477","display_name":"Packing problems","level":2,"score":0.6810917854309082},{"id":"https://openalex.org/C2777267654","wikidata":"https://www.wikidata.org/wiki/Q3519023","display_name":"Test (biology)","level":2,"score":0.5958682894706726},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5826394557952881},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.5753955841064453},{"id":"https://openalex.org/C146599234","wikidata":"https://www.wikidata.org/wiki/Q511093","display_name":"Centroid","level":2,"score":0.5400996208190918},{"id":"https://openalex.org/C2781018962","wikidata":"https://www.wikidata.org/wiki/Q5164884","display_name":"Container (type theory)","level":2,"score":0.4960871636867523},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4611767530441284},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4534861445426941},{"id":"https://openalex.org/C205148227","wikidata":"https://www.wikidata.org/wiki/Q2558948","display_name":"Turning radius","level":2,"score":0.4478128254413605},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4125860929489136},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.368941992521286},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25857841968536377},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2249317765235901},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21541699767112732},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08503609895706177},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160903045436","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160903045436","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1585335425","https://openalex.org/W1595159159","https://openalex.org/W1855408646","https://openalex.org/W1907706552","https://openalex.org/W1985329511","https://openalex.org/W2014977077","https://openalex.org/W2015945847","https://openalex.org/W2024060531","https://openalex.org/W2032612581","https://openalex.org/W2061917993","https://openalex.org/W2085137170","https://openalex.org/W2096590200","https://openalex.org/W2104670598","https://openalex.org/W2106625051","https://openalex.org/W2107172243","https://openalex.org/W2155312717","https://openalex.org/W2157122594","https://openalex.org/W2249956314","https://openalex.org/W2318644615","https://openalex.org/W4246598646","https://openalex.org/W4298110920","https://openalex.org/W4387688680"],"related_works":["https://openalex.org/W4251859436","https://openalex.org/W2568571446","https://openalex.org/W2174352574","https://openalex.org/W3190219083","https://openalex.org/W2057845274","https://openalex.org/W4383104139","https://openalex.org/W854593937","https://openalex.org/W125149659","https://openalex.org/W2039006199","https://openalex.org/W2731736014"],"abstract_inverted_index":{"AbstractTaking":[0],"a":[1,27,56],"satellite":[2],"module":[3,152],"layout":[4],"design":[5],"as":[6,120,122],"engineering":[7],"background,":[8],"this":[9],"paper":[10],"gives":[11],"constrained":[12],"test":[13,35,99,118,137,147],"problems":[14,100,119,138],"for":[15,176],"an":[16],"unequal":[17],"circle":[18],"packing":[19],"whose":[20],"optimal":[21,114],"solutions":[22],"are":[23,47,72,80,88,101,128],"all":[24],"given.":[25],"Given":[26],"circular":[28],"container":[29],"D":[30,50],"with":[31,55],"radius":[32,86],"R,":[33],"the":[34,41,61,69,77,95,105,117,136,165,171,177],"problem":[36],"can":[37,139],"be":[38],"constructed":[39,102],"in":[40,82],"following":[42],"steps.":[43],"First,":[44],"M=217":[45],"circles":[46,79,106],"packed":[48],"into":[49,90],"without":[51],"overlaps":[52],"by":[53,74],"\u2018packing":[54],"tangent":[57],"circle\u2019":[58],"to":[59,94,104,116,163],"get":[60],"values":[62],"of":[63,68,85,107,143,170,174],"radii":[64],"and":[65,87,125],"centroid":[66],"coordinates":[67],"circles,":[70],"which":[71],"expressed":[73],"R.":[75],"Then":[76],"217":[78],"arranged":[81],"descending":[83],"sequence":[84],"divided":[89],"23":[91],"groups":[92],"according":[93,103],"radius.":[96],"Finally,":[97],"seven":[98],"q=1,":[108],"2,":[109],"\u2026,":[110],"7":[111],"groups.":[112],"The":[113,131],"solution":[115],"well":[121],"its":[123],"optimality":[124],"uniqueness":[126],"proof":[127],"also":[129],"presented.":[130],"experimental":[132],"results":[133],"show":[134],"that":[135],"effectively":[140],"evaluate":[141],"performances":[142],"different":[144],"evolutionary":[145],"algorithms.Keywords:":[146],"problemcircle":[148],"packingperformance":[149],"constraintevolutionary":[150],"algorithmssatellite":[151],"layout2000":[153],"AMS":[154],"Subject":[155],"Classification:":[156],"52C26C.R.":[157],"Categories:":[158],"I.2.8":[159],"AcknowledgementsWe":[160],"would":[161],"like":[162],"acknowledge":[164],"National":[166],"Natural":[167],"Science":[168],"Foundation":[169],"People's":[172],"Republic":[173],"China":[175],"sponsorship":[178],"(Grants":[179],"No.":[180],"50275019,":[181],"50335040,":[182],"50575031).":[183]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
