{"id":"https://openalex.org/W2940092338","doi":"https://doi.org/10.1051/ro/2019041","title":"New proposals for modelling and solving the problem of covering solids using spheres of different radii","display_name":"New proposals for modelling and solving the problem of covering solids using spheres of different radii","publication_year":2019,"publication_date":"2019-04-09","ids":{"openalex":"https://openalex.org/W2940092338","doi":"https://doi.org/10.1051/ro/2019041","mag":"2940092338"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2019041","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2019041","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","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/A5067057133","display_name":"Pedro Henrique Gonzalez Silva","orcid":null},"institutions":[{"id":"https://openalex.org/I122140584","display_name":"Universidade Federal do Rio de Janeiro","ror":"https://ror.org/03490as77","country_code":"BR","type":"education","lineage":["https://openalex.org/I122140584"]},{"id":"https://openalex.org/I158509141","display_name":"Federal Center for Technological Education Celso Suckow da Fonseca","ror":"https://ror.org/03j8tnm47","country_code":"BR","type":"education","lineage":["https://openalex.org/I1293487690","https://openalex.org/I158509141","https://openalex.org/I2801200668"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Pedro Henrique Gonz\u00e1lez Silva","raw_affiliation_strings":["Departamento de Inform\u00e1tica, Centro Federal de Educa\u00e7\u00e3o Tecnol\u00f3gica Celso Suckow da Fonseca, Brazil","Programa de Engenharia de Sistemas e Computa\u00e7\u00e3o, Universidade Federal do Rio de Janeiro, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Inform\u00e1tica, Centro Federal de Educa\u00e7\u00e3o Tecnol\u00f3gica Celso Suckow da Fonseca, Brazil","institution_ids":["https://openalex.org/I158509141"]},{"raw_affiliation_string":"Programa de Engenharia de Sistemas e Computa\u00e7\u00e3o, Universidade Federal do Rio de Janeiro, Brazil","institution_ids":["https://openalex.org/I122140584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005740112","display_name":"Ana Fl\u00e1via Uz\u00eada dos Santos Macambira","orcid":"https://orcid.org/0000-0002-1590-8113"},"institutions":[{"id":"https://openalex.org/I169045520","display_name":"Universidade Federal da Para\u00edba","ror":"https://ror.org/00p9vpz11","country_code":"BR","type":"education","lineage":["https://openalex.org/I169045520"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Ana Fl\u00e1via U. S. Macambira","raw_affiliation_strings":["Departamento de Estat\u00edstica, Universidade Federal da Para\u00edba, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Estat\u00edstica, Universidade Federal da Para\u00edba, Brazil","institution_ids":["https://openalex.org/I169045520"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045342661","display_name":"Renan Vicente Pinto","orcid":"https://orcid.org/0000-0002-8965-4961"},"institutions":[{"id":"https://openalex.org/I161460629","display_name":"Universidade Federal Rural do Rio de Janeiro","ror":"https://ror.org/00xwgyp12","country_code":"BR","type":"education","lineage":["https://openalex.org/I161460629"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Renan Vicente Pinto","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Universidade Federal Rural do Rio de Janeiro, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidade Federal Rural do Rio de Janeiro, Brazil","institution_ids":["https://openalex.org/I161460629"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091887801","display_name":"Luidi Simonetti","orcid":"https://orcid.org/0000-0001-8273-9439"},"institutions":[{"id":"https://openalex.org/I122140584","display_name":"Universidade Federal do Rio de Janeiro","ror":"https://ror.org/03490as77","country_code":"BR","type":"education","lineage":["https://openalex.org/I122140584"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Luidi Simonetti","raw_affiliation_strings":["Programa de Engenharia de Sistemas e Computa\u00e7\u00e3o, Universidade Federal do Rio de Janeiro, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Programa de Engenharia de Sistemas e Computa\u00e7\u00e3o, Universidade Federal do Rio de Janeiro, Brazil","institution_ids":["https://openalex.org/I122140584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091887230","display_name":"Nelson Maculan","orcid":"https://orcid.org/0000-0002-3897-3356"},"institutions":[{"id":"https://openalex.org/I122140584","display_name":"Universidade Federal do Rio de Janeiro","ror":"https://ror.org/03490as77","country_code":"BR","type":"education","lineage":["https://openalex.org/I122140584"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Nelson Maculan","raw_affiliation_strings":["Programa de Engenharia de Sistemas e Computa\u00e7\u00e3o, Universidade Federal do Rio de Janeiro, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Programa de Engenharia de Sistemas e Computa\u00e7\u00e3o, Universidade Federal do Rio de Janeiro, Brazil","institution_ids":["https://openalex.org/I122140584"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016889937","display_name":"Philippe Michelon","orcid":"https://orcid.org/0000-0001-6648-5651"},"institutions":[{"id":"https://openalex.org/I198415970","display_name":"Universit\u00e9 d'Avignon et des Pays de Vaucluse","ror":"https://ror.org/00mfpxb84","country_code":"FR","type":"education","lineage":["https://openalex.org/I198415970"]},{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques Blaise Pascal","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Philippe Michelon","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques d\u2019Avignon, Universit\u00e9 d\u2019Avignon et des Pays de Vaucluse, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques d\u2019Avignon, Universit\u00e9 d\u2019Avignon et des Pays de Vaucluse, France","institution_ids":["https://openalex.org/I198415970","https://openalex.org/I4210155549"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":0,"currency":"EUR","value_usd":0},"apc_paid":null,"fwci":0.3821,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69386202,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":96},"biblio":{"volume":"54","issue":"3","first_page":"873","last_page":"882"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9955000281333923,"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":0.9955000281333923,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9793000221252441,"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/T12782","display_name":"Assembly Line Balancing Optimization","score":0.9769999980926514,"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/intersection","display_name":"Intersection (aeronautics)","score":0.7086837291717529},{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.6904614567756653},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.6191814541816711},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5855962634086609},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5608533620834351},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5188897252082825},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5095465779304504},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.500457763671875},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4634428322315216},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45079025626182556},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4392446279525757},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43626904487609863},{"id":"https://openalex.org/keywords/set-cover-problem","display_name":"Set cover problem","score":0.4351137578487396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39501795172691345},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3755747377872467},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14129957556724548},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11771467328071594}],"concepts":[{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.7086837291717529},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.6904614567756653},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.6191814541816711},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5855962634086609},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5608533620834351},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5188897252082825},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5095465779304504},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.500457763671875},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4634428322315216},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45079025626182556},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4392446279525757},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43626904487609863},{"id":"https://openalex.org/C100808899","wikidata":"https://www.wikidata.org/wiki/Q1192100","display_name":"Set cover problem","level":3,"score":0.4351137578487396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39501795172691345},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3755747377872467},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14129957556724548},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11771467328071594},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","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},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ro/2019041","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2019041","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:RO_2020__54_3_873_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2019041/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.800000011920929,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320322749","display_name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro","ror":"https://ror.org/03kk0s825"},{"id":"https://openalex.org/F4320324077","display_name":"Funda\u00e7\u00e3o Coordena\u00e7\u00e3o de Projetos, Pesquisas e Estudos Tecnol\u00f3gicos","ror":"https://ror.org/05wkrjp12"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W66234578","https://openalex.org/W988732486","https://openalex.org/W1974425783","https://openalex.org/W2061779725","https://openalex.org/W2062480190","https://openalex.org/W2155597788","https://openalex.org/W4245709321"],"related_works":["https://openalex.org/W3193357262","https://openalex.org/W2138488418","https://openalex.org/W1569572113","https://openalex.org/W2030434620","https://openalex.org/W2348909947","https://openalex.org/W2992657610","https://openalex.org/W2781507331","https://openalex.org/W2765471166","https://openalex.org/W3006241023","https://openalex.org/W2028438572"],"abstract_inverted_index":{"Given":[0],"a":[1,6,19,24,68,80,103],"solid":[2],"T,":[3],"represented":[4],"by":[5,23,49,72],"compact":[7],"set":[8,26],"in":[9,64,130],"\u211d3,":[10],"the":[11,37,43,46,50,53,65,123,127,131],"aim":[12],"of":[13,21,27,29,34,55,67],"this":[14,92],"work":[15],"is":[16,39,57],"to":[17,41],"find":[18],"covering":[20],"T":[22,56],"finite":[25],"spheres":[28,38,51],"different":[30],"radii.":[31],"Some":[32],"level":[33],"intersection":[35],"between":[36],"necessary":[40],"cover":[42],"solid.":[44],"Moreover,":[45],"volume":[47],"occupied":[48],"on":[52],"outside":[54],"limited.":[58],"This":[59],"problem":[60,83],"has":[61],"an":[62,116],"application":[63],"planning":[66],"radio-surgery":[69],"treatment":[70],"known":[71],"Gamma":[73],"Knife":[74],"and":[75,87,102,115],"can":[76],"be":[77],"formulated":[78],"as":[79],"non-convex":[81],"optimization":[82],"with":[84,99],"quadratic":[85],"constraints":[86],"linear":[88,96],"objective":[89],"function.":[90],"In":[91],"work,":[93],"two":[94],"new":[95],"mathematical":[97],"formulations":[98],"binary":[100],"variables":[101],"hybrid":[104,109],"method":[105,110],"are":[106],"proposed.":[107],"The":[108],"combines":[111],"heuristic,":[112],"data":[113],"mining":[114],"exact":[117],"method.":[118],"Computational":[119],"results":[120],"show":[121],"that":[122],"proposed":[124],"methods":[125],"outperform":[126],"ones":[128],"presented":[129],"literature.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-08-29T07:29:34.045763","created_date":"2025-10-10T00:00:00"}