{"id":"https://openalex.org/W2018262123","doi":"https://doi.org/10.1109/cec.2010.5585920","title":"Meta-heuristic search and square erickson matrices","display_name":"Meta-heuristic search and square erickson matrices","publication_year":2010,"publication_date":"2010-07-01","ids":{"openalex":"https://openalex.org/W2018262123","doi":"https://doi.org/10.1109/cec.2010.5585920","mag":"2018262123"},"language":"en","primary_location":{"id":"doi:10.1109/cec.2010.5585920","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2010.5585920","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Congress on Evolutionary Computation","raw_type":"proceedings-article"},"type":"preprint","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/A5045208034","display_name":"Denis Robilliard","orcid":"https://orcid.org/0000-0003-1836-6679"},"institutions":[{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]},{"id":"https://openalex.org/I2802487185","display_name":"Universit\u00e9 du littoral c\u00f4te d'opale","ror":"https://ror.org/02gdcg342","country_code":"FR","type":"education","lineage":["https://openalex.org/I2802487185"]},{"id":"https://openalex.org/I4387154658","display_name":"Laboratoire d\u2019Informatique Signal et Image de la C\u00f4te d\u2019Opale","ror":"https://ror.org/00tm1qp20","country_code":null,"type":"facility","lineage":["https://openalex.org/I2802487185","https://openalex.org/I4387154658"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Denis Robilliard","raw_affiliation_strings":["Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, Universidad Lille Nord de France, Calais, France","Univ Lille Nord de France, Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, 50 rue Ferdinand Buisson - BP 719, 62228 CALAIS Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, Universidad Lille Nord de France, Calais, France","institution_ids":["https://openalex.org/I2802487185"]},{"raw_affiliation_string":"Univ Lille Nord de France, Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, 50 rue Ferdinand Buisson - BP 719, 62228 CALAIS Cedex, France","institution_ids":["https://openalex.org/I2279609970","https://openalex.org/I4387154658"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082660969","display_name":"Amine Boumaza","orcid":null},"institutions":[{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]},{"id":"https://openalex.org/I2802487185","display_name":"Universit\u00e9 du littoral c\u00f4te d'opale","ror":"https://ror.org/02gdcg342","country_code":"FR","type":"education","lineage":["https://openalex.org/I2802487185"]},{"id":"https://openalex.org/I4387154658","display_name":"Laboratoire d\u2019Informatique Signal et Image de la C\u00f4te d\u2019Opale","ror":"https://ror.org/00tm1qp20","country_code":null,"type":"facility","lineage":["https://openalex.org/I2802487185","https://openalex.org/I4387154658"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Amine Boumaza","raw_affiliation_strings":["Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, Universidad Lille Nord de France, Calais, France","Univ Lille Nord de France, Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, 50 rue Ferdinand Buisson - BP 719, 62228 CALAIS Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, Universidad Lille Nord de France, Calais, France","institution_ids":["https://openalex.org/I2802487185"]},{"raw_affiliation_string":"Univ Lille Nord de France, Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, 50 rue Ferdinand Buisson - BP 719, 62228 CALAIS Cedex, France","institution_ids":["https://openalex.org/I2279609970","https://openalex.org/I4387154658"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048171249","display_name":"Virginie Marion-Poty","orcid":null},"institutions":[{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]},{"id":"https://openalex.org/I2802487185","display_name":"Universit\u00e9 du littoral c\u00f4te d'opale","ror":"https://ror.org/02gdcg342","country_code":"FR","type":"education","lineage":["https://openalex.org/I2802487185"]},{"id":"https://openalex.org/I4387154658","display_name":"Laboratoire d\u2019Informatique Signal et Image de la C\u00f4te d\u2019Opale","ror":"https://ror.org/00tm1qp20","country_code":null,"type":"facility","lineage":["https://openalex.org/I2802487185","https://openalex.org/I4387154658"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Virginie Marion-Poty","raw_affiliation_strings":["Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, Universidad Lille Nord de France, Calais, France","Univ Lille Nord de France, Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, 50 rue Ferdinand Buisson - BP 719, 62228 CALAIS Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, Universidad Lille Nord de France, Calais, France","institution_ids":["https://openalex.org/I2802487185"]},{"raw_affiliation_string":"Univ Lille Nord de France, Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, 50 rue Ferdinand Buisson - BP 719, 62228 CALAIS Cedex, France","institution_ids":["https://openalex.org/I2279609970","https://openalex.org/I4387154658"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7457,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.73028879,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"5","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9965999722480774,"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"}},"topics":[{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9965999722480774,"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/T11574","display_name":"Artificial Intelligence in Games","score":0.9907000064849854,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9891999959945679,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.544983983039856},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5113667845726013},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.460812509059906},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3704502582550049},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3207830786705017},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3073533773422241},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06103876233100891}],"concepts":[{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.544983983039856},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5113667845726013},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.460812509059906},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3704502582550049},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3207830786705017},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3073533773422241},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06103876233100891}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cec.2010.5585920","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2010.5585920","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Congress on Evolutionary Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W18216792","https://openalex.org/W1562606923","https://openalex.org/W1575155528","https://openalex.org/W1576660662","https://openalex.org/W1839839470","https://openalex.org/W2056897909","https://openalex.org/W2097571405","https://openalex.org/W2099861483","https://openalex.org/W2106371135","https://openalex.org/W2117396900","https://openalex.org/W2167913911","https://openalex.org/W2171964388","https://openalex.org/W2323697554","https://openalex.org/W2331734388","https://openalex.org/W2484510618","https://openalex.org/W3023540311","https://openalex.org/W4232876664","https://openalex.org/W4392750738","https://openalex.org/W6600754543","https://openalex.org/W6634249717","https://openalex.org/W6636850861","https://openalex.org/W6674896183","https://openalex.org/W6675709134","https://openalex.org/W6677244241","https://openalex.org/W6702391514"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"A":[0],"Ramsey":[1],"theory":[2],"problem,":[3,92],"that":[4,34,78,98,179],"can":[5],"be":[6],"seen":[7],"as":[8],"a":[9,57,87,103,161,171],"2":[10],"dimensional":[11],"extension":[12],"of":[13,39,49,56,90,102,109,113,134,148,156,175],"the":[14,30,36,54,63,95,100,114,157],"Van":[15],"der":[16],"Waerden":[17],"theorem,":[18],"was":[19,66],"posed":[20],"by":[21,69],"Martin":[22],"J.":[23],"Erickson":[24],"in":[25,73],"his":[26],"book":[27],"[1]:":[28],"\u201cfind":[29],"minimum":[31,96],"n":[32,79,97,180],"such":[33,170],"if":[35],"lattice":[37],"points":[38,48],"[n]":[40,42,110,112,135],"\u00d7":[41,106,111,123,136,153],"are":[43],"two-colored,":[44],"there":[45],"exist":[46],"four":[47],"one":[50],"color":[51],"lying":[52],"on":[53,141,164],"vertices":[55],"square":[58,173],"with":[59],"sides":[60],"parallel":[61],"to":[62,145],"axes\u201d.":[64],"This":[65],"solved":[67],"recently":[68],"Bacher":[70],"and":[71],"Eliahou":[72],"2009":[74],"[2],":[75],"who":[76],"showed":[77],"=":[80],"15.":[81],"In":[82,166],"this":[83,91,142],"paper":[84],"we":[85,168],"tackle":[86],"derived":[88],"version":[89],"searching":[93],"for":[94,131],"forces":[99],"existence":[101],"monochromatic":[104,151],"[3]":[105,107,152,154],"subgrid":[108,155],"form":[115],"{i,":[116],"i":[117,120],"+":[118,121,126,129],"t,":[119,127],"2t}":[122,130],"{j,":[124],"j":[125,128],"any":[132],"2-coloring":[133],"[n].":[137],"We":[138],"use":[139],"meta-heuristics":[140],"open":[143],"problem":[144],"find":[146],"instances":[147],"2-colorations":[149],"without":[150],"above":[158],"form,":[159],"setting":[160],"lower":[162],"bound":[163],"n.":[165],"particular":[167],"found":[169],"binary":[172],"grid":[174],"size":[176],"662,":[177],"implying":[178],">":[181],"662.":[182]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
