{"id":"https://openalex.org/W1986179299","doi":"https://doi.org/10.1155/2015/836925","title":"Construction Example for Algebra System Using Harmony Search Algorithm","display_name":"Construction Example for Algebra System Using Harmony Search Algorithm","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1986179299","doi":"https://doi.org/10.1155/2015/836925","mag":"1986179299"},"language":"en","primary_location":{"id":"doi:10.1155/2015/836925","doi":"https://doi.org/10.1155/2015/836925","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2015/836925","pdf_url":"https://downloads.hindawi.com/journals/mpe/2015/836925.pdf","source":{"id":"https://openalex.org/S178238111","display_name":"Mathematical Problems in Engineering","issn_l":"1024-123X","issn":["1024-123X","1026-7077","1563-5147"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","poland-20","vabb-shw"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Problems in Engineering","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/journals/mpe/2015/836925.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"FangAn Deng","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I187175081","display_name":"Shaanxi University of Technology","ror":"https://ror.org/056m91h77","country_code":"CN","type":"education","lineage":["https://openalex.org/I187175081"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"FangAn Deng","raw_affiliation_strings":["School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723000, China","institution_ids":["https://openalex.org/I187175081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045481342","display_name":"Shouheng Tuo","orcid":"https://orcid.org/0000-0002-6696-0085","observed_orcids":["https://orcid.org/0000-0002-6696-0085"]},"institutions":[{"id":"https://openalex.org/I187175081","display_name":"Shaanxi University of Technology","ror":"https://ror.org/056m91h77","country_code":"CN","type":"education","lineage":["https://openalex.org/I187175081"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shouheng Tuo","raw_affiliation_strings":["School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723000, China","institution_ids":["https://openalex.org/I187175081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088729692","display_name":"Longquan Yong","orcid":"https://orcid.org/0000-0002-9679-1446","observed_orcids":["https://orcid.org/0000-0002-9679-1446"]},"institutions":[{"id":"https://openalex.org/I187175081","display_name":"Shaanxi University of Technology","ror":"https://ror.org/056m91h77","country_code":"CN","type":"education","lineage":["https://openalex.org/I187175081"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Longquan Yong","raw_affiliation_strings":["School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723000, China"],"raw_orcid":"https://orcid.org/0000-0002-9679-1446","affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723000, China","institution_ids":["https://openalex.org/I187175081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067280360","display_name":"Tao Zhou","orcid":"https://orcid.org/0000-0002-8145-712X","observed_orcids":["https://orcid.org/0000-0002-8145-712X"]},"institutions":[{"id":"https://openalex.org/I4210127460","display_name":"Ningxia Medical University","ror":"https://ror.org/02h8a1848","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210127460"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Zhou","raw_affiliation_strings":["School of Science, Ningxia Medical University, Yinchuan, Ningxia 750004, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Ningxia Medical University, Yinchuan, Ningxia 750004, China","institution_ids":["https://openalex.org/I4210127460"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045481342"],"corresponding_institution_ids":["https://openalex.org/I187175081"],"apc_list":{"value":2550,"currency":"USD","value_usd":2550},"apc_paid":{"value":2550,"currency":"USD","value_usd":2550},"fwci":0.2998,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.66809686,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"2015","issue":null,"first_page":"1","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9951000213623047,"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"}},"topics":[{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9951000213623047,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/harmony-search-algorithm","display_name":"harmony search algorithm","score":0.8349999785423279},{"id":"https://openalex.org/keywords/np-hard-problems","display_name":"NP-hard problems","score":0.7200000286102295},{"id":"https://openalex.org/keywords/optimization-model","display_name":"optimization model","score":0.8790000081062317},{"id":"https://openalex.org/keywords/exploration-exploitation-trade-off","display_name":"exploration-exploitation balance","score":0.7919999957084656},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"combinatorial optimization","score":0.6779999732971191}],"concepts":[{"id":"https://openalex.org/C33099171","wikidata":"https://www.wikidata.org/wiki/Q26208718","display_name":"Harmony search","level":2,"score":0.7384230494499207},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5959241390228271},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4663485884666443},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45428869128227234},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41798102855682373},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41551387310028076},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1117994487285614}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2015/836925","doi":"https://doi.org/10.1155/2015/836925","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2015/836925","pdf_url":"https://downloads.hindawi.com/journals/mpe/2015/836925.pdf","source":{"id":"https://openalex.org/S178238111","display_name":"Mathematical Problems in Engineering","issn_l":"1024-123X","issn":["1024-123X","1026-7077","1563-5147"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","poland-20","vabb-shw"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Problems in Engineering","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jnlmpe:836925","doi":null,"is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/MPE/2015/836925.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:453a40a662104f82b3e3a44dbdaae5eb","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/453a40a662104f82b3e3a44dbdaae5eb","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Problems in Engineering, Vol 2015 (2015)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2015/836925","doi":"https://doi.org/10.1155/2015/836925","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2015/836925","pdf_url":"https://downloads.hindawi.com/journals/mpe/2015/836925.pdf","source":{"id":"https://openalex.org/S178238111","display_name":"Mathematical Problems in Engineering","issn_l":"1024-123X","issn":["1024-123X","1026-7077","1563-5147"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","poland-20","vabb-shw"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Problems in Engineering","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1653467573","display_name":null,"funder_award_id":"11401357","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1976174519","display_name":null,"funder_award_id":"2013hzzx-39","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G371023732","display_name":"\u591a\u6e90\u533b\u5b66\u56fe\u50cf\u878d\u5408\u4e0e\u8bc6\u522b\u7814\u7a76","funder_award_id":"81160183","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320325627","display_name":"Education Department of Shaanxi Province","ror":"https://ror.org/00jb7xy46"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1986179299.pdf","grobid_xml":"https://content.openalex.org/works/W1986179299.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W127103380","https://openalex.org/W1985334587","https://openalex.org/W1988113391","https://openalex.org/W1988854130","https://openalex.org/W1993885071","https://openalex.org/W1997337230","https://openalex.org/W2001283591","https://openalex.org/W2031933719","https://openalex.org/W2039271569","https://openalex.org/W2040564044","https://openalex.org/W2061935875","https://openalex.org/W2065509522","https://openalex.org/W2084424327","https://openalex.org/W2129121437","https://openalex.org/W2130343325","https://openalex.org/W2492058730","https://openalex.org/W4252618966"],"related_works":["https://openalex.org/W2733465426","https://openalex.org/W4242699880","https://openalex.org/W2099239187","https://openalex.org/W4237237266","https://openalex.org/W2559616272","https://openalex.org/W4414196914","https://openalex.org/W6922551015","https://openalex.org/W2275678054","https://openalex.org/W7051875255","https://openalex.org/W3185020979"],"abstract_inverted_index":{"The":[0,116],"construction":[1,37,100,130],"example":[2,38,131],"of":[3,11,29,39,102,114,133],"algebra":[4,14,40,103,134],"system":[5,41,104],"is":[6,18,42,55],"to":[7,25,57,73,107],"verify":[8],"the":[9,65,69,75,84,109,121],"existence":[10],"a":[12,19,32,87],"complex":[13,129],"system,":[15],"and":[16,80,91,112],"it":[17],"NP-hard":[20],"problem.":[21],"In":[22],"this":[23,27],"paper,":[24],"solve":[26],"kind":[28],"problems,":[30],"firstly,":[31],"mathematical":[33],"optimization":[34,66,110],"model":[35,111],"for":[36,64,127],"established.":[43],"Secondly,":[44],"an":[45],"improved":[46],"harmony":[47],"search":[48,85],"algorithm":[49,53,123],"based":[50],"on":[51],"NGHS":[52],"(INGHS)":[54],"proposed":[56,70,122],"find":[58],"as":[59,62],"more":[60],"solutions":[61],"possible":[63],"model;":[67],"in":[68,83],"INGHS":[71],"algorithm,":[72],"achieve":[74],"balance":[76],"between":[77],"exploration":[78],"power":[79,82],"exploitation":[81],"process,":[86],"global":[88],"best":[89],"strategy":[90],"parameters":[92],"dynamic":[93],"adjustment":[94],"method":[95],"are":[96,105],"present.":[97],"Finally,":[98],"nine":[99],"examples":[101],"used":[106],"evaluate":[108],"performance":[113,126],"INGHS.":[115],"experimental":[117],"results":[118],"show":[119],"that":[120],"has":[124],"strong":[125],"solving":[128],"problems":[132],"system.":[135]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}