{"id":"https://openalex.org/W4313461565","doi":"https://doi.org/10.3390/computers12010011","title":"The Fifteen Puzzle\u2014A New Approach through Hybridizing Three Heuristics Methods","display_name":"The Fifteen Puzzle\u2014A New Approach through Hybridizing Three Heuristics Methods","publication_year":2023,"publication_date":"2023-01-03","ids":{"openalex":"https://openalex.org/W4313461565","doi":"https://doi.org/10.3390/computers12010011"},"language":"en","primary_location":{"id":"doi:10.3390/computers12010011","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computers12010011","pdf_url":"https://www.mdpi.com/2073-431X/12/1/11/pdf?version=1673599574","source":{"id":"https://openalex.org/S4210228075","display_name":"Computers","issn_l":"2073-431X","issn":["2073-431X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-431X/12/1/11/pdf?version=1673599574","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075955319","display_name":"Dler O. Hasan","orcid":"https://orcid.org/0000-0001-9457-9655"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dler O. Hasan","raw_affiliation_strings":["Department of Applied Computer, College of Medicals and Applied Sciences, Charmo University, Sulaymaniyah, Chamchamal 46023, Iraq"],"raw_orcid":"https://orcid.org/0000-0001-9457-9655","affiliations":[{"raw_affiliation_string":"Department of Applied Computer, College of Medicals and Applied Sciences, Charmo University, Sulaymaniyah, Chamchamal 46023, Iraq","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025177724","display_name":"Aso M. Aladdin","orcid":"https://orcid.org/0000-0002-8734-0811"},"institutions":[{"id":"https://openalex.org/I3133014862","display_name":"Sulaimani Polytechnic University","ror":"https://ror.org/05v9vy052","country_code":"IQ","type":"education","lineage":["https://openalex.org/I3133014862"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Aso M. Aladdin","raw_affiliation_strings":["Department of Applied Computer, College of Medicals and Applied Sciences, Charmo University, Sulaymaniyah, Chamchamal 46023, Iraq","Department of Technical Information Systems Engineering, Erbil Technical Engineering College, Erbil Polytechnic University, Erbil 44001, Iraq"],"raw_orcid":"https://orcid.org/0000-0002-8734-0811","affiliations":[{"raw_affiliation_string":"Department of Applied Computer, College of Medicals and Applied Sciences, Charmo University, Sulaymaniyah, Chamchamal 46023, Iraq","institution_ids":[]},{"raw_affiliation_string":"Department of Technical Information Systems Engineering, Erbil Technical Engineering College, Erbil Polytechnic University, Erbil 44001, Iraq","institution_ids":["https://openalex.org/I3133014862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054477837","display_name":"Hardi Sabah Talabani","orcid":"https://orcid.org/0000-0001-6042-0064"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hardi Sabah Talabani","raw_affiliation_strings":["Department of Applied Computer, College of Medicals and Applied Sciences, Charmo University, Sulaymaniyah, Chamchamal 46023, Iraq"],"raw_orcid":"https://orcid.org/0000-0001-6042-0064","affiliations":[{"raw_affiliation_string":"Department of Applied Computer, College of Medicals and Applied Sciences, Charmo University, Sulaymaniyah, Chamchamal 46023, Iraq","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065801825","display_name":"Tarik A. Rashid","orcid":"https://orcid.org/0000-0002-8661-258X"},"institutions":[{"id":"https://openalex.org/I3151615967","display_name":"University of Kurdistan Hewler","ror":"https://ror.org/00268wk31","country_code":"IQ","type":"education","lineage":["https://openalex.org/I3151615967"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Tarik Ahmed Rashid","raw_affiliation_strings":["Computer Science and Engineering Department, University of Kurdistan Hewler, Erbil 44001, Iraq"],"raw_orcid":"https://orcid.org/0000-0002-8661-258X","affiliations":[{"raw_affiliation_string":"Computer Science and Engineering Department, University of Kurdistan Hewler, Erbil 44001, Iraq","institution_ids":["https://openalex.org/I3151615967"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091500375","display_name":"Seyedali Mirjalili","orcid":"https://orcid.org/0000-0002-1443-9458"},"institutions":[{"id":"https://openalex.org/I11701301","display_name":"Griffith University","ror":"https://ror.org/02sc3r913","country_code":"AU","type":"education","lineage":["https://openalex.org/I11701301"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Seyedali Mirjalili","raw_affiliation_strings":["School of Information and Communication Technology, Griffith University, Brisbane, QLD 4111, Australia"],"raw_orcid":"https://orcid.org/0000-0002-1443-9458","affiliations":[{"raw_affiliation_string":"School of Information and Communication Technology, Griffith University, Brisbane, QLD 4111, Australia","institution_ids":["https://openalex.org/I11701301"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5075955319"],"corresponding_institution_ids":[],"apc_list":{"value":1600,"currency":"CHF","value_usd":1732},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1732},"fwci":1.1104,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.80195487,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"12","issue":"1","first_page":"11","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10906","display_name":"AI-based Problem Solving and Planning","score":0.9984999895095825,"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/T10906","display_name":"AI-based Problem Solving and Planning","score":0.9984999895095825,"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":0.9868000149726868,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9765999913215637,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.9488552808761597},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5533221364021301},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5407516956329346},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5388057231903076},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5174827575683594},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5057337284088135},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4622601568698883},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3754986822605133},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.053394705057144165}],"concepts":[{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.9488552808761597},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5533221364021301},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5407516956329346},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5388057231903076},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5174827575683594},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5057337284088135},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4622601568698883},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3754986822605133},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.053394705057144165},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/computers12010011","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computers12010011","pdf_url":"https://www.mdpi.com/2073-431X/12/1/11/pdf?version=1673599574","source":{"id":"https://openalex.org/S4210228075","display_name":"Computers","issn_l":"2073-431X","issn":["2073-431X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2302.02985","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2302.02985","pdf_url":"https://arxiv.org/pdf/2302.02985","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:99b71618177148af8f0c2e681c90bb65","is_oa":true,"landing_page_url":"https://doaj.org/article/99b71618177148af8f0c2e681c90bb65","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,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computers, Vol 12, Iss 1, p 11 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/computers12010011","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computers12010011","pdf_url":"https://www.mdpi.com/2073-431X/12/1/11/pdf?version=1673599574","source":{"id":"https://openalex.org/S4210228075","display_name":"Computers","issn_l":"2073-431X","issn":["2073-431X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4313461565.pdf"},"referenced_works_count":67,"referenced_works":["https://openalex.org/W96218255","https://openalex.org/W134248414","https://openalex.org/W170032574","https://openalex.org/W178326615","https://openalex.org/W1480140957","https://openalex.org/W1505083629","https://openalex.org/W1514775172","https://openalex.org/W1539048696","https://openalex.org/W1558870289","https://openalex.org/W1775783412","https://openalex.org/W1814515812","https://openalex.org/W1968808691","https://openalex.org/W1968994430","https://openalex.org/W1969483458","https://openalex.org/W1971267722","https://openalex.org/W1974700506","https://openalex.org/W2083355299","https://openalex.org/W2110927808","https://openalex.org/W2114629047","https://openalex.org/W2114857598","https://openalex.org/W2131910799","https://openalex.org/W2132636780","https://openalex.org/W2136791927","https://openalex.org/W2150470619","https://openalex.org/W2155675331","https://openalex.org/W2156494678","https://openalex.org/W2166799707","https://openalex.org/W2405683058","https://openalex.org/W2588410419","https://openalex.org/W2735814871","https://openalex.org/W2747118187","https://openalex.org/W2783827472","https://openalex.org/W2933860896","https://openalex.org/W2990173267","https://openalex.org/W3013301076","https://openalex.org/W3021228199","https://openalex.org/W3081739105","https://openalex.org/W3098265530","https://openalex.org/W3098281028","https://openalex.org/W3153066392","https://openalex.org/W3155153111","https://openalex.org/W3165368361","https://openalex.org/W3176485119","https://openalex.org/W3182253415","https://openalex.org/W3183153856","https://openalex.org/W3186910487","https://openalex.org/W3197354642","https://openalex.org/W3208643628","https://openalex.org/W3209266892","https://openalex.org/W3209420330","https://openalex.org/W3211997524","https://openalex.org/W3215779613","https://openalex.org/W3217542308","https://openalex.org/W4200031930","https://openalex.org/W4220878860","https://openalex.org/W4230542890","https://openalex.org/W4245894815","https://openalex.org/W4248795023","https://openalex.org/W4296004336","https://openalex.org/W6603932855","https://openalex.org/W6630734404","https://openalex.org/W6676513180","https://openalex.org/W6677288201","https://openalex.org/W6679237040","https://openalex.org/W6682976889","https://openalex.org/W6684549237","https://openalex.org/W6746527747"],"related_works":["https://openalex.org/W2280422768","https://openalex.org/W3143197806","https://openalex.org/W4252555497","https://openalex.org/W3121175838","https://openalex.org/W3016293053","https://openalex.org/W1690653314","https://openalex.org/W2401723157","https://openalex.org/W2065055572","https://openalex.org/W2784269775","https://openalex.org/W2952904874"],"abstract_inverted_index":{"The":[0,90],"Fifteen":[1,48,87],"Puzzle":[2,49,88],"problem":[3],"is":[4,19],"one":[5],"of":[6,22,26,106,120,130,139],"the":[7,23,27,47,60,86,104,110,124,128,140,146],"most":[8],"classical":[9],"problems":[10],"that":[11,34,100],"has":[12,81],"captivated":[13],"mathematics":[14],"enthusiasts":[15],"for":[16],"centuries.":[17],"This":[18],"mainly":[20],"because":[21],"huge":[24],"size":[25],"state":[28,58],"space":[29,147],"with":[30,66],"approximately":[31],"1013":[32],"states":[33,107,132],"have":[35,42],"to":[36,45,54,84],"be":[37,95],"explored,":[38],"and":[39,77,133,149],"several":[40],"algorithms":[41],"been":[43,82],"applied":[44],"solve":[46,85],"instances.":[50],"In":[51],"this":[52,56],"paper,":[53],"manage":[55],"large":[57],"space,":[59],"bidirectional":[61],"A*":[62],"(BA*)":[63],"search":[64,142],"algorithm":[65,125],"three":[67,91],"heuristics,":[68],"such":[69],"as":[70],"Manhattan":[71],"distance":[72,79],"(MD),":[73],"linear":[74],"conflict":[75],"(LC),":[76],"walking":[78],"(WD),":[80],"used":[83],"problem.":[89],"mentioned":[92],"heuristics":[93,115],"will":[94],"hybridized":[96],"in":[97],"a":[98],"way":[99],"can":[101,143],"dramatically":[102],"reduce":[103,127,145],"number":[105,129],"generated":[108,131],"by":[109],"algorithm.":[111],"Moreover,":[112],"all":[113],"these":[114],"require":[116],"only":[117],"25":[118],"KB":[119],"storage,":[121],"but":[122],"help":[123],"effectively":[126],"expand":[134],"fewer":[135],"nodes.":[136],"Our":[137],"implementation":[138],"BA*":[141],"significantly":[144],"complexity,":[148],"guarantee":[150],"either":[151],"optimal":[152],"or":[153],"near-optimal":[154],"solutions.":[155]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2023-01-06T00:00:00"}