{"id":"https://openalex.org/W3082412394","doi":"https://doi.org/10.1007/978-3-030-58112-1_22","title":"A Permutational Boltzmann Machine with Parallel Tempering for Solving Combinatorial Optimization Problems","display_name":"A Permutational Boltzmann Machine with Parallel Tempering for Solving Combinatorial Optimization Problems","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3082412394","doi":"https://doi.org/10.1007/978-3-030-58112-1_22","mag":"3082412394"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-58112-1_22","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-58112-1_22","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-58112-1_22.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-58112-1_22.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008846358","display_name":"Mohammad Bagherbeik","orcid":"https://orcid.org/0000-0003-1834-7371"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Mohammad Bagherbeik","raw_affiliation_strings":["University of Toronto, Toronto, ON, M5S2E8, Canada"],"affiliations":[{"raw_affiliation_string":"University of Toronto, Toronto, ON, M5S2E8, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055462549","display_name":"Parastoo Ashtari","orcid":"https://orcid.org/0000-0001-8280-1976"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Parastoo Ashtari","raw_affiliation_strings":["University of Toronto, Toronto, ON, M5S2E8, Canada"],"affiliations":[{"raw_affiliation_string":"University of Toronto, Toronto, ON, M5S2E8, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040710483","display_name":"Seyed Farzad Mousavi","orcid":"https://orcid.org/0000-0002-2279-3043"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Seyed Farzad Mousavi","raw_affiliation_strings":["University of Toronto, Toronto, ON, M5S2E8, Canada"],"affiliations":[{"raw_affiliation_string":"University of Toronto, Toronto, ON, M5S2E8, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103550099","display_name":"Kouichi Kanda","orcid":null},"institutions":[{"id":"https://openalex.org/I2252096349","display_name":"Fujitsu (Japan)","ror":"https://ror.org/038e2g226","country_code":"JP","type":"company","lineage":["https://openalex.org/I2252096349"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kouichi Kanda","raw_affiliation_strings":["Fujitsu Laboratories Limited, Kawasaki, Kanagawa, 211-8588, Japan"],"affiliations":[{"raw_affiliation_string":"Fujitsu Laboratories Limited, Kawasaki, Kanagawa, 211-8588, Japan","institution_ids":["https://openalex.org/I2252096349"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076932154","display_name":"Hirotaka Tamura","orcid":"https://orcid.org/0000-0002-4152-1406"},"institutions":[{"id":"https://openalex.org/I2252096349","display_name":"Fujitsu (Japan)","ror":"https://ror.org/038e2g226","country_code":"JP","type":"company","lineage":["https://openalex.org/I2252096349"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hirotaka Tamura","raw_affiliation_strings":["Fujitsu Laboratories Limited, Kawasaki, Kanagawa, 211-8588, Japan"],"affiliations":[{"raw_affiliation_string":"Fujitsu Laboratories Limited, Kawasaki, Kanagawa, 211-8588, Japan","institution_ids":["https://openalex.org/I2252096349"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077605824","display_name":"Ali Sheikholeslami","orcid":"https://orcid.org/0000-0003-0970-6897"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Ali Sheikholeslami","raw_affiliation_strings":["University of Toronto, Toronto, ON, M5S2E8, Canada"],"affiliations":[{"raw_affiliation_string":"University of Toronto, Toronto, ON, M5S2E8, Canada","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5008846358"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":1.2599,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.87590833,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"317","last_page":"331"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10036","display_name":"Advanced Neural Network Applications","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T12072","display_name":"Machine Learning and Algorithms","score":0.982200026512146,"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/computer-science","display_name":"Computer science","score":0.8490942716598511},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.817029595375061},{"id":"https://openalex.org/keywords/boltzmann-machine","display_name":"Boltzmann machine","score":0.6333996057510376},{"id":"https://openalex.org/keywords/mimd","display_name":"MIMD","score":0.5874603390693665},{"id":"https://openalex.org/keywords/simd","display_name":"SIMD","score":0.5673734545707703},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5514196753501892},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5103749632835388},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"Combinatorial optimization","score":0.47055840492248535},{"id":"https://openalex.org/keywords/cuda","display_name":"CUDA","score":0.42875513434410095},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4246862232685089},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3611918091773987},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1727100908756256}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8490942716598511},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.817029595375061},{"id":"https://openalex.org/C192576344","wikidata":"https://www.wikidata.org/wiki/Q194706","display_name":"Boltzmann machine","level":3,"score":0.6333996057510376},{"id":"https://openalex.org/C21032095","wikidata":"https://www.wikidata.org/wiki/Q1149237","display_name":"MIMD","level":2,"score":0.5874603390693665},{"id":"https://openalex.org/C150552126","wikidata":"https://www.wikidata.org/wiki/Q339387","display_name":"SIMD","level":2,"score":0.5673734545707703},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5514196753501892},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5103749632835388},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.47055840492248535},{"id":"https://openalex.org/C2778119891","wikidata":"https://www.wikidata.org/wiki/Q477690","display_name":"CUDA","level":2,"score":0.42875513434410095},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4246862232685089},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3611918091773987},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1727100908756256},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-030-58112-1_22","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-58112-1_22","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-58112-1_22.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-030-58112-1_22","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-58112-1_22","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F978-3-030-58112-1_22.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3082412394.pdf","grobid_xml":"https://content.openalex.org/works/W3082412394.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W35065443","https://openalex.org/W1503085769","https://openalex.org/W1874649147","https://openalex.org/W1993697459","https://openalex.org/W1993937075","https://openalex.org/W2002664623","https://openalex.org/W2013145865","https://openalex.org/W2015206516","https://openalex.org/W2022223388","https://openalex.org/W2045767693","https://openalex.org/W2076237888","https://openalex.org/W2084512390","https://openalex.org/W2170171286","https://openalex.org/W2382768677","https://openalex.org/W2494917411","https://openalex.org/W2554099796","https://openalex.org/W2886607182","https://openalex.org/W2888513756","https://openalex.org/W2914275007","https://openalex.org/W2937335791","https://openalex.org/W2990475267","https://openalex.org/W3011234689","https://openalex.org/W3098919389","https://openalex.org/W3101006260"],"related_works":["https://openalex.org/W1980986440","https://openalex.org/W3158884034","https://openalex.org/W2163078645","https://openalex.org/W4388314704","https://openalex.org/W2014030893","https://openalex.org/W1971361763","https://openalex.org/W2399578218","https://openalex.org/W2167983067","https://openalex.org/W156928674","https://openalex.org/W2125719717"],"abstract_inverted_index":{"Boltzmann":[0,27],"Machines":[1],"are":[2],"recurrent":[3],"neural":[4,30],"networks":[5],"that":[6,92],"have":[7],"been":[8],"used":[9],"extensively":[10],"in":[11,42,97],"combinatorial":[12],"optimization":[13,36],"due":[14],"to":[15,59],"their":[16],"simplicity":[17],"and":[18,90,116],"ease":[19],"of":[20,33,52,74,84,99],"parallelization.":[21],"This":[22],"paper":[23],"introduces":[24],"the":[25,72,85],"Permutational":[26],"Machine,":[28],"a":[29,45,56,60,64],"network":[31,41],"capable":[32],"solving":[34],"permutation":[35],"problems.":[37],"We":[38,70],"implement":[39],"this":[40,75],"combination":[43],"with":[44,49,67],"Parallel":[46],"Tempering":[47],"algorithm":[48],"varying":[50],"degrees":[51],"parallelism":[53],"ranging":[54],"from":[55],"single-thread":[57],"variant":[58],"multi-threaded":[61],"system":[62,77,95],"using":[63,82],"64-core":[65],"CPU":[66,113],"SIMD":[68],"instructions.":[69],"benchmark":[71],"performance":[73],"new":[76],"on":[78,112],"Quadratic":[79],"Assignment":[80],"Problems,":[81],"some":[83],"most":[86],"difficult":[87],"known":[88,106],"instances,":[89],"show":[91],"our":[93],"parallel":[94],"performs":[96],"excess":[98],"100":[100],"$$\\times":[101],"$$":[102],"faster":[103],"than":[104],"any":[105],"dedicated":[107],"solver,":[108],"including":[109],"those":[110],"implemented":[111],"clusters,":[114],"GPUs,":[115],"FPGAs.":[117]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-26T15:22:09.906841","created_date":"2025-10-10T00:00:00"}