{"id":"https://openalex.org/W4415534398","doi":"https://doi.org/10.1007/s10489-025-06932-1","title":"An improved graph attention network combined with reinforcement learning for capacitated vehicle routing problem","display_name":"An improved graph attention network combined with reinforcement learning for capacitated vehicle routing problem","publication_year":2025,"publication_date":"2025-10-25","ids":{"openalex":"https://openalex.org/W4415534398","doi":"https://doi.org/10.1007/s10489-025-06932-1"},"language":"en","primary_location":{"id":"doi:10.1007/s10489-025-06932-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10489-025-06932-1","pdf_url":null,"source":{"id":"https://openalex.org/S74726891","display_name":"Applied Intelligence","issn_l":"0924-669X","issn":["0924-669X","1573-7497"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Intelligence","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/A5016731062","display_name":"Y. Bai","orcid":"https://orcid.org/0000-0002-3080-7062"},"institutions":[{"id":"https://openalex.org/I62853816","display_name":"Beijing University of Civil Engineering and Architecture","ror":"https://ror.org/02yj0p855","country_code":"CN","type":"education","lineage":["https://openalex.org/I62853816"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yu Bai","raw_affiliation_strings":["School of Science, Beijing University of Civil Engineering and Architecture, No.1 Exhibition Hall Road, Beijing, 100044, Xicheng District, China"],"raw_orcid":"https://orcid.org/0000-0002-3080-7062","affiliations":[{"raw_affiliation_string":"School of Science, Beijing University of Civil Engineering and Architecture, No.1 Exhibition Hall Road, Beijing, 100044, Xicheng District, China","institution_ids":["https://openalex.org/I62853816"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080589649","display_name":"Xiaohan Xing","orcid":"https://orcid.org/0000-0002-9992-3387"},"institutions":[{"id":"https://openalex.org/I62853816","display_name":"Beijing University of Civil Engineering and Architecture","ror":"https://ror.org/02yj0p855","country_code":"CN","type":"education","lineage":["https://openalex.org/I62853816"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaohan Xing","raw_affiliation_strings":["School of Science, Beijing University of Civil Engineering and Architecture, No.1 Exhibition Hall Road, Beijing, 100044, Xicheng District, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Beijing University of Civil Engineering and Architecture, No.1 Exhibition Hall Road, Beijing, 100044, Xicheng District, China","institution_ids":["https://openalex.org/I62853816"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100333082","display_name":"Jian Wang","orcid":"https://orcid.org/0000-0002-1751-7060"},"institutions":[{"id":"https://openalex.org/I62853816","display_name":"Beijing University of Civil Engineering and Architecture","ror":"https://ror.org/02yj0p855","country_code":"CN","type":"education","lineage":["https://openalex.org/I62853816"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Wang","raw_affiliation_strings":["School of Geomatics and Urban Spatial Informatics, Beijing University of Civil Engineering and Architecture, No.1 Exhibition Hall Road, Beijing, 100044, Xicheng District, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Geomatics and Urban Spatial Informatics, Beijing University of Civil Engineering and Architecture, No.1 Exhibition Hall Road, Beijing, 100044, Xicheng District, China","institution_ids":["https://openalex.org/I62853816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016731062"],"corresponding_institution_ids":["https://openalex.org/I62853816"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.7655,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.76288638,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"55","issue":"16","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12292","display_name":"Graph Theory and Algorithms","score":0.9836000204086304,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.9836000204086304,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9822999835014343,"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/T12016","display_name":"Web Data Mining and Analysis","score":0.9429000020027161,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/node","display_name":"Node (physics)","score":0.5655999779701233},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.565500020980835},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5619000196456909},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5350000262260437},{"id":"https://openalex.org/keywords/vehicle-routing-problem","display_name":"Vehicle routing problem","score":0.5148000121116638},{"id":"https://openalex.org/keywords/encoder","display_name":"Encoder","score":0.48019999265670776},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4553000032901764},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4399999976158142}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8389000296592712},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5655999779701233},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.565500020980835},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5619000196456909},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5350000262260437},{"id":"https://openalex.org/C123784306","wikidata":"https://www.wikidata.org/wiki/Q944041","display_name":"Vehicle routing problem","level":3,"score":0.5148000121116638},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5013999938964844},{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.48019999265670776},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4553000032901764},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4399999976158142},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4043000042438507},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.3896999955177307},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.37229999899864197},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36899998784065247},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.3644999861717224},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.3610000014305115},{"id":"https://openalex.org/C176809094","wikidata":"https://www.wikidata.org/wiki/Q15401496","display_name":"Traverse","level":2,"score":0.35249999165534973},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C76522221","wikidata":"https://www.wikidata.org/wiki/Q5035396","display_name":"Multipath routing","level":5,"score":0.33160001039505005},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3179999887943268},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3003999888896942},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2919999957084656},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.2816999852657318},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.25949999690055847},{"id":"https://openalex.org/C159674985","wikidata":"https://www.wikidata.org/wiki/Q6823718","display_name":"Method of mean weighted residuals","level":4,"score":0.2533000111579895}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10489-025-06932-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10489-025-06932-1","pdf_url":null,"source":{"id":"https://openalex.org/S74726891","display_name":"Applied Intelligence","issn_l":"0924-669X","issn":["0924-669X","1573-7497"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Intelligence","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1537591644","display_name":null,"funder_award_id":"No. 42274029","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G471552457","display_name":null,"funder_award_id":"No. 42374024","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5120394691","display_name":null,"funder_award_id":"No. X24019","funder_id":"https://openalex.org/F4320325174","funder_display_name":"Beijing University of Civil Engineering and Architecture"},{"id":"https://openalex.org/G6168648571","display_name":null,"funder_award_id":"No. 42574052","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/F4320325174","display_name":"Beijing University of Civil Engineering and Architecture","ror":"https://ror.org/02yj0p855"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1972385709","https://openalex.org/W2897864152","https://openalex.org/W2921047495","https://openalex.org/W2980006675","https://openalex.org/W3085644258","https://openalex.org/W3103176522","https://openalex.org/W3109714359","https://openalex.org/W3146106549","https://openalex.org/W3180008386","https://openalex.org/W3199468096","https://openalex.org/W3212283129","https://openalex.org/W4224138275","https://openalex.org/W4313678757","https://openalex.org/W4323870466","https://openalex.org/W4385736039","https://openalex.org/W4385895629","https://openalex.org/W4394909995","https://openalex.org/W4400641188","https://openalex.org/W4401363951","https://openalex.org/W4401519383","https://openalex.org/W4401844157","https://openalex.org/W4403783401","https://openalex.org/W4403783471","https://openalex.org/W4408471876","https://openalex.org/W4409778229"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-25T00:00:00"}
