{"id":"https://openalex.org/W4385545081","doi":"https://doi.org/10.3390/a16080372","title":"Applying Particle Swarm Optimization Variations to Solve the Transportation Problem Effectively","display_name":"Applying Particle Swarm Optimization Variations to Solve the Transportation Problem Effectively","publication_year":2023,"publication_date":"2023-08-03","ids":{"openalex":"https://openalex.org/W4385545081","doi":"https://doi.org/10.3390/a16080372"},"language":"en","primary_location":{"id":"doi:10.3390/a16080372","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16080372","pdf_url":"https://www.mdpi.com/1999-4893/16/8/372/pdf?version=1691058598","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/16/8/372/pdf?version=1691058598","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092591380","display_name":"Chrysanthi Aroniadi","orcid":null},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Chrysanthi Aroniadi","raw_affiliation_strings":["Department of Food Science and Technology, University of Patras, Agrinio Campus, G. Seferi 2, 30100 Agrinio, Greece","Department of Food Science and Technology, University of Patras, Agrinio Campus, G. Seferi 2, 30100 Agrinio, Greece;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Food Science and Technology, University of Patras, Agrinio Campus, G. Seferi 2, 30100 Agrinio, Greece","institution_ids":["https://openalex.org/I174878644"]},{"raw_affiliation_string":"Department of Food Science and Technology, University of Patras, Agrinio Campus, G. Seferi 2, 30100 Agrinio, Greece;","institution_ids":["https://openalex.org/I174878644"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064070003","display_name":"Grigorios N. Beligiannis","orcid":"https://orcid.org/0000-0002-6896-5218"},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Grigorios N. Beligiannis","raw_affiliation_strings":["Department of Food Science and Technology, University of Patras, Agrinio Campus, G. Seferi 2, 30100 Agrinio, Greece","Department of Food Science and Technology, University of Patras, Agrinio Campus, G. Seferi 2, 30100 Agrinio, Greece;"],"raw_orcid":"https://orcid.org/0000-0002-6896-5218","affiliations":[{"raw_affiliation_string":"Department of Food Science and Technology, University of Patras, Agrinio Campus, G. Seferi 2, 30100 Agrinio, Greece","institution_ids":["https://openalex.org/I174878644"]},{"raw_affiliation_string":"Department of Food Science and Technology, University of Patras, Agrinio Campus, G. Seferi 2, 30100 Agrinio, Greece;","institution_ids":["https://openalex.org/I174878644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064070003"],"corresponding_institution_ids":["https://openalex.org/I174878644"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.2239,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.87750391,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"16","issue":"8","first_page":"372","last_page":"372"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T14228","display_name":"Religion and Sociopolitical Dynamics in Nigeria","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/3300","display_name":"General Social Sciences"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.9011510014533997},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7345182299613953},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.6292823553085327},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5845106840133667},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49700310826301575},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46148720383644104},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.41970184445381165},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3613440990447998}],"concepts":[{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.9011510014533997},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7345182299613953},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.6292823553085327},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5845106840133667},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49700310826301575},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46148720383644104},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.41970184445381165},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3613440990447998},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a16080372","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16080372","pdf_url":"https://www.mdpi.com/1999-4893/16/8/372/pdf?version=1691058598","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:142b52663f694410b2202807892a42c5","is_oa":true,"landing_page_url":"https://doaj.org/article/142b52663f694410b2202807892a42c5","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":"Algorithms, Vol 16, Iss 8, p 372 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/16/8/372/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a16080372","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Algorithms; Volume 16; Issue 8; Pages: 372","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a16080372","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16080372","pdf_url":"https://www.mdpi.com/1999-4893/16/8/372/pdf?version=1691058598","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385545081.pdf","grobid_xml":"https://content.openalex.org/works/W4385545081.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1991972552","https://openalex.org/W2011609932","https://openalex.org/W2059115408","https://openalex.org/W2108388069","https://openalex.org/W2153851348","https://openalex.org/W2164422526","https://openalex.org/W2212016480","https://openalex.org/W2291505919","https://openalex.org/W2317065341","https://openalex.org/W2328725012","https://openalex.org/W2573137292","https://openalex.org/W2735565064","https://openalex.org/W2796986051","https://openalex.org/W2914423730","https://openalex.org/W2921828164","https://openalex.org/W2924884701","https://openalex.org/W3045460713","https://openalex.org/W3101025102","https://openalex.org/W4225000890","https://openalex.org/W4229373113","https://openalex.org/W4293027896","https://openalex.org/W4327971417","https://openalex.org/W6676058556","https://openalex.org/W6682852635","https://openalex.org/W6684237752","https://openalex.org/W6740449017","https://openalex.org/W6761163035","https://openalex.org/W6781767973"],"related_works":["https://openalex.org/W2811413325","https://openalex.org/W2170286667","https://openalex.org/W2791328260","https://openalex.org/W1982719520","https://openalex.org/W1509031531","https://openalex.org/W2006709159","https://openalex.org/W4214682109","https://openalex.org/W3092185379","https://openalex.org/W2163159773","https://openalex.org/W4244977292"],"abstract_inverted_index":{"The":[0,102],"Transportation":[1],"Problem":[2],"(TP)":[3],"is":[4,15],"a":[5,22,25,30,58],"special":[6],"type":[7],"of":[8,20,27,32,72,104,124,236],"linear":[9],"programming":[10],"problem,":[11],"where":[12],"the":[13,18,38,54,63,73,81,87,100,105,122,125,145,160,166,173,180,190,227],"objective":[14],"to":[16,29,98,120,138,242],"minimize":[17],"cost":[19],"distributing":[21],"product":[23],"from":[24],"number":[26,31],"sources":[28],"destinations.":[33],"Many":[34],"methods":[35,47,153],"for":[36,204],"solving":[37],"TP":[39],"have":[40,135],"been":[41,136],"studied":[42],"over":[43],"time.":[44],"However,":[45],"exact":[46,152,245],"do":[48],"not":[49,188],"always":[50],"succeed":[51],"in":[52,234],"finding":[53],"optimal":[55,64],"solution":[56,59],"or":[57,246],"that":[60,200,226],"effectively":[61],"approximates":[62],"one.":[65],"This":[66],"paper":[67],"introduces":[68],"two":[69,130],"new":[70],"variations":[71,107,148,192,199,229],"well-established":[74],"Particle":[75,213],"Swarm":[76,214],"Optimization":[77,215],"(PSO)":[78],"algorithm":[79],"named":[80],"Trigonometric":[82],"Acceleration":[83,91,220],"Coefficients-PSO":[84],"(TrigAc-PSO)":[85],"and":[86,95,110,140,175,179,207,217,239],"Four":[88],"Sectors":[89],"Varying":[90,219],"Coefficients":[92,221],"PSO":[93,127,147,198],"(FSVAC-PSO)":[94],"applies":[96],"them":[97],"solve":[99],"TP.":[101],"performances":[103],"proposed":[106,126,146,191,228],"are":[108,201],"examined":[109],"validated":[111],"by":[112],"carrying":[113],"out":[114],"extensive":[115],"experimental":[116],"tests.":[117],"In":[118],"order":[119],"demonstrate":[121,141],"efficiency":[123,238],"variations,":[128],"thirty":[129],"problems":[131],"with":[132,151,196],"different":[133],"sizes":[134],"solved":[137],"evaluate":[139],"their":[142,205,237],"performance.":[143],"Moreover,":[144],"were":[149,193],"compared":[150,195,241],"such":[154,209],"as":[155,210],"Vogel\u2019s":[156],"Approximation":[157],"Method":[158,163,177],"(VAM),":[159],"Total":[161,167,171],"Differences":[162],"1":[164],"(TDM1),":[165],"Opportunity":[168],"Cost":[169],"Matrix-Minimal":[170],"(TOCM-MT),":[172],"Juman":[174],"Hoque":[176],"(JHM)":[178],"Bilqis":[181],"Chastine":[182],"Erma":[183],"method":[184],"(BCE).":[185],"Last":[186],"but":[187],"least,":[189],"also":[194],"other":[197],"well":[202],"known":[203],"completeness":[206],"efficiency,":[208],"Decreasing":[211],"Weight":[212],"(DWPSO)":[216],"Time":[218],"(TVAC).":[222],"Experimental":[223],"results":[224,233],"show":[225],"achieve":[230],"very":[231],"satisfactory":[232],"terms":[235],"effectiveness":[240],"existing":[243],"either":[244],"heuristic":[247],"methods.":[248]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":11}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}