{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T20:37:07Z","timestamp":1773002227476,"version":"3.50.1"},"reference-count":65,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,8,24]],"date-time":"2025-08-24T00:00:00Z","timestamp":1755993600000},"content-version":"vor","delay-in-days":235,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Intelligent Systems"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>The rapid growth of e\u2010commerce has amplified the need for efficient logistics and delivery route planning. The Traveling Salesman Problem (TSP) provides a mathematical framework to address this challenge by finding optimal delivery routes. In this study, we propose a novel algorithm, DPSO\u2010Q, which synergizes the adaptability of reinforcement learning from Ant\u2010Q with the computational efficiency of Discrete Particle Swarm Optimization (DPSO). By leveraging swarm intelligence and adaptive learning mechanisms, DPSO\u2010Q achieves a balance between computational efficiency and high\u2010quality solutions. Experimental evaluations demonstrate its potential for large\u2010scale logistics optimization, making it a promising tool for addressing the complexities of modern supply chain systems. DPSO\u2010Q reduces tour lengths by up to 7.5% compared to DPSO and achieves execution times over 90% faster than ACO and Ant\u2010Q on standard datasets such as ch130 and zi929.<\/jats:p>","DOI":"10.1155\/int\/8918171","type":"journal-article","created":{"date-parts":[[2025,8,25]],"date-time":"2025-08-25T05:49:27Z","timestamp":1756100967000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["DPSO\u2010Q: A Reinforcement Learning\u2013Enhanced Swarm Algorithm for Solving the Traveling Salesman Problem"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6497-5390","authenticated-orcid":false,"given":"Sivayazi","family":"Kappagantula","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0008-0382-2209","authenticated-orcid":false,"given":"Rohit","family":"Sangubotla","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0000-6202-7186","authenticated-orcid":false,"given":"Vippagunta Vidhu Sri","family":"Varenya","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0009-3249-714X","authenticated-orcid":false,"given":"Srishti","family":"Gupta","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5296-1936","authenticated-orcid":false,"given":"Satya Veerendra","family":"Arigela","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1837-9835","authenticated-orcid":false,"given":"Ramya S.","family":"Moorthy","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4861-3311","authenticated-orcid":false,"given":"Jeane Marina","family":"D\u2019souza","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2842-2112","authenticated-orcid":false,"given":"Praveen Kumar","family":"Bonthagorla","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2025,8,24]]},"reference":[{"key":"e_1_2_9_1_2","volume-title":"The Traveling Salesman Problem: A Computational Study, Ser. Princeton Series in Applied Mathematics","author":"Applegate D.","year":"2011"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.25.5.741"},{"key":"e_1_2_9_3_2","unstructured":"RevenantP. CambazardH. andCatusseN. A Note About a Transition of Ratliff and Rosenthal\u2019s Order Picking Algorithm for Rectangular Warehouses 2024 https:\/\/arxiv.org\/abs\/2405.15464."},{"key":"e_1_2_9_4_2","first-page":"310","article-title":"Solution D\u2019Une Question Curieuse Que Ne Paroit Soumise \u00c0 Aucune Analyse","author":"Euler L.","year":"1766","journal-title":"M\u00e9moires de l\u2019acad\u00e9mie des sciences de Berlin"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2007.06.006"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0893-6080(02)00017-5"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0893-6080(97)00023-3"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.10.059"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0305-0548(98)00069-0"},{"key":"e_1_2_9_10_2","unstructured":"KuehnerI. Swarm Intelligence for Solving a Traveling Salesman Problem 2020."},{"key":"e_1_2_9_11_2","volume-title":"Stochastic Local Search: Foundations & Applications","author":"Hoos H.","year":"2004"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1145\/937503.937505"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00202901"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/icnnb.2005.1614565"},{"key":"e_1_2_9_15_2","doi-asserted-by":"crossref","unstructured":"SajiY. RiffiM. E. andAhiodB. Discrete bat-inspired Algorithm for Travelling Salesman Problem 2014 Second World Conference on Complex Systems (WCCS) 2014 28\u201331 https:\/\/doi.org\/10.1109\/icocs.2014.7060983 2-s2.0-84988306331.","DOI":"10.1109\/ICoCS.2014.7060983"},{"key":"e_1_2_9_16_2","doi-asserted-by":"crossref","unstructured":"AmaraJ. HamdaniT. M. andAlimiA. M. A New Hybrid Discrete Bat Algorithm for Traveling Salesman Problem Using Ordered Crossover and 3-opt Operators for Bat\u2019s Local Search 2015 15th International Conference on Intelligent Systems Design and Applications (ISDA) 2015 154\u2013159 https:\/\/doi.org\/10.1109\/isda.2015.7489217 2-s2.0-84978416151.","DOI":"10.1109\/ISDA.2015.7489217"},{"key":"e_1_2_9_17_2","doi-asserted-by":"crossref","unstructured":"ZhaoH. Improved Bat Algorithm for Solving Traveling Salesman Problems 2023 IEEE 3rd International Conference on Electronic Communications Internet of Things and Big Data (ICEIB) 2023 257\u2013261 https:\/\/doi.org\/10.1109\/iceib57887.2023.10170026.","DOI":"10.1109\/ICEIB57887.2023.10170026"},{"key":"e_1_2_9_18_2","doi-asserted-by":"crossref","unstructured":"WongL.-P. LowM. Y. H. andChongC. S. A Bee Colony Optimization Algorithm for Traveling Salesman Problem 2008 Second Asia International Conference on Modelling and Simulation (AMS) 2008 818\u2013823 https:\/\/doi.org\/10.1109\/ams.2008.27 2-s2.0-50249161577.","DOI":"10.1109\/AMS.2008.27"},{"key":"e_1_2_9_19_2","doi-asserted-by":"crossref","unstructured":"LiX.andZhengY. Artificial Bee Colony Algorithm and Its Application in Traveling Salesman Problems 2019 Chinese Control and Decision Conference (CCDC) 2019 1\u20135 https:\/\/doi.org\/10.1109\/ccdc.2019.8832491 2-s2.0-85073112601.","DOI":"10.1109\/CCDC.2019.8832491"},{"key":"e_1_2_9_20_2","doi-asserted-by":"crossref","unstructured":"KarabogaD.andGorkemliB. A Combinatorial Artificial Bee Colony Algorithm for Traveling Salesman Problem 2011 International Symposium on Innovations in Intelligent Systems and Applications 2011 50\u201353 https:\/\/doi.org\/10.1109\/inista.2011.5946125 2-s2.0-79961180341.","DOI":"10.1109\/INISTA.2011.5946125"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2018.08.004"},{"key":"e_1_2_9_22_2","doi-asserted-by":"crossref","unstructured":"ZhangJ. ZhangZ. andLinX. An Improved Artificial Bee Colony with self-adaptive Strategies and Application 2021 International Conference on Computer Network Electronic and Automation (ICCNEA) 2021 101\u2013104 https:\/\/doi.org\/10.1109\/iccnea53019.2021.00032.","DOI":"10.1109\/ICCNEA53019.2021.00032"},{"key":"e_1_2_9_23_2","doi-asserted-by":"crossref","unstructured":"AkayR.andBasturkA. Parallel Artificial Bee Colony Algorithm for Traveling Salesman Problem 2014 22nd Signal Processing and Communications Applications Conference (SIU) 2014 501\u2013505 https:\/\/doi.org\/10.1109\/siu.2014.6830275 2-s2.0-84903784640.","DOI":"10.1109\/SIU.2014.6830275"},{"key":"e_1_2_9_24_2","unstructured":"RekabyA. YoussifA. andSharaf EldinA. Introducing Adaptive Artificial Bee Colony Algorithm and Using it in Solving Traveling Salesman Problem 2013 Science and Information Conference 2013 502\u2013506."},{"key":"e_1_2_9_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.iswa.2023.200242"},{"key":"e_1_2_9_26_2","doi-asserted-by":"publisher","DOI":"10.1109\/indin.2008.4618252"},{"key":"e_1_2_9_27_2","first-page":"53","article-title":"Ant Colony System: a Cooperative Learning Approach to the Traveling Salesman Problem","volume":"1","author":"Dorigo M.","year":"1997","journal-title":"IEEE Transactions on"},{"key":"e_1_2_9_28_2","doi-asserted-by":"publisher","DOI":"10.1109\/3477.484436"},{"key":"e_1_2_9_29_2","doi-asserted-by":"crossref","unstructured":"YangJ. ShiX. MarcheseM. andLiangY. Ant Colony Optimization Method for Generalized Tsp Problem Progress in Natural Science: PROG NAT SCI 18 no. 11.","DOI":"10.1016\/j.pnsc.2008.03.028"},{"key":"e_1_2_9_30_2","doi-asserted-by":"publisher","DOI":"10.1109\/ccdc.2019.8833167"},{"key":"e_1_2_9_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2005.05.020"},{"key":"e_1_2_9_32_2","first-page":"25","article-title":"A New Rank Based Version of the Ant System: A Computational Study","volume":"7","author":"Bullnheimer B.","year":"1999","journal-title":"Central European Journal of Operations Research"},{"key":"e_1_2_9_33_2","unstructured":"IntellektikF. InformatikF. DarmstadtT. St\u00fctzleT. andHoosH. Improvements on ant-system: Introducing max-min Ant System 1998."},{"key":"e_1_2_9_34_2","doi-asserted-by":"publisher","DOI":"10.1109\/icaci.2012.6463177"},{"key":"e_1_2_9_35_2","doi-asserted-by":"publisher","DOI":"10.1109\/itc-cscc58803.2023.10212945"},{"key":"e_1_2_9_36_2","unstructured":"IntellektikF. InformatikF. DarmstadtT.et al. Parallelization Strategies for Ant Colony Optimization 1970."},{"key":"e_1_2_9_37_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2003.10.013"},{"key":"e_1_2_9_38_2","doi-asserted-by":"publisher","DOI":"10.1109\/CGIV.2009.20"},{"key":"e_1_2_9_39_2","doi-asserted-by":"publisher","DOI":"10.1109\/icnc.2012.22"},{"key":"e_1_2_9_40_2","doi-asserted-by":"crossref","unstructured":"QianH.andSuT. Hybrid Algorithm Based on Max and Min Ant System and Particle Swarm Optimization for Solving Tsp Problem 2018 33rd Youth Academic Annual Conference of Chinese Association of Automation (YAC) 2018 683\u2013687 https:\/\/doi.org\/10.1109\/yac.2018.8406459 2-s2.0-85050589510.","DOI":"10.1109\/YAC.2018.8406459"},{"key":"e_1_2_9_41_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2014.09.031"},{"key":"e_1_2_9_42_2","doi-asserted-by":"crossref","unstructured":"GoldbargE. GoldbargM. andSouzaG. Particle Swarm Optimization Algorithm for the Traveling Salesman Problem 2008.","DOI":"10.5772\/5580"},{"key":"e_1_2_9_43_2","unstructured":"WangK. HuangL. ZhouC. andPangW. Particle Swarm Optimization for Traveling Salesman Problem 3 2003 International Conference on Machine Learning and Cybernetics November 2003 IEEE Press 1583\u20131585."},{"key":"e_1_2_9_44_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-18041-5_12"},{"key":"e_1_2_9_45_2","unstructured":"ShiY.andEberhartR. Empirical Study of Particle Swarm Optimization 1999."},{"key":"e_1_2_9_46_2","doi-asserted-by":"publisher","DOI":"10.1007\/bfb0040812"},{"key":"e_1_2_9_47_2","doi-asserted-by":"publisher","DOI":"10.1142\/9789812701534_0083"},{"key":"e_1_2_9_48_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-39930-8_8"},{"key":"e_1_2_9_49_2","doi-asserted-by":"publisher","DOI":"10.4028\/www.scientific.net\/amm.513-517.1773"},{"key":"e_1_2_9_50_2","doi-asserted-by":"publisher","DOI":"10.1109\/icnc.2009.601"},{"key":"e_1_2_9_51_2","volume-title":"Particle Swarm Optimization Based on Neighborhood Encoding for Traveling Salesman Problem","author":"Lin D.","year":"2008"},{"key":"e_1_2_9_52_2","doi-asserted-by":"publisher","DOI":"10.1109\/cccm.2009.5267468"},{"key":"e_1_2_9_53_2","doi-asserted-by":"crossref","unstructured":"Shakouri GH. ShojaeeK. andZahediH. An Effective Particle Swarm Optimization Algorithm Embedded in Sa to Solve the Traveling Salesman Problem 2009 Chinese Control and Decision Conference 2009 5545\u20135550 https:\/\/doi.org\/10.1109\/ccdc.2009.5195184 2-s2.0-70449380176.","DOI":"10.1109\/CCDC.2009.5195184"},{"key":"e_1_2_9_54_2","doi-asserted-by":"publisher","DOI":"10.1109\/cis.2009.117"},{"key":"e_1_2_9_55_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00992698"},{"key":"e_1_2_9_56_2","doi-asserted-by":"publisher","DOI":"10.1109\/EEBDA56825.2023.10090654"},{"key":"e_1_2_9_57_2","doi-asserted-by":"publisher","DOI":"10.1016\/b978-1-55860-377-6.50039-6"},{"key":"e_1_2_9_58_2","article-title":"A Study of Some Properties of ant-q","volume":"10","author":"Dorigo M.","year":"2000","journal-title":"Lecture Notes in Computer Science"},{"key":"e_1_2_9_59_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICASERT.2019.8934450"},{"key":"e_1_2_9_60_2","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316887"},{"key":"e_1_2_9_61_2","doi-asserted-by":"publisher","DOI":"10.5120\/20674-3466"},{"key":"e_1_2_9_62_2","doi-asserted-by":"publisher","DOI":"10.20533\/ijicr.2042.4655.2015.0080"},{"key":"e_1_2_9_63_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-97-2272-3_20"},{"key":"e_1_2_9_64_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-76357-6_17"},{"key":"e_1_2_9_65_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-27000-5_19"}],"container-title":["International Journal of Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/int\/8918171","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/int\/8918171","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/int\/8918171","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T18:12:53Z","timestamp":1772993573000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/int\/8918171"}},"subtitle":[],"editor":[{"given":"Vasudevan","family":"Rajamohan","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":65,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/int\/8918171"],"URL":"https:\/\/doi.org\/10.1155\/int\/8918171","archive":["Portico"],"relation":{},"ISSN":["0884-8173","1098-111X"],"issn-type":[{"value":"0884-8173","type":"print"},{"value":"1098-111X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"2024-12-07","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-07-16","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-08-24","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"8918171"}}