{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T17:05:54Z","timestamp":1765040754406,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,9,12]],"date-time":"2017-09-12T00:00:00Z","timestamp":1505174400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 61402070","No.61672122","No.61602077"],"award-info":[{"award-number":["No. 61402070","No.61672122","No.61602077"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Liaoning Province of China","award":["No. 2015020023"],"award-info":[{"award-number":["No. 2015020023"]}]},{"name":"Educational Commission of Liaoning Province of China","award":["No. L2015060"],"award-info":[{"award-number":["No. L2015060"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["No. 3132016348"],"award-info":[{"award-number":["No. 3132016348"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The dynamic vehicle routing problem (DVRP) is a variant of the Vehicle Routing Problem (VRP) in which customers appear dynamically. The objective is to determine a set of routes that minimizes the total travel distance. In this paper, we propose a monarch butterfly optimization (MBO) algorithm to solve DVRPs, utilizing a greedy strategy. Both migration operation and the butterfly adjusting operator only accept the offspring of butterfly individuals that have better fitness than their parents. To improve performance, a later perturbation procedure is implemented, to maintain a balance between global diversification and local intensification. The computational results indicate that the proposed technique outperforms the existing approaches in the literature for average performance by at least 9.38%. In addition, 12 new best solutions were found. This shows that this proposed technique consistently produces high-quality solutions and outperforms other published heuristics for the DVRP.<\/jats:p>","DOI":"10.3390\/a10030107","type":"journal-article","created":{"date-parts":[[2017,9,12]],"date-time":"2017-09-12T10:40:04Z","timestamp":1505212804000},"page":"107","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":44,"title":["A Monarch Butterfly Optimization for the Dynamic Vehicle Routing Problem"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3858-0309","authenticated-orcid":false,"given":"Shifeng","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Information Science and Technology, Dalian Maritime University, Dalian 116026, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5848-6398","authenticated-orcid":false,"given":"Rong","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Information Science and Technology, Dalian Maritime University, Dalian 116026, China"}]},{"given":"Jian","family":"Gao","sequence":"additional","affiliation":[{"name":"Department of Information Science and Technology, Dalian Maritime University, Dalian 116026, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,9,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"161","DOI":"10.3844\/jmssp.2008.161.167","article-title":"Solving the vehicle routing problem with stochastic demands via hybrid genetic algorithm-tabu search","volume":"4","author":"Ismail","year":"2008","journal-title":"J. Math. Stat."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Oliveira, S., de Souza, S.R., and Silva, M.A.L. (2008, January 26\u201330). A solution of dynamic vehicle routing problem with time window via ant colony system metaheuristic. Proceedings of the 10th Brazilian Symposium on Neural Networks, (SBRN \u201808), Salvador, Brazil.","DOI":"10.1109\/SBRN.2008.20"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1016\/j.ejor.2008.08.003","article-title":"Scatter search for a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries in brazil","volume":"199","author":"Belfiore","year":"2009","journal-title":"Eur. J. Oper. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1287\/trsc.1050.0133","article-title":"Dynamic column generation for dynamic vehicle routing with time windows","volume":"40","author":"Chen","year":"2006","journal-title":"Transp. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Rojas, I., Joya, G., and Cabestany, J. (2013). Restricted Dynamic Heterogeneous Fleet Vehicle Routing Problem with Time Windows. Advances in Computational Intelligence, Part II, Proceedings of the 12th International Work-Conference on Artificial Neural Networks (IWANN 2013), Puerto de la Cruz, Tenerife, Spain, 12\u201314 June 2013, Springer.","DOI":"10.1007\/978-3-642-38679-4"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wang, G.G., Zhao, X., and Deb, S. (2015, January 23\u201324). A novel monarch butterfly optimization with greedy strategy and self-adaptive. Proceedings of the 2015 Second International Conference on Soft Computing and Machine Intelligence (ISCMI), Hong Kong, China.","DOI":"10.1109\/ISCMI.2015.19"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ghetas, M., Yong, C.H., and Sumari, P. (2015, January 27\u201329). Harmony-based monarch butterfly optimization algorithm. Proceedings of the 2015 IEEE International Conference on Control System, Computing and Engineering (ICCSCE), George Town, Malaysia.","DOI":"10.1109\/ICCSCE.2015.7482176"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Feng, Y., Yang, J., Wu, C., Lu, M., and Zhao, X.J. (2016). Solving 0\u20131 knapsack problems by chaotic monarch butterfly optimization algorithm with gaussian mutation. Memet. Comput., 1\u201316.","DOI":"10.1007\/s12293-016-0211-4"},{"key":"#cr-split#-ref_9.1","unstructured":"Tan, Y., Shi, Y., and Niu, B. (2016). A discrete monarch butterfly optimization for chinese TSP problem. Advances in Swarm Intelligence, Part I"},{"key":"#cr-split#-ref_9.2","unstructured":"Proceedings of the 7th International Conference (ICSI 2016), Bali, Indonesia, 25-30 June 2016, Springer."},{"key":"ref_10","unstructured":"Wang, G.-G., Deb, S., and Cui, Z. (2015). Monarch butterfly optimization. Neural Comput. Appl., 1\u201320. Available online: https:\/\/link.springer.com\/article\/10.1007\/s00521-015-1923-y."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1109\/3477.484436","article-title":"Ant system: Optimization by a colony of cooperating agents","volume":"26","author":"Dorigo","year":"1996","journal-title":"IEEE Trans. Syst. Man Cybern. Part B Cybern."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1109\/TEVC.2008.919004","article-title":"Biogeography-based optimization","volume":"12","author":"Simon","year":"2008","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","article-title":"Differential evolution\u2014A simple and efficient heuristic for global optimization over continuous spaces","volume":"11","author":"Storn","year":"1997","journal-title":"J. Glob. Optim."},{"key":"ref_14","unstructured":"Kilby, P., Prosser, P., and Shaw, P. (1998). Dynamic VRPS: A Study of Scenarios, University of Strathclyde. Technical Report APES-06-1998."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s10878-005-4922-6","article-title":"Ant colony system for a dynamic vehicle routing problem","volume":"10","author":"Montemanni","year":"2005","journal-title":"J. Comb. Optim."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1426","DOI":"10.1016\/j.asoc.2011.10.023","article-title":"A comparative study between dynamic adapted PSO and VNS for the vehicle routing problem with dynamic requests","volume":"12","author":"Khouadjia","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Lu, Z., Kim, D., Wu, W., Li, W., and Du, D.-Z. (2015). A hybrid large neighborhood search for dynamic vehicle routing problem with time deadline. Combinatorial Optimization and Applications, Proceedings of the 9th International Conference (COCOA 2015), Houston, TX, USA, 18\u201320 December 2015, Springer.","DOI":"10.1007\/978-3-319-26626-8"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ejor.2012.08.015","article-title":"A review of dynamic vehicle routing problems","volume":"225","author":"Pillac","year":"2013","journal-title":"Eur. J. Oper. Res."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Toth, P., and Vigo, D. (2014). Dynamic vehicle routing problems. Vehicle Routing: Problems, Methods, and Applications, Society for Industrial and Applied Mathematics. [2nd ed.].","DOI":"10.1137\/1.9781611973594"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1002\/net.21628","article-title":"Dynamic vehicle routing problems: Three decades and counting","volume":"67","author":"Psaraftis","year":"2016","journal-title":"Networks"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Elhassania, M., Jaouad, B., and Ahmed, E.A. (2014, January 5\u20137). Solving the dynamic vehicle routing problem using genetic algorithms. Proceedings of the 2nd IEEE International Conference on Logistics Operations Management, Rabat, Morocco.","DOI":"10.1109\/GOL.2014.6887419"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.swevo.2014.12.003","article-title":"The dynamic vehicle routing problem: Solution with hybrid metaheuristic approach","volume":"21","author":"Euchi","year":"2015","journal-title":"Swarm Evol. Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1016\/j.asoc.2016.06.032","article-title":"A memetic approach to vehicle routing problem with dynamic requests","volume":"48","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1287\/trsc.33.4.381","article-title":"Parallel tabu search for real-time vehicle routing and dispatching","volume":"33","author":"Gendreau","year":"1999","journal-title":"Transp. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1287\/opre.1040.0124","article-title":"Scenario-based planning for partially dynamic vehicle routing with stochastic customers","volume":"52","author":"Bent","year":"2004","journal-title":"Oper. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1002\/net.3230230804","article-title":"Parallel iterative search methods for vehicle routing problems","volume":"23","author":"Taillard","year":"1993","journal-title":"Networks"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1002\/net.3230140205","article-title":"The period routing problem","volume":"14","author":"Christofides","year":"1984","journal-title":"Networks"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0927-0507(05)80105-7","article-title":"Vehicle routing","volume":"Volume 8","author":"Ball","year":"1995","journal-title":"Handbooks in Operations Research and Management Science"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/s10489-006-0033-z","article-title":"Dynamic vehicle routing using genetic algorithms","volume":"27","author":"Hanshar","year":"2007","journal-title":"Appl. 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