{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T13:26:55Z","timestamp":1775222815647,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,3]],"date-time":"2024-10-03T00:00:00Z","timestamp":1727913600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Fundamental Research Funds for the Central Universities","award":["222201917006"],"award-info":[{"award-number":["222201917006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study presents a bi-objective optimization model for the Green Vehicle-Routing Problem in cold chain logistics, with a focus on symmetric distance matrices, aiming to minimize total costs, including carbon emissions, while maximizing customer satisfaction. To address this complex challenge, we developed a Stage-Specific Multi-Objective Five-Element Cycle Optimization algorithm (MOFECO-SS), which dynamically adjusts optimization strategies across different stages of the process, thereby enhancing overall efficiency. Extensive comparative analyses with existing algorithms demonstrate that MOFECO-SS consistently outperforms in solving the multi-objective optimization model, particularly in reducing total costs and carbon emissions while maintaining high levels of customer satisfaction. The symmetric nature of the distance matrix further aids in achieving balanced and optimized route planning. The results highlight that MOFECO-SS offers decision-makers flexible route planning options that balance cost efficiency with environmental sustainability, ultimately improving the effectiveness of cold chain logistics operations.<\/jats:p>","DOI":"10.3390\/sym16101305","type":"journal-article","created":{"date-parts":[[2024,10,3]],"date-time":"2024-10-03T06:45:52Z","timestamp":1727937952000},"page":"1305","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Stage-Specific Multi-Objective Five-Element Cycle Optimization Algorithm in Green Vehicle-Routing Problem with Symmetric Distance Matrix: Balancing Carbon Emissions and Customer Satisfaction"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5279-9307","authenticated-orcid":false,"given":"Yue","family":"Xiang","sequence":"first","affiliation":[{"name":"Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingjing","family":"Guo","sequence":"additional","affiliation":[{"name":"Department of Aerospace Science and Technology, Space Engineering University, Beijing 101416, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3280-7322","authenticated-orcid":false,"given":"Zhengyan","family":"Mao","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of Computer Software Testing & Evaluating, Shanghai Development Center of Computer Software Technology, Shanghai 201112, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8106-4740","authenticated-orcid":false,"given":"Chao","family":"Jiang","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Beijing Key Laboratory of Computational Intelligence and Intelligent System, Engineering Research Center of Digital Community, Ministry of Education, Beijing Artificial Intelligence Institute and Beijing Laboratory for Intelligent Environmental Protection, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5928-4656","authenticated-orcid":false,"given":"Mandan","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1359","DOI":"10.1016\/j.aej.2016.03.024","article-title":"Sustaining the shelf life of fresh food in cold chain\u2014A burden on the environment","volume":"55","author":"Adekomaya","year":"2016","journal-title":"Alex. Eng. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1016\/j.tifs.2021.01.066","article-title":"A comprehensive review of cold chain logistics for fresh agricultural products: Current status, challenges, and future trends","volume":"109","author":"Han","year":"2021","journal-title":"Trends Food Sci. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"107484","DOI":"10.1016\/j.cie.2021.107484","article-title":"Supply chain network design considering customer psychological behavior-a 4PL perspective","volume":"159","author":"Huang","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/S1665-6423(14)72340-5","article-title":"An optimization model for the vehicle routing problem in multi-product frozen food delivery","volume":"12","author":"Zhang","year":"2014","journal-title":"J. Appl. Res. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/j.jfoodeng.2007.07.008","article-title":"A vehicle routing algorithm for the distribution of fresh vegetables and similar perishable food","volume":"85","author":"Osvald","year":"2008","journal-title":"J. Food Eng."},{"key":"ref_6","first-page":"146","article-title":"Optimization and efficiency of multi-temperature joint distribution of cold chain products: Comparative study based on cold accumulation mode and mechanical refrigeration mode","volume":"33","author":"Wang","year":"2016","journal-title":"J. Highw. Transp. Res. Dev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"125637","DOI":"10.1016\/j.physa.2020.125637","article-title":"How to achieve a win\u2013win scenario between cost and customer satisfaction for cold chain logistics?","volume":"566","author":"Wang","year":"2021","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/j.measurement.2016.04.043","article-title":"Measurement, evaluation and minimization of CO2, NOx, and CO emissions in the open time dependent vehicle routing problem","volume":"90","author":"Naderipour","year":"2016","journal-title":"Measurement"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"104715","DOI":"10.1016\/j.resconrec.2020.104715","article-title":"Vehicle routing problem in cold Chain logistics: A joint distribution model with carbon trading mechanisms","volume":"156","author":"Liu","year":"2020","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wang, S., Tao, F., Shi, Y., and Wen, H. (2017). Optimization of vehicle routing problem with time windows for cold chain logistics based on carbon tax. Sustainability, 9.","DOI":"10.3390\/su9050694"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1108\/IMDS-06-2020-0345","article-title":"Low-carbon VRP for cold chain logistics considering real-time traffic conditions in the road network","volume":"122","author":"Bai","year":"2022","journal-title":"Ind. Manag. Data Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.jclepro.2019.05.306","article-title":"Low-carbon cold chain logistics using ribonucleic acid-ant colony optimization algorithm","volume":"233","author":"Zhang","year":"2019","journal-title":"J. Clean. Prod."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Yao, Q., Zhu, S., and Li, Y. (2022). Green vehicle-routing problem of fresh agricultural products considering carbon emission. Int. J. Environ. Res. Public Health, 19.","DOI":"10.3390\/ijerph19148675"},{"key":"ref_14","first-page":"183","article-title":"Optimization on cold chain distribution routes considering carbon emissions based on improved ant colony algorithm","volume":"36","author":"Bao","year":"2024","journal-title":"J. Syst. Simul."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1093\/ijlct\/ctad021","article-title":"Research on cold chain logistics optimization model considering low-carbon emissions","volume":"18","author":"Tao","year":"2023","journal-title":"Int. J.-Low-Carbon Technol."},{"key":"ref_16","unstructured":"Chen, J.K.C., Yu, Y.W., and Batnasan, J. (2014, January 27\u201331). Services innovation impact to customer satisfaction and customer value enhancement in airport. Proceedings of the Portland International Conference on Management of Engineering & Technology, Kanazawa, Japan."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/j.aej.2022.12.067","article-title":"A multi-objective model for cold chain logistics considering customer satisfaction","volume":"67","author":"Li","year":"2023","journal-title":"Alex. Eng. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"879614","DOI":"10.1155\/2012\/879614","article-title":"Multiobjective quantum evolutionary algorithm for the vehicle routing problem with customer satisfaction","volume":"2012","author":"Zhang","year":"2012","journal-title":"Math. Probl. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"7139","DOI":"10.1007\/s00500-023-09599-3","article-title":"Mean\u2013standard-deviation-based electric vehicle routing problem with time windows using Lagrangian relaxation and extended alternating direction method of multipliers-based decomposition algorithm","volume":"28","author":"Xia","year":"2024","journal-title":"Soft Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"18041","DOI":"10.1007\/s00500-023-09013-y","article-title":"Optimization of multipath cold-chain logistics network","volume":"27","author":"Zhang","year":"2023","journal-title":"Soft Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13677-020-0157-4","article-title":"An efficient parallel genetic algorithm solution for vehicle routing problem in cloud implementation of the intelligent transportation systems","volume":"9","author":"Abbasi","year":"2020","journal-title":"J. Cloud Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.ins.2019.03.070","article-title":"A hybrid ant colony optimization algorithm for a multi-objective vehicle routing problem with flexible time windows","volume":"490","author":"Zhang","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Shen, L., Tao, F., and Wang, S. (2018). Multi-depot open vehicle routing problem with time windows based on carbon trading. Int. J. Environ. Res. Public Health, 15.","DOI":"10.3390\/ijerph15092025"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zhang, L., Fu, M., Fei, T., Lim, M.K., and Tseng, M.L. (2024). A cold chain logistics distribution optimization model: Beijing-Tianjin-Hebei region low-carbon site selection. Ind. Manag. Data Syst.","DOI":"10.1108\/IMDS-08-2023-0558"},{"key":"ref_25","unstructured":"Cao, C., Zhang, X., and Guo, Z. (2020, January 21\u201322). Vehicle routing problem with time windows arising in urban delivery. Proceedings of the 4th International Conference on Electrical, Automation and Mechanical Engineering, Beijing, China."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Qin, G., Tao, F., and Li, L. (2019). A vehicle routing optimization problem for cold chain logistics considering customer satisfaction and carbon emissions. Int. J. Environ. Res. Public Health, 16.","DOI":"10.3390\/ijerph16040576"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Liu, M. (2017, January 10\u201312). Five-elements cycle optimization algorithm for the travelling salesman problem. Proceedings of the 2017 18th International Conference on Advanced Robotics (ICAR), IEEE, Hong Kong, China.","DOI":"10.1109\/ICAR.2017.8023672"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Ye, C., Mao, Z., and Liu, M. (2019). A Novel Multi-Objective Five-Elements Cycle Optimization Algorithm. Algorithms, 12.","DOI":"10.3390\/a12110244"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Deb, K., Agrawal, S., Pratap, A., and Meyarivan, T. (2000, January 18\u201320). A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. Proceedings of the Parallel Problem Solving from Nature PPSN VI: 6th International Conference, Paris, France. Proceedings 6.","DOI":"10.1007\/3-540-45356-3_83"},{"key":"ref_30","unstructured":"Xiaoning, W. (2014). Vehicles\u2019 Distribution Route Research of Fresh Agricultural Products of Cold Chain Logistics under the Agricultural Super-Docking Mode. [Master\u2019s Thesis, East China Jiaotong University]."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Xiang, Y., Guo, J., Jiang, C., Ma, H., and Liu, M. (2024). Multi-Objective Five-Element Cycle Optimization Algorithm Based on Multi-Strategy Fusion for the Bi-Objective Traveling Thief Problem. Appl. Sci., 14.","DOI":"10.3390\/app14177468"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1002\/(SICI)1099-1360(199801)7:1<34::AID-MCDA161>3.0.CO;2-6","article-title":"Pareto simulated annealing\u2013A metaheuristic technique for multiple-objective combinatorial optimization","volume":"7","author":"Jaszkiewicz","year":"1998","journal-title":"J.-Multi-Criteria Decis. Anal."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1109\/TEVC.2003.810758","article-title":"Performance assessment of multiobjective optimizers: An analysis and review","volume":"7","author":"Zitzler","year":"2003","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_34","unstructured":"Van Veldhuizen, D.A., and Lamont, G.B. (1998, January 22\u201325). Evolutionary computation and convergence to a pareto front. Proceedings of the Late Breaking Papers at the Genetic Programming 1998 Conference, Madison, WI, USA."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.advengsoft.2016.06.004","article-title":"An effective multi-objective discrete grey wolf optimizer for a real-world scheduling problem in welding production","volume":"99","author":"Lu","year":"2016","journal-title":"Adv. Eng. Softw."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Kumawat, I.R., Nanda, S.J., and Maddila, R.K. (2017, January 5\u20138). Multi-objective whale optimization. Proceedings of the Tencon 2017\u20132017 IEEE Region 10 Conference, IEEE, Penang, Malaysia.","DOI":"10.1109\/TENCON.2017.8228329"},{"key":"ref_37","first-page":"2B","article-title":"A novel feature selection algorithm using multi-objective improved honey badger algorithm and strength pareto evolutionary algorithm-II","volume":"11","author":"Papasani","year":"2022","journal-title":"J. Eng. Res."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Ali, M.H., Salawudeen, A.T., Kamel, S., Salau, H.B., Habil, M., and Shouran, M. (2022). Single-and multi-objective modified aquila optimizer for optimal multiple renewable energy resources in distribution network. Mathematics, 10.","DOI":"10.3390\/math10122129"},{"key":"ref_39","unstructured":"Zeleny, M. (1982). Multiple Criteria Decision Making, McGraw-Hill Company."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/10\/1305\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:09:50Z","timestamp":1760112590000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/10\/1305"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,3]]},"references-count":39,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["sym16101305"],"URL":"https:\/\/doi.org\/10.3390\/sym16101305","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,3]]}}}