{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T20:33:25Z","timestamp":1777322005887,"version":"3.51.4"},"reference-count":29,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,13]],"date-time":"2021-09-13T00:00:00Z","timestamp":1631491200000},"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":["61104166"],"award-info":[{"award-number":["61104166"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In order to solve the problem of traffic congestion and emission optimization of urban multi-class expressways, a robust dynamic nondominated sorting multi-objective genetic algorithm DFCM-RDNSGA-III based on density fuzzy c-means clustering method is proposed in this paper. Considering the three performance indicators of travel time, ramp queue and traffic emissions, the ramp metering and variable speed limit control schemes of an expressway are optimized to improve the main road and ramp traffic congestion, therefore achieving energy conservation and emission reduction. In the VISSIM simulation environment, a multi-on-ramp and multi-off-ramp road network is built to verify the performance of the algorithm. The results show that, compared with the existing algorithm NSGA-III, the DFCM-RDNSGA-III algorithm proposed in this paper can provide better ramp metering and variable speed limit control schemes in the process of road network peak formation and dissipation. In addition, the traffic congestion of expressways can be improved and energy conservation as well as emission reduction can also be realized.<\/jats:p>","DOI":"10.3390\/a14090266","type":"journal-article","created":{"date-parts":[[2021,9,13]],"date-time":"2021-09-13T21:37:12Z","timestamp":1631569032000},"page":"266","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Multi-Class Freeway Congestion and Emission Based on Robust Dynamic Multi-Objective Optimization"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0631-8370","authenticated-orcid":false,"given":"Juan","family":"Chen","sequence":"first","affiliation":[{"name":"SHU-UTS SILC Business School, Shanghai University, Shanghai 201899, China"},{"name":"Smart City Research Institute, Shanghai University, Shanghai 201899, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qinxuan","family":"Feng","sequence":"additional","affiliation":[{"name":"SHU-UTS SILC Business School, Shanghai University, Shanghai 201899, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qi","family":"Guo","sequence":"additional","affiliation":[{"name":"SHU-UTS SILC Business School, Shanghai University, Shanghai 201899, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,13]]},"reference":[{"key":"ref_1","first-page":"16","article-title":"Urban traffic big data research and practice","volume":"2","author":"Liang","year":"2018","journal-title":"China Stat."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1016\/j.scitotenv.2017.09.081","article-title":"Impact of reduced mass of light commercial vehicles on fuel consumption, CO2 emissions, air quality, and socio-economic costs","volume":"613\u2013614","author":"Cecchel","year":"2018","journal-title":"Sci. Total Environ."},{"key":"ref_3","unstructured":"Zhou, Y., Wang, Y., and Chen, Y. (2016). Frontier Theory and Method of Transportation System Engineering, People\u2019s Communications Press."},{"key":"ref_4","first-page":"151","article-title":"LWR model of mixed traffic flow in intelligent network environment","volume":"31","author":"Qin","year":"2018","journal-title":"Chin. J. Highw."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1930","DOI":"10.1109\/TITS.2018.2848246","article-title":"Distributed Optimization and Coordination Algorithms for Dynamic Traffic Metering in Urban Street Networks","volume":"20","author":"Mohebifard","year":"2018","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.1002\/rnc.3500","article-title":"Robust receding horizon parameterized control for multi-class freeway networks: A tractable scenario-based approach","volume":"26","author":"Liu","year":"2016","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1109\/TITS.2016.2573306","article-title":"Model Predictive Control for Freeway Networks Based on Multi-Class Traffic Flow and Emission Models","volume":"18","author":"Liu","year":"2016","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/j.trc.2017.04.007","article-title":"A multi-class model-based control scheme for reducing congestion and emissions in freeway networks by combining ramp metering and route guidance","volume":"80","author":"Pasquale","year":"2017","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_9","first-page":"68","article-title":"Collaborative optimization strategy for variable speed limit and ramp control of Expressway","volume":"17","author":"Zhou","year":"2017","journal-title":"Transp. Syst. Eng. Inf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1109\/TITS.2019.2891314","article-title":"Variable Speed Release (VSR): Speed Control to Increase Bottleneck Capacity","volume":"21","author":"Han","year":"2019","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1007\/s13369-016-2263-7","article-title":"Traffic Control Method on Efficiency of Urban Expressway Accompanied Frequent Aggressive Driving Behavior","volume":"42","author":"Yu","year":"2016","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_12","first-page":"315","article-title":"Method of vehicle road coordinated speed restriction for freeway ramp merging area","volume":"64","author":"Liping","year":"2019","journal-title":"Chin. J. Highw."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1109\/TITS.2016.2636302","article-title":"Feedback-Based Integrated Motorway Traffic Flow Control with Delay Balancing","volume":"18","author":"Iordanidou","year":"2017","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Sarasola, B., and Alba, E. (2013). Quantitative Performance Measures for Dynamic Optimization Problems, Springer.","DOI":"10.1007\/978-3-642-30665-5_2"},{"key":"ref_15","unstructured":"Min, L., and Wenhua, Z. (2012, January 14\u201317). A fast evolutionary algorithm for dynamic bi-objective optimization problems. Proceedings of the International Conference on Computer Science & Education, Melbourne, Australia."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1840048","DOI":"10.1142\/S0217984918400481","article-title":"Uncertainty quantification-based robust aerodynamic optimization of laminar flow nacelle","volume":"32","author":"Xiong","year":"2018","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3743","DOI":"10.1109\/TFUZZ.2018.2848261","article-title":"Robust Multiobjective Optimization with Robust Consensus","volume":"26","author":"Nag","year":"2018","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2758","DOI":"10.1109\/TCYB.2018.2834466","article-title":"A Clustering-Based Adaptive Evolutionary Algorithm for Multiobjective Optimization with Irregular PARETO Fronts","volume":"49","author":"Hua","year":"2018","journal-title":"IEEE Trans. Cybern."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1109\/TPAMI.2002.1017616","article-title":"An efficient k-means clustering algorithm: Analysis and implementation","volume":"24","author":"Kanungo","year":"2002","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Zhang, H., Song, S., Zhou, A., and Gao, X.-Z. (2014, January 6\u201311). A clustering based multiobjective evolutionary algorithm. Proceedings of the 2014 IEEE World Congress on Computational Intelligence, Beijing, China.","DOI":"10.1109\/CEC.2014.6900519"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1109\/TFUZZ.2017.2686804","article-title":"Fuzzy Double C-Means Clustering Based on Sparse Self-Representation","volume":"26","author":"Gu","year":"2017","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1109\/TFUZZ.2018.2883033","article-title":"Deviation-Sparse Fuzzy C-Means with Neighbor Information Constraint","volume":"27","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1109\/TEVC.2013.2281535","article-title":"An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach","volume":"18","author":"Deb","year":"2013","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1109\/TCYB.2013.2245892","article-title":"A Population Prediction Strategy for Evolutionary Dynamic Multi-objective Optimization","volume":"44","author":"Zhou","year":"2013","journal-title":"IEEE Trans. Cybern."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1109\/TEVC.2016.2587749","article-title":"Performance of Decomposition-Based Many-Objective Algorithms Strongly Depends on Pareto Front Shapes","volume":"21","author":"Ishibuchi","year":"2016","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1145\/3068335","article-title":"DBSCAN Revisited, Revisited: Why and How You Should (Still) Use DBSCAN","volume":"42","author":"Schubert","year":"2017","journal-title":"ACM Trans. Database Syst."},{"key":"ref_27","first-page":"1001","article-title":"Signal optimization of mixed traffic flow based on multi population co evolutionary algorithm","volume":"26","author":"Juan","year":"2020","journal-title":"J. Shanghai Univ. Nat. Sci. Ed."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1002\/mp.12025","article-title":"Comparison of five cluster validity indices performance in brain [18 F]FET-PET image segmentation using k -means","volume":"44","author":"Abualhaj","year":"2017","journal-title":"Med. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.knosys.2016.11.007","article-title":"Synchronization clustering based on central force optimization and its extension for large-scale datasets","volume":"118","author":"Hang","year":"2017","journal-title":"Knowl. Based Syst."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/9\/266\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:01:57Z","timestamp":1760166117000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/9\/266"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,13]]},"references-count":29,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["a14090266"],"URL":"https:\/\/doi.org\/10.3390\/a14090266","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,13]]}}}