{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T13:21:51Z","timestamp":1783516911834,"version":"3.55.0"},"reference-count":43,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T00:00:00Z","timestamp":1782345600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Against the backdrop of the advancing Transportation Power Strategy, long and large tunnels face critical challenges in ensuring the safety and efficiency of transportation scheduling due to their harsh environment, complex traffic network, and the need for coordination among multiple types of vehicles. Addressing the shortcomings of existing research\u2014such as the disconnection between path planning and dynamic environments, insufficient coordination between timetables and paths, and incomplete conflict management\u2014this paper constructs a comprehensive optimization model for the scheduling of construction vehicles in tunnel traffic networks. Firstly, integrating the improved social force model with the BPR function, an adaptive social force-BPR path planning model with a collision compensation mechanism is proposed, and the weights of sub-items are optimized using the improved AHP algorithm. Secondly, a constraint system covering paths, spatio-temporal logic, and three types of conflicts (crossing conflicts, head-on conflicts, and congestion conflicts) is established, and a bi-objective function of \u201cminimum total scheduling time\u201d and \u201cminimum number of conflicts\u201d is designed. Combined with the improved NSGA-II algorithm, the collaborative optimization of departure intervals and paths is realized. In particular, a conflict entropy repair operator is introduced to quantify the conflict chaos through node conflict entropy and vehicle conflict entropy, and the scheduling strategy is accurately adjusted based on the logic of \u201cpriority ranking-dynamic delay\u201d to balance conflict resolution and efficiency loss. Finally, a case verification is carried out relying on a tunnel topological network with 30 nodes and 41 edges. The experimental results show that the optimal repulsion coefficient kf of the social force model is 20, and the maximum departure interval of 8 min is the best configuration after introducing the repair operator. At this time, the total scheduling time is 136 min, and the total number of conflicts is only 2, completely avoiding high-risk head-on conflicts and congestion conflicts. The research outputs a vehicle scheduling scheme, enriches the theory of tunnel traffic scheduling, and provides scientific and feasible technical support for the coordinated scheduling of construction vehicles in long and large tunnels.<\/jats:p>","DOI":"10.3390\/e28070728","type":"journal-article","created":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T14:27:52Z","timestamp":1783434472000},"page":"728","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Conflict Entropy-Based Optimization of Vehicle Scheduling in Tunnel Traffic Networks"],"prefix":"10.3390","volume":"28","author":[{"given":"Yalong","family":"Xie","sequence":"first","affiliation":[{"name":"School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China"},{"name":"Institute of Computing Technology, China Academy of Railway Sciences Corporation Limited, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuming","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xianhui","family":"Nie","sequence":"additional","affiliation":[{"name":"Beijing Jingwei Information Technology Co., Ltd., China Academy of Railway Sciences Corporation Limited, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiaao","family":"Guo","sequence":"additional","affiliation":[{"name":"Beijing Jingwei Information Technology Co., Ltd., China Academy of Railway Sciences Corporation Limited, Beijing 100081, China"},{"name":"School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chengfeng","family":"Huang","sequence":"additional","affiliation":[{"name":"Beijing Jingwei Information Technology Co., Ltd., China Academy of Railway Sciences Corporation Limited, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"130041","DOI":"10.1016\/j.physa.2024.130041","article-title":"A spatiotemporal optimization method for connected and autonomous vehicle operations in long tunnel constructions","volume":"651","author":"Jiang","year":"2024","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_2","first-page":"1241","article-title":"Research on traffic control technology during the construction period of special long tunnels based on digital twins","volume":"Volume 13421","author":"Huang","year":"2024","journal-title":"Eighth International Conference on Traffic Engineering and Transportation System (ICTETS 2024)"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"9650147","DOI":"10.1155\/2024\/9650147","article-title":"Development of Synchronous Transportation Model for Trackless Vehicle Dispatching During the Construction of Long-Distance Single-Headed Shield Tunnel","volume":"2024","author":"Wu","year":"2024","journal-title":"Adv. Civ. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.trb.2017.01.001","article-title":"Dynamic passenger demand oriented metro train scheduling with energy-efficiency and waiting time minimization: Mixed-integer linear programming approaches","volume":"97","author":"Yin","year":"2017","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Tian, T., Wu, H., Wei, H., Wu, F., and Xu, M. (2025). An Efficient Route Planning Algorithm for Special Vehicles with Large-Scale Road Network Data. ISPRS Int. J. Geo-Inf., 14.","DOI":"10.3390\/ijgi14020071"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.aej.2023.12.044","article-title":"Intelligent path planning by an improved RRT algorithm with dual grid map","volume":"88","author":"Zhang","year":"2024","journal-title":"Alex. Eng. J."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Kvitko, D., Rybin, V., Bayazitov, O., Karimov, A., Karimov, T., and Butusov, D. (2024). Chaotic path-planning algorithm based on Courbage\u2013Nekorkin artificial neuron model. Mathematics, 12.","DOI":"10.3390\/math12060892"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Tong, N., Hu, Z., and Li, F. (2025). Achieving Optimized Allocation of Road Resources: A Path Planning Strategy for a Multivehicle Evolutionary Game Based on a Correlation Model. Transp. Res. Rec., 03611981251391734.","DOI":"10.1177\/03611981251391734"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1016\/j.aej.2025.01.055","article-title":"A multi-strategy enhanced Dung Beetle Optimization for real-world engineering problems and UAV path planning","volume":"118","author":"Yu","year":"2025","journal-title":"Alex. Eng. J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"130702","DOI":"10.1016\/j.physa.2025.130702","article-title":"Adaptive congestion index-based A* algorithm for dynamic vehicle path planning optimization","volume":"672","author":"Du","year":"2025","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Shi, Y., Huang, S., and Li, M. (2024). An Improved Global and Local Fusion Path-Planning Algorithm for Mobile Robots. Sensors, 24.","DOI":"10.3390\/s24247950"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Rong, S., Meng, R., Guo, J., Cui, P., and Qiao, Z. (2024). Multi-Vehicle Collaborative Planning Technology under Automatic Driving. Sustainability, 16.","DOI":"10.3390\/su16114578"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"e12766","DOI":"10.1049\/cth2.12766","article-title":"A game-theoretic cooperative path planning strategy using hybrid heuristic optimization algorithm","volume":"19","author":"Zhu","year":"2025","journal-title":"IET Control Theory Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"121241","DOI":"10.1016\/j.oceaneng.2025.121241","article-title":"Energy-constrained collaborative path planning for heterogeneous amphibious unmanned surface vehicles in obstacle-cluttered environments","volume":"330","author":"Yin","year":"2025","journal-title":"Ocean Eng."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Wang, F., Yang, Q., and Xie, Z. (2025). Dynamic Route Planning Strategy for Emergency Vehicles with Government\u2013Enterprise Collaboration: A Regional Simulation Perspective. Appl. Sci., 15.","DOI":"10.3390\/app152111496"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1007\/s12555-022-0495-8","article-title":"An improved dynamic window path planning algorithm using multi-algorithm fusion","volume":"22","author":"Zhou","year":"2024","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Li, P., Li, Y., and Dai, X. (2024). VNS-BA*: An Improved Bidirectional A* Path Planning Algorithm Based on Variable Neighborhood Search. Sensors, 24.","DOI":"10.3390\/s24216929"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Bhaskar, D., Chandrasekar, S.K., and Subramanian, S.P. (2024). Congestion-Aware Path Planning for Multiple Shelf-Carrying Mobile Robots in Robotic Mobile Fulfillment System. International Conference on Industry 4.0 and Advanced Manufacturing, Springer Nature.","DOI":"10.1007\/978-981-97-7150-9_26"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"105078","DOI":"10.1016\/j.trc.2025.105078","article-title":"Two-step optimization of train timetables rescheduling and response vehicles on a disrupted metro line","volume":"174","author":"Wang","year":"2025","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_20","unstructured":"Patzner, J., and M\u00fcller-Hannemann, M. (2024). Dynamic Traffic Assignment for Public Transport with Vehicle Capacities. arXiv."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3365603","DOI":"10.1155\/atr\/3365603","article-title":"Shortest Path Planning in Multimodal Metropolitan Transportation Networks Under Timetable and Label Constraints","volume":"2025","author":"Chen","year":"2025","journal-title":"J. Adv. Transp."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Bulkov\u00e1, Z., Brumer\u010d\u00edkov\u00e1, E., Bukov\u00e1, B., and Mihalik, T. (2025). Concept of an Integrated Urban Public Transport System Linked to a Railway Network Based on the Principles of a Timed-Transfer Timetable in the City of Prievidza. Systems, 13.","DOI":"10.3390\/systems13070543"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"14053","DOI":"10.1109\/TITS.2025.3539565","article-title":"An Intelligent Blockchain-Enabled Authentication Protocol for Transportation Cyber-Physical Systems","volume":"26","author":"Chen","year":"2025","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1177\/03611981241297980","article-title":"Identifying Key Technologies and Cluster Patterns in Intelligent Transportation Systems","volume":"2679","author":"Huang","year":"2025","journal-title":"Transp. Res. Rec."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"107180","DOI":"10.1016\/j.cor.2025.107180","article-title":"Distributed train timetable synchronization in metro network: An ADMM-based decomposition framework","volume":"183","author":"Liu","year":"2025","journal-title":"Comput. Oper. Res."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Calzada-Infante, L., Adenso-D\u00edaz, B., and Carbajal, S.G. (2024). Improving Transfer Connectivity in Railway Timetables Based on Closeness Centrality: The Case of the European International Network. Systems, 12.","DOI":"10.3390\/systems12090327"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5828","DOI":"10.1109\/TCSS.2024.3379214","article-title":"Coordinated rescheduling of train timetable and crew scheme for passenger-freight collinear railway","volume":"11","author":"Wang","year":"2024","journal-title":"IEEE Trans. Comput. Soc. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"130509","DOI":"10.1016\/j.physa.2025.130509","article-title":"Vehicle navigation path optimization based on complex networks","volume":"665","author":"Ma","year":"2025","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Li, Q.L., and Lai, X.J. (2025). Deep Reinforcement Learning for Path Optimization of Industrial Robots. 2025 4th International Symposium on Robotics, Artificial Intelligence and Information Engineering (RAIIE), IEEE.","DOI":"10.1109\/RAIIE65740.2025.11140274"},{"key":"ref_30","first-page":"1","article-title":"Solving the combined flexible job shop scheduling and vehicle routing problem with stochastic features","volume":"19","year":"2025","journal-title":"J. Simul."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Chen, A., and Li, T. (2024). Modeling and solving the multi-objective vehicle routing problem with soft and fuzzy time windows. Systems, 12.","DOI":"10.3390\/systems12120560"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"8387","DOI":"10.1109\/TITS.2024.3373634","article-title":"Public transit for special events: Ridership prediction and train scheduling","volume":"25","author":"Santanam","year":"2024","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Shi, H., Hong, Y., Zhang, Q., and Qin, J. (2025). Research on Cold Chain Logistics Joint Distribution Vehicle Routing Optimization Based on Uncertainty Entropy and Time-Varying Network. Entropy, 27.","DOI":"10.3390\/e27050540"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Marde\u0161i\u0107, N., Erdeli\u0107, T., Cari\u0107, T., and \u0110urasevi\u0107, M. (2023). Review of stochastic dynamic vehicle routing in the evolving urban logistics environment. Mathematics, 12.","DOI":"10.3390\/math12010028"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Yu, V.F., Lin, C.H., Maglasang, R.S., Lin, S.-W., and Chen, K.-F. (2024). An Efficient Simulated Annealing Algorithm for the Vehicle Routing Problem in Omnichannel Distribution. Mathematics, 12.","DOI":"10.3390\/math12233664"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"106333","DOI":"10.1109\/ACCESS.2024.3438079","article-title":"Guided genetic algorithm for solving capacitated vehicle routing problem with unmanned-aerial-vehicles","volume":"12","author":"Jasim","year":"2024","journal-title":"IEEE Access"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Yin, X., Yu, Z., Liu, Y., Chen, Y., and Guo, A. (2025). An Improved Approach for Vehicle Routing Problem with Three-Dimensional Loading Constraints Based on Genetic Algorithm and Residual Space Optimized Strategy. Processes, 13.","DOI":"10.3390\/pr13051449"},{"key":"ref_38","first-page":"1508","article-title":"Collaborative Optimization of Timetable and Operation Path for Long Tunnel Construction Vehicles","volume":"60","author":"Hu","year":"2025","journal-title":"J. Southwest Jiaotong Univ."},{"key":"ref_39","first-page":"54","article-title":"Simulation of subway passenger flow during station evacuation based on K\u2043shortest path planning and an improved social force model","volume":"52","author":"Zhao","year":"2025","journal-title":"J. Beijing Univ. Chem. Technol. (Nat. Sci.)"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"9943825","DOI":"10.1049\/sfw2\/9943825","article-title":"Automated Hybrid Methodology for Software Architecture Style Selection Using Analytic Hierarchy Process and Fuzzy Analytic Hierarchy Process","volume":"2025","author":"Alrazgan","year":"2025","journal-title":"IET Softw."},{"key":"ref_41","first-page":"403","article-title":"Analytic Hierarchy Process Based on Intuitionistic Fuzzy Sets with Ordered Pairs","volume":"46","author":"Kahraman","year":"2025","journal-title":"J. Mult.-Valued Log. Soft Comput."},{"key":"ref_42","first-page":"134","article-title":"Fuzzy-improved AHP evaluation of ecological restoration schemes: A case study of Panshitou Reservoir","volume":"44","author":"Li","year":"2025","journal-title":"J. Henan Polytech. Univ."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2895320","DOI":"10.1155\/2020\/2895320","article-title":"An Improved NSGA-II Algorithm for Transit Network Design and Frequency Setting Problem","volume":"2020","author":"Chai","year":"2020","journal-title":"J. Adv. Transp."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/7\/728\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T12:57:11Z","timestamp":1783515431000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/7\/728"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,25]]},"references-count":43,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2026,7]]}},"alternative-id":["e28070728"],"URL":"https:\/\/doi.org\/10.3390\/e28070728","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,25]]}}}