Transit Dynamic Operation Optimization Using Combination of Stop-Skipping Strategy and Local Route Optimization
Abstract
:1. Introduction
- (1)
- Some scholars simply used one of the strategies of bus-holding, stop-skipping, or signal control to avoid bus crosstown or late buses, which is for the control of two adjacent buses, without considering that changes in the status of adjacent buses will have an impact on the overall operation of the bus line, so the final scheduling program has a large optimization space.
- (2)
- Research on the real-time dynamic adjustment of bus running routes is limited to demand-responsive buses, and has not been applied to the operation optimization of conventional buses. There is a lack of research on the possible impacts of the localized and limited dynamic adjustment optimization of conventional bus running routes, which is not conducive to releasing the full potential of the bus system or improving the refinement level of bus operations.
- (1)
- From the perspective of overall system optimization, a dynamic control strategy for public transportation is proposed by combining bus-skipping control and operation path optimization.
- (2)
- With the dual optimization objectives of minimizing bus operation costs and minimizing passenger travel costs, the optimization objectives and constraints are clarified and a dynamic optimization model for single-line bus operations is established.
- (3)
- A hybrid heuristic algorithm based on simulated annealing principles and the genetic algorithm is designed for the model characteristics, based on which, a two-stage optimization model-solving scheme is proposed.
2. Dynamic Optimization Strategies for Public Transportation Operations
2.1. Research Scenario Definition
2.2. Stop-Skipping Strategy
2.3. Path Optimization Strategy
- (1)
- Vehicle operation topology network construction with branching.
- (2)
- Bus operation strategy construction based on relaxation time window.
2.4. Optimization Model Formulation
2.4.1. Basic Assumptions of the Model
- (1)
- Buses will not be subject to sudden situations such as abnormal speed reductions or stopping due to the influence of other vehicles and non-motorized vehicles in the operation path, but their average speed will be reduced due to congestion of the driving section.
- (2)
- Buses can receive the scheduling plan issued by the dispatch center before they depart from the first stop, and their drivers are familiar with the road conditions, so they can accurately understand and execute adjustment strategies.
- (3)
- The stops are vacant and not occupied by buses of other routes before the buses arrive at the respective bus stops.
- (4)
- When a transit vehicle passes through a roadway intersection, the average waiting time of the node at different times of the day is used to replace the passing process, without considering the specific effects of traffic crossing and signal phasing.
- (5)
- Buses will depart on time in accordance with the scheduling program, and the frequency of departures will be consistent during the same operating hours.
- (6)
- During the vehicle path optimization process, the generated feasible paths corresponding to the city roads are allowed to be passed by public transport vehicles, and there is no width, height, or speed limit requirement.
- (7)
- The technical conditions of bus routes should meet the requirements of real-time communication and multi-source data processing.
2.4.2. Description of Model Parameters
2.4.3. Objective Function
- (1)
- Cost of bus operating
- (2)
- Cost of passenger travel
2.4.4. Constraints
- (1)
- Bus skipping constraints
- (2)
- Stop skipping protection constraint
- (3)
- Bus operating speed constraint
- (4)
- Bus capacity constraint
- (5)
- Departure interval constraint
- (6)
- Service rate constraint
3. Algorithm
- (1)
- Chromosome coding
- (2)
- Population initialization
- (3)
- Adaptation function
- (4)
- Simulated annealing perturbation
- (5)
- Selection, crossover, and mutation
- (6)
- Algorithm termination conditions
4. Case Study
4.1. Data Description
4.2. Parameter Setting
4.3. Analysis of Results
- (1)
- The trips for which the stop-skipping control strategy was implemented were concentrated in the morning and evening peak hours, and none of the trips during the weekday peak hours were implemented. This was mainly due to the large departure interval during peak hours; if a vehicle crossed the station, the passengers at that station would incur a high cost of waiting time and penalty cost. On the other hand, the peak hour routes were densely populated, and the next vehicle would arrive soon after a vehicle crossed the station, so the total cost increase was limited and easy for passengers to accept.
- (2)
- The numbers of the bus stops that buses skipped were 5, 9, 12, 13, 19, 23, 25, and 26 (specific station names are listed in Table 2). These stops generally have low patronage, the distribution of passengers is closely related to time of day, or the spacing between stations is small and transportation conditions are poor. Therefore, decision makers can discover the problems of the line station layout through the skipping frequency of the stops in the program, so as to provide reference evidence for the relocation of original bus stops and the setting of new stops.
- (3)
- The numbers of the bus stops where buses changed route were 9 and 26. Bus stop 9 (Dragon Mall) is prone to congestion in the vicinity of the Londo Mall, but there are multiple roads to choose from, thus making it easy to find a more reasonable path. For bus stop 26 (Yunlong Garden), there are too many intersections near it, tending to make buses choose to cross the stop in the calculation process. Therefore, the results of this model can also help to identify difficult route segments, which can be used as a theoretical basis for bus operators in the path optimization of existing routes and the laying of new routes.
5. Conclusions
- (1)
- The dynamic optimization program used in the single-route bus is mainly based on the stop-skipping control strategy. Although the example results prove that this method can effectively reduce the average travel time and waiting time of passengers, the impact of vehicle crossing on individual passengers’ willingness to ride is difficult to completely eliminate.
- (2)
- The optimization model only considered a single-line bus, but in reality, multiple lines with public routes and stops will have mutual interference with each other, affecting the optimization effect of the scheduling scheme. In the future, the interactions between other lines and this line can be considered to be included in the research scenarios for quantification and modeling, so that the model can be closer to the real operating environment and the applicability of the model can be improved.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Hall, R.; Dessouky, M.; Lu, Q. Optimal holding times at transfer stations. Comput. Ind. Eng. 2001, 40, 379–397. [Google Scholar] [CrossRef]
- Cats, O.; Larijani, A.N.; Ólafsdóttir, Á.; Burghout, W.; Andréasson, I.J.; Koutsopoulos, H.N. Bus-Holding Control Strategies: Simulation-Based Evaluation and Guidelines for Implementation. Transp. Res. Rec. 2012, 2274, 100–108. [Google Scholar] [CrossRef]
- Muñoz, J.C.; Cortés, C.E.; Giesen, R. Comparison of Dynamic Control Strategies for Transit Operations. Transp. Res. Part C Emerg. Technol. 2013, 28, 101–113. [Google Scholar] [CrossRef]
- Cortés, C.E.; Sáez, D.; Milla, F. Hybrid Predictive Control for Real-time Optimization of Public Transport Systems Operations Based on Evolutionary Multi-objective Optimization. Transp. Res. Part C Emerg. Technol. 2010, 18, 757–769. [Google Scholar] [CrossRef]
- Daganzo, C.F.; Pilachowski, J. Reducing Bunching with Bus-to-bus Cooperation. Transp. Res. Part B Methodol. 2011, 45, 267–277. [Google Scholar] [CrossRef]
- Teng, J.; Jin, W.M. A Section-speed Guiding Method for Bus Operation Control. J. Tongji Univ. (Nat. Sci.) 2015, 43, 1194–1199. [Google Scholar] [CrossRef]
- He, S.X. An Anti-bunching Strategy to Improve Bus Schedule and Headway Reliability by Making Use of the Available Accurate Information. Comput. Ind. Eng. 2015, 85, 17–32. [Google Scholar] [CrossRef]
- Estrada, M.; Mensión, J.; Aymamí, J.M. Bus Control Strategies in Corridors with Signalized Intersections. Transp. Res. Part C Emerg. Technol. 2016, 71, 500–520. [Google Scholar] [CrossRef]
- Yang, M.; Sun, G.; Wang, W.; Sun, X.; Ding, J.; Han, J. Evaluation of the Pre-detective Signal Priority for Bus Rapid Transit: Coordinating the Primary and Secondary Intersections. Transport 2018, 33, 41–51. [Google Scholar] [CrossRef]
- Ma, W.; Yang, X.; Liu, Y. Development and Evaluation of a Coordinated and Conditional Bus Priority Approach. Transp. Res. Rec. 2010, 2145, 49–58. [Google Scholar] [CrossRef]
- Anderson, P.; Daganzo, C.F. Effect of Transit Signal Priority on Bus Service Reliability. Transp. Res. Part B Methodol. 2020, 132, 2–14. [Google Scholar] [CrossRef]
- Cvijovic, Z.; Zlatkovic, M.; Stevanovic, A.; Song, Y. Conditional Transit Signal Priority for Connected Transit Vehicles. Transp. Res. Rec. 2022, 2676, 490–503. [Google Scholar] [CrossRef]
- Chandrasekar, P.; Long, C.R.; Chin, H.C. Simulation Evaluation of Route-based Control of Bus Operations. J. Transp. Eng. 2002, 128, 519–527. [Google Scholar] [CrossRef]
- Sun, A.; Hickman, M. The Real-time Stop-skipping Problem. J. Intell. Transp. Syst. 2005, 9, 91–109. [Google Scholar] [CrossRef]
- Delgado, F.; Munoz, J.C.; Giesen, R. Real-time Control of Buses in A Transit Corridor Based on Vehicle Holding and Boarding Limits. Transp. Res. Rec. 2009, 2090, 59–67. [Google Scholar] [CrossRef]
- Daganzo, C.F. A Headway-based Approach to Eliminate Bus Bunching: Systematic Analysis and Comparisons. Transp. Res. Part B Methodol. 2009, 43, 913–921. [Google Scholar] [CrossRef]
- Delgado, F.; Munoz, J.C.; Giesen, R. How Much Can Holding and/or Limiting Boarding Improve Transit Performance? Transp. Res. Part B Methodol. 2012, 46, 1202–1217. [Google Scholar] [CrossRef]
- Xuan, Y.; Argote, J.; Daganzo, C.F. Dynamic Bus Holding Strategies for Schedule Reliability: Optimal Linear Control and Performance Analysis. Transp. Res. Part B Methodol. 2011, 45, 1831–1845. [Google Scholar] [CrossRef]
- Bartholdi, J.J.; Eisenstein, D.D. A Self-Coordinating Bus Route to Resist Bus Bunching. Transp. Res. Part B Methodol. 2012, 46, 481–491. [Google Scholar] [CrossRef]
- Zheng, S.Y. Research on Public Transit Real-time Scheduling Method under the Condition of V2V Communication. Master’s Thesis, Beijing Jiaotong University, Beijing, China, 2016. [Google Scholar]
- Konstantinos, G. Stop-skipping in Rolling Horizons. Transp. A Transp. Sci. 2021, 17, 492–520. [Google Scholar] [CrossRef]
- Chen, C.X.; Chen, Z.Y.; Chen, W.Y. A Real-time Control Method for Single Bus Line Based on Fuzzy Logic. J. Highw. Transp. Res. Dev. 2016, 33, 141–147. [Google Scholar] [CrossRef]
- Zhao, J.; Bukkapatnam, S.; Dessouky, M.M. Distributed Architecture for Real-time Coordination of Bus Holding in Transit Networks. IEEE Trans. Intell. Transp. Syst. 2003, 4, 43–51. [Google Scholar] [CrossRef]
- Cats, O.; Larijani, A.N.; Koutsopoulos, H.N. Impacts of Holding Control Strategies on Transit Performance: Bus Simulation Model Analysis. Transp. Res. Rec. 2011, 2216, 51–58. [Google Scholar] [CrossRef]
- Sáez, D.; Cortés, C.E.; Milla, F. Hybrid Predictive Control Strategy for a Public Transport System with Uncertain Demand. Transportmetrica 2012, 8, 61–86. [Google Scholar] [CrossRef]
- Zhang, H.; Liang, S.D.; Zhao, J.; He, S.X.; Zhao, T.Y. Coordinated Headway-Based Control Method to Improve Public Transit Reliability considering Control Points Layout. J. Adv. Transp. 2020, 2020, 3236841. [Google Scholar] [CrossRef]
- Foletta, N.; Estrada-Romeu, M.; Roca-Riu, M. New Modifications to Bus Network Design Methodology. Transp. Res. Rec. 2010, 2197, 43–53. [Google Scholar] [CrossRef]
- Joaquín, A.P.; Caballero, R.; Laguna, M. Bi-Objective Bus Routing: An Application to School Buses in Rural Areas. Transp. Sci. 2013, 47, 397–411. [Google Scholar] [CrossRef]
- Fan, W.; Machemehl, M. Bi-Level Optimization Model for Public Transportation Network Redesign Problem. Transp. Res. Rec. 2011, 2263, 151–162. [Google Scholar] [CrossRef]
- Muhammad, A.N.; Rahman, M.K.; Rahman, M.S. Transit network design by genetic algorithm with elitism. Transp. Res. Part C Emerg. Technol. 2014, 46, 30–45. [Google Scholar] [CrossRef]
- Wang, Y.; Du, B.W.; Rong, Q.N.; Lin, X. Travel Patterns Analysis of Urban Residents Using Automated Fare Collection System. Chin. J. Electron. 2016, 25, 4047. [Google Scholar] [CrossRef]
- Bagloee, S.A.; Ceder, A. Transit-network Design Methodology for Actual-size Road Networks. Transp. Res. Part B Methodol. 2011, 45, 1787–1804. [Google Scholar] [CrossRef]
- Xiong, J.; Guan, W.; Huang, A.L. Research on Optimal Routing of Community Shuttle Connect Rail Transit Line. J. Transp. Syst. Eng. Inf. Technol. 2014, 14, 166–173. [Google Scholar] [CrossRef]
- Zhang, Y. Time-Constrained Routing Optimization Models and Algorithms under Uncertain Travel Times. Master’s Thesis, Dongbei University, Shenyang, China, 2017. [Google Scholar]
- Yu, L.J.; Zhu, Y.Z.; Yu, Z.Q.; Li, X.; Liu, W. Optimal Design for Trunk-and-feeder Bus Transit Tree Network with Heterogeneous Demand. China J. Highw. Transp. 2021, 34, 139–156. [Google Scholar] [CrossRef]
- Lin, J.J.; Wong, H.I. Optimization of a Feeder-bus Route Design by Using a Multiobjective Programming Approach. Transp. Plan. Technol. 2014, 37, 430–449. [Google Scholar] [CrossRef]
- Lyu, Y.; Chow, C.Y.; Lee, V.C.S. CB-Planner: A Bus Line Planning Framework for Customized Bus Systems. Transp. Res. Part C Emerg. Technol. 2019, 101, 233–253. [Google Scholar] [CrossRef]
- Huang, D.; Gu, Y.; Wang, S. A Two-phase Optimization Model for the Demand-responsive Customized Bus Network Design. Transp. Res. Part C Emerg. Technol. 2020, 111, 1–21. [Google Scholar] [CrossRef]
- Ma, C.; Wang, C.; Xu, X. A Multi-Objective Robust Optimization Model for Customized Bus Routes. IEEE Trans. Intell. Transp. Syst. 2021, 22, 2359–2370. [Google Scholar] [CrossRef]
- Shen, C.; Yao, S.; Bai, Z. Real-time Customized Bus Routes Design with Optimal Passenger and Vehicle Matching Based on Column Generation Algorithm. Phys. A Stat. Mech. Its Appl. 2021, 571, 125836. [Google Scholar] [CrossRef]
- Dunbar, M.; Simon, B.; Nagesh, S. A Genetic Column Generation Algorithm for Sustainable Spare Part Delivery: Application to the Sydney DropPoint Network. Ann. Oper. Res. 2020, 290, 923–941. [Google Scholar] [CrossRef]
- Qiu, G. Research on Optimizing Design Method of Customized Bus Route Based on Passenger Travel Mode Choice. Master’s Thesis, Beijing Jiaotong University, Beijing, China, 2019. [Google Scholar]
Parameters | Description |
---|---|
Cost of bus operating (CNY) | |
Cost of passenger travel (CNY) | |
Cost of passenger waiting time (CNY) | |
Cost of passenger traveling time (CNY) | |
Judgment function that enforces the stop-skipping strategy of bus at stop | |
Judgment function that enforces the path optimization strategy of bus at stop | |
Total length of the route (km) | |
Total number of buses on the route | |
Total number of bus stops on the route | |
Total number of time periods | |
Length of the time period (s) | |
Variable operating cost control factor for buses | |
Cost control factor for passenger waiting time | |
Cost control factor for passengers waiting time with satisfaction penalties | |
Cost control factor for passenger in-transit time | |
Number of passengers embarking when bus arrives at stop | |
Number of passengers disembarking when bus arrives at stop | |
Number of passengers on bus from stop | |
Number of passengers waiting for bus at stop | |
Authorized number of passengers | |
Traveling distance of the bus traveling from the stop to (km) | |
Traveling speed of the bus traveling from the stop to (km) | |
Minimum speed limit of the buses (m/s) | |
Maximum speed limit of the buses (m/s) | |
Minimum departure time interval (s) | |
Maximum departure time interval (s) | |
Decision variable, the departure interval during the time period | |
0–1 Decision variable, to control the bus whether skip stop or not | |
0–1 Decision variable, to control the bus whether adjust the path or not |
Bus Stop Number | Bus Stop Name | Longitude Coordinates (E) | Latitude Coordinates (N) | Distance between Stations (m) |
---|---|---|---|---|
1 | Station | 114.96962 | 25.82529 | - |
2 | Ganzhou Trade Mart | 114.96907 | 25.82199 | 458 |
3 | Jitai New City District | 114.96069 | 25.81343 | 1104 |
4 | Ganzhou Technician College | 114.94987 | 25.80440 | 1527 |
5 | Hydraulic Turbine Factory | 114.93209 | 25.79220 | 1472 |
6 | Forestry Driving School | 114.92605 | 25.78712 | 835 |
7 | Ganzhou Nursing School | 114.91183 | 25.77602 | 2513 |
8 | Yide Rongcheng | 114.89716 | 25.76614 | 1037 |
9 | Dragon Mall | 114.89024 | 25.76112 | 491 |
10 | Tannenbaum Station | 114.88210 | 25.76404 | 1562 |
11 | Tamdong Farmers’ Market | 114.87817 | 25.76199 | 394 |
12 | Tandong Township Government | 114.87508 | 25.76040 | 363 |
13 | Livestock Farm | 114.85419 | 25.75046 | 1610 |
14 | Tankou Township Government | 114.84575 | 25.74649 | 1435 |
15 | Xiaba village | 114.84056 | 25.74327 | 649 |
16 | Taitou village | 114.83032 | 25.73573 | 1090 |
17 | Longling New Street | 114.82053 | 25.72631 | 1466 |
18 | Fourth secondary school | 114.81620 | 25.71934 | 814 |
19 | Lighting Mart | 114.80983 | 25.70938 | 1228 |
20 | Nankang Jia Bo Mart | 114.80016 | 25.69786 | 1470 |
21 | Guangming Furniture Mart | 114.79160 | 25.69191 | 998 |
22 | Nankang Furniture Mart | 114.78697 | 25.68922 | 546 |
23 | Sixth Secondary School | 114.77771 | 25.68364 | 1095 |
24 | Traffic Control Brigade | 114.77315 | 25.68095 | 590 |
25 | Dongshan Park | 114.77195 | 25.67654 | 490 |
26 | Yunlong Garden | 114.76569 | 25.67311 | 661 |
27 | District Bus Company | 114.77242 | 25.68854 | 3140 |
Parameter | Value |
---|---|
Population size | 200 |
Crossover probability | 0.8 |
Probability of mutation | 0.2 |
Adaptive variance probability control factor | 0.6 |
Initial temperature | 1000 |
Cooling factor | 0.98 |
Maximum number of iterations | 300 |
Parameter | Value |
---|---|
24 | |
0.0105 | |
0.0155 | |
0.0085 | |
1.5 | |
12.5 | |
65 | |
240 | |
1200 |
Bus Number | Departure Time | Arrival Time | Running Time | Passenger Flow (Person) | Passenger Service Rate | Average Speed (km/h) |
---|---|---|---|---|---|---|
01 | 6:00 | 7:14 | 74′32″ | 63 | 100% | 23.4 |
02 | 6:16 | 7:32 | 76′13″ | 131 | 100% | 22.9 |
03 | 6:32 | 7:49 | 77′25″ | 79 | 100% | 22.6 |
04 | 6:48 | 8:10 | 82′41″ | 133 | 100% | 21.1 |
05 | 7:04 | 8:21 | 77′11″ | 148 | 95.94% | 22.6 |
06 | 7:13 | 8:33 | 80′39″ | 204 | 100% | 21.6 |
07 | 7:22 | 8:41 | 79′26″ | 173 | 100% | 22.0 |
08 | 7:31 | 8:46 | 75′21″ | 75 | 96.00% | 23.2 |
09 | 7:40 | 9:02 | 82′01″ | 142 | 100% | 21.3 |
10 | 7:49 | 9:14 | 85′04″ | 88 | 100% | 20.5 |
11 | 7:58 | 9:22 | 84′58″ | 163 | 97.55% | 20.5 |
12 | 8:07 | 9:35 | 88′15″ | 204 | 100% | 19.8 |
13 | 8:13 | 9:37 | 83′41″ | 179 | 96.09% | 20.9 |
14 | 8:19 | 9:45 | 86′23″ | 238 | 100% | 20.2 |
15 | 8:25 | 9:56 | 91′02″ | 97 | 100% | 19.2 |
16 | 8:31 | 9:59 | 88′17″ | 152 | 96.05% | 19.8 |
17 | 8:37 | 10:02 | 85′50″ | 177 | 95.48% | 20.3 |
18 | 8:43 | 10:13 | 90′33″ | 91 | 100% | 19.3 |
19 | 8:49 | 10:16 | 87′43″ | 53 | 100% | 19.9 |
20 | 8:55 | 10:21 | 86′00″ | 82 | 100% | 20.3 |
21 | 9:01 | 10:23 | 82′42″ | 91 | 96.70% | 21.1 |
22 | 9:18 | 10:38 | 80′35″ | 36 | 100% | 21.7 |
23 | 9:35 | 10:51 | 76′54″ | 67 | 100% | 22.7 |
24 | 9:52 | 11:09 | 77′11″ | 51 | 100% | 22.6 |
25 | 10:09 | 11:26 | 77′22″ | 42 | 100% | 22.6 |
26 | 10:29 | 11:47 | 78′35″ | 51 | 100% | 22.2 |
27 | 10:49 | 12:03 | 74′29″ | 38 | 100% | 23.4 |
28 | 11:09 | 12:24 | 75′14″ | 35 | 100% | 23.2 |
29 | 11:27 | 12:42 | 75′07″ | 49 | 100% | 23.2 |
30 | 11:45 | 13:01 | 76′03″ | 46 | 100% | 23.0 |
31 | 12:03 | 13:22 | 79′18″ | 37 | 100% | 22.0 |
32 | 12:23 | 13:36 | 73′34″ | 41 | 100% | 23.7 |
33 | 12:43 | 14:00 | 77′31″ | 43 | 100% | 22.5 |
34 | 13:03 | 14:18 | 75′28″ | 48 | 100% | 23.1 |
35 | 13:23 | 14:35 | 72′26″ | 44 | 100% | 24.1 |
36 | 13:43 | 14:58 | 75′33″ | 55 | 100% | 23.1 |
37 | 14:03 | 15:23 | 80′48″ | 50 | 100% | 21.6 |
38 | 14:23 | 15:42 | 79′59″ | 24 | 100% | 21.8 |
39 | 14:43 | 15:57 | 74′05″ | 39 | 100% | 23.6 |
40 | 15:03 | 16:21 | 78′28″ | 35 | 100% | 22.3 |
41 | 15:23 | 16:35 | 72′20″ | 48 | 100% | 24.1 |
42 | 15:43 | 17:00 | 77′15″ | 51 | 100% | 22.6 |
43 | 16:03 | 17:20 | 77′17″ | 63 | 100% | 22.6 |
44 | 16:19 | 17:37 | 78′15″ | 55 | 100% | 22.3 |
45 | 16:35 | 17:50 | 75′08″ | 79 | 100% | 23.2 |
46 | 16:51 | 18:10 | 79′44″ | 88 | 100% | 21.9 |
Bus Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
05 | △ | △ | △ | ||||||||||||||||||||||||
07 | △ | ||||||||||||||||||||||||||
08 | △ | △ | |||||||||||||||||||||||||
11 | ▲ | △ | |||||||||||||||||||||||||
13 | △ | ▲ | △ | △ | |||||||||||||||||||||||
16 | △ | △ | △ | ||||||||||||||||||||||||
17 | △ | △ | ▲ | ||||||||||||||||||||||||
20 | △ | △ | |||||||||||||||||||||||||
21 | △ | △ | △ | ||||||||||||||||||||||||
48 | △ | △ | |||||||||||||||||||||||||
50 | ▲ | △ | △ | ||||||||||||||||||||||||
52 | △ | △ | △ | ||||||||||||||||||||||||
54 | △ | △ | ▲ | ||||||||||||||||||||||||
57 | △ | ||||||||||||||||||||||||||
58 | ▲ | △ | ▲ | ||||||||||||||||||||||||
59 | △ | ||||||||||||||||||||||||||
61 | △ | △ | △ |
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Zhou, X.; Guo, H.; Li, B.; Zhao, X. Transit Dynamic Operation Optimization Using Combination of Stop-Skipping Strategy and Local Route Optimization. Appl. Sci. 2024, 14, 7783. https://doi.org/10.3390/app14177783
Zhou X, Guo H, Li B, Zhao X. Transit Dynamic Operation Optimization Using Combination of Stop-Skipping Strategy and Local Route Optimization. Applied Sciences. 2024; 14(17):7783. https://doi.org/10.3390/app14177783
Chicago/Turabian StyleZhou, Xuemei, Huanwu Guo, Boqian Li, and Xiaochi Zhao. 2024. "Transit Dynamic Operation Optimization Using Combination of Stop-Skipping Strategy and Local Route Optimization" Applied Sciences 14, no. 17: 7783. https://doi.org/10.3390/app14177783