Demand Response Transit Scheduling Research Based on Urban and Rural Transportation Station Optimization
Abstract
:1. Introduction
- (1)
- Considering the distribution characteristics of passenger reservation demand in urban and rural areas, an optimization strategy for bus stops is designed.
- (2)
- Reducing the number of bus route excursions, improving the efficiency of bus operations and reducing environmental pollution.
- (3)
- Aiming at the lowest operating cost of public transport enterprises and the lowest cost of travel time for passengers, a variable-route bus scheduling model is established.
2. Model Construction
2.1. Problem Description
2.2. Model Assumptions
- (1)
- Passenger reservation information is submitted prior to the departure of the bus, and reservation requests are not changed or cancelled after submission.
- (2)
- Except for requests that have no responses, passengers who respond are expected to board the bus and arrive at the reserved terminal within the agreed time window in accordance with notified information.
- (3)
- The time required for responding passengers to get on and off the bus remains the same.
- (4)
- The average speed of a bus vehicle running smoothly on the road does not vary significantly and is not affected by traffic congestion, signals, or other internal and external conditions.
- (5)
- The bus vehicle models and the rated passenger capacity are known.
- (6)
- The vehicle departs from the site and returns to the site after completing the demand response.
- (7)
- To simplify the calculation, the distance travelled by the bus is assumed to be a straight line between two points.
2.3. Scheduling Model
2.3.1. Aiming for the Shortest Running Time
2.3.2. Achieving Lowest Operating Costs for Urban and Rural Public Transport Enterprises
2.3.3. Multiobjective Analysis
2.3.4. Constraints
- 1.
- All vehicles must pass through a fixed station, as expressed in Equations (5) and (6).
- 2.
- In all stations in the area served by intercity and rural vehicles, the vehicle arrives and leaves the station at most once, as described in Equations (7) and (8).
- 3.
- The actual operating routes of vehicles between urban and rural areas will not be duplicated, as described in Equation (9).
- 4.
- If there is a succession of bus services between the two sites and , the time the bus vehicle arrives at site j will not be earlier than the time it leaves at site i; the time spent by passengers getting on and off at bus site and the sum of the travel times between the two bus sites and , as expressed in Equation (10).
- 5.
- The number of bus passengers always satisfies the condition that it is less than the rated capacity of the vehicle and greater than the number of passengers boarding at the station, as described in Equation (11).
- 6.
- The variables are restricted to be assigned with values, as shown in Equation (12).
3. Model Solution
3.1. Clustering Algorithm for Urban and Rural Bus Stops
- (1)
- Input the dataset A containing travel and reservation histories of the passengers in the region, parameter field radius δ, minimum data point threshold Minpts, and number of parameter clusters k.
- (2)
- Calculate the distance between each point in the data and the other points.
- (3)
- Determine whether the number of points in the δ domain of any demand point is greater than the threshold Minpts, mark the point as a core point, and classify the points in its neighborhood as a class; otherwise, mark the point as a noisy point.
- (4)
- Determine whether all points are classified. Repeat steps (2) and (3) until all points are classified as class or noisy points.
- (5)
- After eliminating the noisy points in the dataset, select the k points, including the core points, as the initial centroids.
- (6)
- Calculate the distance between the centroid and other points and assign each point in the new dataset to the class with the closest distance.
- (7)
- Calculate new centroids in the k classes of data points.
- (8)
- Determine whether the centroids change. Repeat steps (6) and (7) until the squared distances and convergence between each point, and the centroids and all the data points are classified into a certain class and no longer change.
- (9)
- Determine the coordinates of the centers of the clusters.
3.2. Genetic Simulated Annealing Algorithm
- (1)
- Coding. The departure frequency and service order were encoded in binary form based on the characteristics of the genetic simulated annealing algorithm.
- (2)
- Initial solution. The simulated annealing algorithm randomly generated the initial schedules and paths at the initial temperature at the initial temperature.
- (3)
- Construction of the adaptation function. The smaller the cost incurred by a vehicle as it travels along a path, the easier it is for the cost incurred by that path to be retained across genetic operations, expressed as , which is generally constructed using the objective function ) of the model. The fitness function is represented by Equation (13).
- (4)
- Genetic operator. It includes the selection, crossover, and variation operators. The selection operator uses a combination of the roulette wheel and elite retention strategy, the single-point crossover is used as the crossover operator of the genetic simulated annealing algorithm, and the variation operator is used to maintain the population diversity, which is typically between 0.0001–0.1.
- (5)
- Simulated annealing operation. To compensate for the poor local search ability of the genetic algorithm, a simulated annealing operation was performed on new individuals derived using the genetic algorithm. The general simulated annealing algorithm operation was divided into two steps: first, the current population was set as and the current temperature as , and the individual fitness in the current population was calculated; second, the size of the individual fitness was determined. If , then a new individual was generated to replace the old one; if , then the generated new individual replaced the old one with the probability of p .
- (6)
- Cooling operation. The cooling function is expressed in Equation (14).
- (7)
- Algorithm termination conditions. The algorithm is terminated if the new solution generated at the set end temperature and the number of iterations of the algorithm are not accepted. Here, we used a pre-set number of iterations and executed the simulated annealing operation continuously until the pre-set number of iterations was reached, then the loop was stopped, and the algorithm was terminated.
4. Case Study
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Yongcheng City–Mangshan Town | Downstream Stations | ||||
---|---|---|---|---|---|
Site 1 | Site 2 | Site 3 | Site 4 | Site 5 | |
First shift | 06:30 | 07:00 | 07:30 | 07:50 | 08:05 |
Second shift | 07:00 | 07:30 | 08:00 | 08:20 | 08:35 |
Third shift | 07:30 | 08:00 | 08:30 | 08:50 | 09:05 |
Fourth shift | 08:00 | 08:30 | 09:00 | 09:20 | 09:35 |
Mangshan Town–Yongcheng City | Upstream Sites | ||||
---|---|---|---|---|---|
Site 5 | Site 4 | Site 3 | Site 2 | Site 1 | |
First shift | 06:30 | 06:45 | 07:05 | 07:35 | 08:05 |
Second shift | 07:00 | 07:15 | 07:35 | 08:05 | 08:35 |
Third shift | 07:30 | 07:45 | 08:05 | 08:35 | 09:05 |
Fourth shift | 08:00 | 08:15 | 08:35 | 09:05 | 09:35 |
Vehicle Shift | Passenger Travel Station Requirements | Total |
---|---|---|
First shift | (1,2) 1 (1,3) 1 (1,4) 1 (1,5) 2 (2,1) 2 (2,8) 1 (2,7) 2 (3,6) 3 (3,4) 2 (3,10) 2 (3,11) 3 (3,12) 3 (6,4) 3 | 26 |
Second shift | (6,2) 2 (6,5) 3 (6,12) 3 (4,3) 1 (2,3) 1 (2,9) 2 (2,6) 2 (2,1) 1 (7,12) 2 (5,1) 2 (12,1) 2 (7,1) 2 (12,5) 2 (4,5) 2 (8,5) 3 (6,5) 2 | 32 |
Third shift | (1,6) 2 (5,1) 1 (5,3) 1 (4,3) 1 (10,4) 1 (10,5) 1 (7,5) 2 (12,9) 3 (8,2) 2 (7,12) 2 (7,8) 4 (3,6) 3 (9,1) 2 (9,3) 2 | 27 |
Fourth shift | (2,1) 1 (7,1) 2 (3,4) 1 (8,12) 2 (1,12) 3 (11,7) 2 (9,5) 2 (9,2) 2 | 15 |
Algorithm | Parameters | Values Used |
---|---|---|
Genetic algorithm | Population size | 200 |
Turnover probability | 0.95 | |
Mutation probability | 0.0005 | |
Simulated annealing algorithm | Number of iterations | 200 |
Initial temperature | 5500 | |
Cooling factor | 0.9 |
Downward Shift | First Shift | Second Shift | Third Shift | Fourth Shift |
---|---|---|---|---|
Site 1 | 06:30 | 07:00 | 07:30 | 08:00 |
Site 2 | 06:55 | 07:32 | 08:03 | 08:25 |
Site 3 | 07:20 | 07:58 | 08:30 | 08:58 |
Site 4 | 07:53 | 08:26 | 08:48 | 09:18 |
Site 5 | 08:02 | 08:33 | 09:04 | 09:28 |
Site 6 | — | 07:06 | 07:36 | — |
Site 7 | — | 07:14 | 07:44 | — |
Site 8 | — | 07:24 | 07:54 | 08:18 |
Site 9 | — | 08:04 | — | 08:45 |
Site 10 | 07:45 | — | 08:40 | — |
Site 11 | 07:34 | — | — | — |
Site 12 | — | 08:20 | 08:54 | 09:12 |
Running line | 1-2-3-11-10-4-5 | 1-6-7-8-2-3-9-12-4-5 | 1-6-7-8-2-3-10-4-12-5 | 1-8-2-9-3-12-4-5 |
Upward Shift | First Shift | Second Shift | Third Shift | Fourth Shift |
---|---|---|---|---|
Site 12 | — | 07:16 | 07:46 | — |
Site 11 | — | — | — | 08:18 |
Site 10 | — | — | — | — |
Site 9 | — | — | 07:56 | 08:39 |
Site 8 | 07:32 | — | — | — |
Site 7 | 07:45 | 08:14 | — | 09:13 |
Site 6 | 07:53 | 08:22 | 08:53 | — |
Site 5 | 06:30 | 07:00 | 07:30 | 08:00 |
Site 4 | 06:40 | 07:10 | 07:40 | 08:10 |
Site 3 | 06:58 | 07:31 | 08:00 | 08:28 |
Site 2 | 07:25 | 08:00 | 08:30 | 08:58 |
Site 1 | 07:59 | 08:32 | 09:00 | 09:32 |
Running line | 5-4-3-2-8-7-6-1 | 5-4-12-3-2-7-6-1 | 5-4-12-9-3-2-6-1 | 5-4-11-3-9-2-7-1 |
Passenger Service Schedule | Regional Flexible DRT | Variable Route DRT (K-Means) | Variable Route DRT (DK-Means) | |||
---|---|---|---|---|---|---|
Cost/yuan | Time/min | Cost/yuan | Time/min | Cost/yuan | Time/min | |
First shift | 178.5 | 216.9 | 168.3 | 202. 5 | 158.6 | 190.9 |
Second shift | 182.2 | 220.4 | 178.5 | 218.8 | 173.2 | 209.8 |
Third shift | 176.8 | 212.2 | 171.9 | 208.9 | 163.4 | 195.1 |
Fourth shift | 155.3 | 174.5 | 138.1 | 160.2 | 132.1 | 154.2 |
Total | 692.8 | 824 | 656.8 | 790.4 | 627.3 | 750 |
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Li, P.; Jiang, L.; Zhang, S.; Jiang, X. Demand Response Transit Scheduling Research Based on Urban and Rural Transportation Station Optimization. Sustainability 2022, 14, 13328. https://doi.org/10.3390/su142013328
Li P, Jiang L, Zhang S, Jiang X. Demand Response Transit Scheduling Research Based on Urban and Rural Transportation Station Optimization. Sustainability. 2022; 14(20):13328. https://doi.org/10.3390/su142013328
Chicago/Turabian StyleLi, Peiqing, Longlong Jiang, Shunfeng Zhang, and Xi Jiang. 2022. "Demand Response Transit Scheduling Research Based on Urban and Rural Transportation Station Optimization" Sustainability 14, no. 20: 13328. https://doi.org/10.3390/su142013328