1. Introduction
With the improvement of living standards and the tendency of the road network to be saturated, traffic accessibility is no longer the main focus for residents’ travel. In order to improve the timeliness and flexibility of bus operation, some scholars have focused on the research of dynamic dispatch on the basis of static dispatch.
Conventional dynamic dispatch strategies include holding, stop-skipping, signal priority, etc. [
1,
2]. Some scholars have undertaken the following research on the single dynamic dispatch strategy of public transport.
Some scholars put forward a stop-skipping strategy that is robust to travel time in view of the common phenomenon that people and vehicles wait for each other during peak hours [
3,
4,
5]. In order to calibrate the arrival time, some scholars proposed a dynamic holding strategy, which proved that this strategy can significantly improve service efficiency [
6,
7,
8]. Based on bus signal priority systems (BSP), some scholars discussed different types of priority control strategies and evaluated the priority process [
9,
10,
11].
However, a single dynamic bus scheduling strategy is not suitable for dealing with the conventional random disturbance. At this time, the quality of the public transport service cannot be significantly improved, which is counterproductive [
12,
13]. To deal with this situation, some scholars have studied combined dynamic scheduling strategies based on a single dynamic scheduling strategy.
In order to maintain the stability of the operation interval and reduce the average waiting time of passengers, some scholars proposed a cooperative control strategy of holding and stop-skipping considering the limitation of bus capacity [
14,
15,
16]. On this basis, Zhang et al. [
17] developed an optimization scheme for a real-time simulation model of holding and stop-skipping. Milla et al. [
18] verified that the combined strategy is better than a single strategy in saving waiting time through global positioning system (GPS) technology and simulation tests.
In order to ensure that buses pass through the intersection, some scholars have proposed an intersection control method combined with speed guidance to provide signal priority for buses. Bie et al. [
19] developed a dynamic headway control method for high-frequency routes with bus lanes. The results show that the proposed method can reduce the bus distance bias for all survey periods. Wu et al. [
20] proposed a new method to optimize bus stop waiting time and give priority to buses at segregated intersections. Finally, the potential of the proposed method to be applied to the bus priority control system is demonstrated. Seredynski et al. [
21] proposed to combine the driver advisory system (DAS) with signal-priority control request, and the results showed that the travel time can be significantly reduced compared with using BSP alone.
In order to solve the problem of delay at intersections and give more road priority, some scholars have proposed a signal-priority control method for dynamic bus lanes [
22,
23]. On this basis, Levin and Khani [
24] proposed a cellular transport model for dynamic bus lanes, which was effectively applied in Austin. Shu et al. [
25] proposed a variable bus approach design with a bus guidance and priority control model, which can reduce the delays of through and left-turn buses and provide optimal signal priority for buses.
In addition, some scholars have undertaken the following research combining signal priority and holding. Zimmermann et al. [
26] proposed a combination strategy of holding, speed adjustment and signal priority, and verified the effectiveness of the combination strategy in Quebec City, Canada. Koehler et al. [
27] proposed a combined control strategy of holding and signal priority to minimize the total delay of passengers, and verified the effectiveness of the proposed strategy in Blumenau, Santa Catarina, Brazil.
To sum up, the research results of the combined dynamic scheduling strategy are rich, but there is still a gap in the combined research of stop-skipping and signal priority in peak hours. At the same time, the signal priority of the intersection is closely related to the bus arrival time, so it is necessary to conduct an overall study of the station and intersection. This study combines speed adjustment and signal priority for coordinated control in the bus stop-skipping mode to fill the gap in this field.
This research mainly focuses on the following three aspects:
Combining the passenger flow of the station at the peak of the line to make the decision of stop-skipping.
Combining the triggering mechanism of the intersection with the arrival time of the bus at the intersection and the signal period.
Combining the cooperative control scheme of the intersection with the speed adjustment.
4. Algorithm Choice
Cruz-Chávez et al. [
36] applied the simulated annealing algorithm to the flexible shop scheduling problem and obtained good solutions. However, the algorithm has low computational accuracy and poor global search ability. Shakibayifar et al. [
37] solved the train rescheduling problem using a variable neighborhood search algorithm, but the algorithm has low convergence. Pecin et al. [
38] used the branch cut-price algorithm to improve vehicle path planning with different capacities, but the convergence of the algorithm still needs to be improved when solving multi-objective complexity problems.
In contrast, the genetic algorithm is a method of searching for optimal solutions by simulating the evolutionary process of natural selection and survival of the fittest. It has the following advantages: (1) It adopts random probability to guide its search direction in the solution, which is relatively objective [
39]. (2) It has strong global search ability when solving multi-objective optimization problems [
40]. (3) Genetic algorithms have strong robustness and high convergence in practical applications [
41].
Therefore, the genetic algorithm was used to solve the cooperative control model. The solution process was divided into the following stages. (1) According to the historical passenger flow data, the stop-skipping decision was made (see
Figure 4a). (2) According to the online passenger flow data, the signal-priority decision and speed adjustment were made on the basis of the stop-skipping decision (see
Figure 4b).
- (1)
Coding method
If there are m vehicles and n stations, the encoding length is m × n, which is 0–1 encoding; if there are m vehicles and q intersections, the encoding length is m × q, which is 0–1 encoding.
- (2)
Variation and crossover
Gene pairing was performed by single-point mutation and two-point crossover. Two parent chromosomes were randomly generated for pairing, and a certain crossover probability was selected to generate two daughter chromosomes.
- (3)
Function calculation
Its objective function value was calculated according to
Section 3.3, and the fitness function can be expressed as:
where
represents the fitness value of chromosome
,
represents the objective function of chromosome
, and
represents the penalty value of chromosome
.
- (4)
Select
The core idea of genetic algorithm is roulette selection, which means that the probability of an individual being selected is proportional to the value of its fitness function. Assuming that the population size is
, the fitness function is expressed as
, and the probability of being selected and inherited to the next generation is
:
6. Conclusions
In order to improve the timeliness and flexibility of public transport during peak hours, the coordinated control method of signal priority and speed adjustment on the basis of stop-skipping was studied. The contributions of this research are as follows:
First of all, this study started with the time correlation between vehicle arrival stations and intersections, and made a stop-skipping decision based on the historical passenger flow data.
Secondly, according to the online passenger flow data and signal cycle characteristics, the time when the vehicle arrived at the intersection was divided into four sections, and the signal-priority decision was made.
In addition, static and dynamic cooperative control was carried out in combination with signal priority and speed regulation. From the perspective of passenger delay time cost and enterprise operation cost, the effectiveness of the collaborative optimization method was proved, providing a theoretical foundation for the formulation of the priority trigger mechanism and scheme of the intersection signal.
In short, the proposed combined scheduling strategy can improve practical optimization methods for bus operation during peak hours. The disadvantage is that only two phases were considered, and the influence of social vehicles was ignored. Next, we will further integrate social vehicles and explore the study of four phases.