1. Introduction
With China’s rapid development of urbanization and frequent changes in residents’ travel demand, it is difficult for traditional public transport to adapt quickly [
1]. Some bus lines are too long with many stations, and the number of passengers at some stations along the line is uneven. As a result, the resources of the public transport system are not fully utilized, and the development of new transport modes is becoming increasingly urgent. Urban residents mainly travel short and medium distances, taxis have high flexibility but their carrying capacity is small, and the subway has a large carrying capacity but is not flexible enough. However, the urban public transport system has the advantage of wide coverage, a large carrying capacity, and high flexibility [
2]. Therefore, it is necessary to combine the existing public transport system of the city to realize the flexible setting of stations and driving routes for vehicles according to the needs of passengers to make them more flexible.
Demand-responsive transport is flexible public transport that provides special travel services for passengers with similar travel needs (starting and ending stations, travel time, etc.) according to the requests sent by passengers [
3]. Its specific characteristics are still “public transportation”. It uses fixed stations and completely unfixed lines to provide citizens in the area with a new type of “public” travel service that can call or book in real time. The system aggregates and matches in real time to generate dynamic lines in real time. Its new service characteristics between private cars and traditional public transport can meet the diversified travel requirements of passengers, especially the high-quality travel requirements, and change the travel mode of some private cars to public transport. Shenzhen, Beijing, Xi’an, and other cities have begun to implement this transit mode; the number of registered users has increased continuously, which has been recognized by the market. However, considering the problems of operating costs and profits, the ticket price of demand-responsive public transport is generally slightly higher than that of conventional public transport, and the vehicle operation time is generally in the morning peak and evening peak hours. The people served are those who make reservations in advance or go to work, so the applicable range of passengers is small [
4]. Poor punctuality and high operating costs keep emerging. In urban areas with incomplete road networks and small populations, difficulties include lines being ignored, low occupancy rates, and insufficient passengers signing up for lines. Therefore, it is of great significance to deeply study the dispatching and optimization of demand-responsive transit and improve the service level of demand-responsive transit.
Flusberg [
5] was the first to explore the public transport service mode, propose a flexible public transport mode, and carry out the actual operation. Later, some scholars studied this public transport service mode [
6,
7,
8,
9,
10,
11,
12]. Through comparison and simulation experiments, they found that demand-responsive and traditional public transport have advantages under different levels of passenger demand. Nourbakhsh et al. [
13] studied the departure interval and line setting in a rectangular area with low-density demand. Jiang et al. [
14,
15,
16] focused on the dispatching and route optimization of the demand-responsive public transport of the feeder type. Ma et al. [
17] established a model with passenger travel cost, took the operating income and cost as optimization objectives, and designed a genetic algorithm to analyze the customized vehicle route scheme. Boyer et al. [
18] mainly considered flexible public transit management, analyzed the human factors related to demand-responsive transit dispatching, and discussed the various impacts of drivers’ rest time, continuous working time, and overtime on dispatching. Nam et al. [
19] studied the vehicle dispatching model with the objective of minimizing the environmental cost of fuel consumption and carbon emissions from the perspective of environmental protection. Bellini [
20] established a DRT vehicle dispatching model. Schilde [
21] studied the impact on DRT service levels under different speeds.
In the 1990s, Malucelli et al. [
22] established a public transport dispatching model with maximum revenue for MAST (Mobility Allowance Shuttle Transit) under different operating environments. To effectively solve the problems related to demand-responsive public transportation, Pan et al. [
23] established a bi-level planning model that can optimize the vehicle operation lines and vehicle service scope. Huang et al. [
24] proposed a dynamic insertion method to deal with the model of the dynamic phase, which integrated the dynamic decision-making process of operators and passengers and solved the passenger travel demand in low-demand areas. Huang [
25] studied a demand-responsive transit (DRT) service to meet the flexibility and convenience requirements of passengers. Nickkar [
26] explored whether demand-responsive feeder transport can be optimized by picking up and sending passengers through door-to-door services or temporary stops and developed a model using meta-heuristic methods. Aalfa et al. [
27] adopted the method of combining 3-Opt and annealing algorithms to solve the large-scale search problem in the VRP solution process, but it is very difficult to solve accurately, which is almost impossible under the current conditions. In the vehicle routing optimization problem, Wang et al. [
28] designed a dual genetic algorithm and conducted an experimental comparison and analysis of demand-responsive vehicle dispatching optimization under the simultaneous pickup/drop-off mode. Compared with the separate pickup/drop off mode, the simultaneous pickup/drop off mode has specific and better seat utilization and cost-saving advantages. Lyu [
29] built an optimization model aimed at maximizing the revenue of operators and designed a heuristic algorithm based on the travel choice behavior of passengers. An [
30] put forward the interval uncertainty stochastic theory to optimize the public transit network. Nassir [
31] optimized the customized transit network through the impedance access theory. Kerkma [
32] put forward the optimization theory of public transport networks combining multi-dimensional space.
To sum up, the existing studies on responding to passenger demand are often determined by experience, which is subjective and lacks quantitative research. Some studies assume that the system only operates a single vehicle, passengers at the same station have the same travel demand, and that there is unlimited vehicle capacity. These research scenarios are too idealistic, and China’s actual road network has not been considered, ignoring the personalized time-window requirements for passengers. Therefore, this paper proposes a high-probability station extraction strategy by analyzing the spatial and temporal distribution of passenger demand and the origin and destination (OD), according to the historical ride request frequency of the station and extracted high-probability demand stations. Under the constraints of vehicle capacity and passenger demand time, a two-phase demand-responsive transit dispatching and routing optimization model was established. Finally, a static vehicle dispatching decision scheme was generated that can cover all high-probability stations, continuously adjust the route scheme through dynamic route optimization, and finally generate a dynamic optimized route that can respond to passenger travel in real time. This research could improve the decision-making efficiency of vehicle dispatching and the utilization rate of buses. It is of great significance to advocate public transport priority and green low-carbon travel.
3. Algorithm Design
3.1. Two-Phase Dispatching Optimizes Model Algorithm Flow
The algorithm consists of two phases: static vehicle dispatching and dynamic route optimization. The static dispatching is a linear integer programming model; this paper uses a genetic algorithm based on LNS Strategy to solve the static vehicle dispatching problem and uses destructive and repair operators to improve the solution quality; the main framework is like that of traditional genetic algorithms. Dynamic route optimization adopts a precise planning algorithm to insert the obtained dynamic requirements into the initial route and continuously update the route.
Figure 1 is a two-phase dispatching optimization process.
3.2. Algorithm Description
- (1)
Coding
The initial route of demand-responsive transits is arranged in a certain order by multiple stations,
indicates a high probability of boarding at a station in the service area, and its corresponding drop-off station is numbered with
. The chromosome is encoded as an integer; when the number of stations is
, the maximum number of vehicles used is
, the length of the chromosome is
, and
divides the number of stations into three segments.
running routes are generated, as shown in
Figure 2.
- (2)
Initial populations
The quality of the initial population will affect the search efficiency of the genetic algorithm; to improve the quality of chromosomes in the initial population and ensure population diversity, the following methods are used to generate chromosomes in the initial population:
STEP1: Randomly disrupt the order of OD pairs for high-probability travel.
STEP2: A pair of high-probability travel OD are randomly selected from all passengers to form the first pair of stations for the first vehicle.
STEP3: Select the next pair of high-probability OD, insert them into the stopover route of the vehicle, abide by the principle of the minimum amount of change in the running distance after insertion, then determine whether the vehicle capacity constraint is met, and if the passengers’ travel time windows constraint is satisfied, adjust the initial route of the vehicle; otherwise, insert the high-probability station pair into the stopover route of the next vehicle. Repeat the above process until the best insertion location that satisfies the constraint is found.
STEP4: Select the remaining high-probability travel OD pairs in turn and repeat STEP3 until all high-probability travel pairs are inserted into the vehicle’s initial route.
- (3)
Adaptation function
To ensure that each delivery route can meet the vehicle capacity and passengers’ travel time-window constraints, using the penalty function
to solve it, we set the violation capacity constraint weight
as 10, and the violation time window constraint weight
as 100. Because the objective function should be minimized, the adaptability function is set to the reciprocal of the penalty function, that is,
. The penalty function equation is:
where
is the penalty function,
is the total operating mileage of the vehicle
,
is the capacity constraint value violated by vehicle
,
is the sum of passengers who violate the time constraint of vehicle
, and the fitness function is the reciprocal of the penalty function.
- (4)
LNS local search operation
The local search uses the destruction operator to remove a number of passengers from the current solution through the similarity equation and then uses the repair operator to reinsert the removed passengers back into the position that causes the least increase in vehicle distance while satisfying the vehicle capacity constraint and the passenger time constraint.
5. Conclusions
To study the operational decisions of dynamic demand response transits, a two-phase optimization model was established, including static vehicle dispatching and dynamic route optimization. Using the vehicle route planning method of the genetic algorithm, a dynamic optimization model of an accurate dynamic programming algorithm is designed for the optimization route, combined with the existing initial operation route, timely response to real-time requests, and true realization of the important feature of demand response.
Aiming at the dynamic transit being highly discrete and with random passenger demand, the high-probability station extraction strategy is proposed, and the dynamic demand response transit service and operation strategy is optimized. In total, 11,909 real data in September in the dynamic transit operation area of a certain district were selected, and 232 valid data at a certain time were extracted according to the actual operation situation; it was found through programming numerical experiments that the genetic algorithm had a small deviation from the solution result of the route and good stability. After extracting the high-probability stations, the operating costs and passenger experience have been significantly optimized; the two-phase dispatching optimization model can maximize the use of vehicle resources, further save operating costs, have feasibility and high use value, and provide application guidance for vehicle dispatching and route optimization.
Due to the small operation data of the study area, small number of passenger flow requests, and number of isolated requests generated, the model focuses on considering the passenger experience, so the full load rate and response rate of the system are not high enough. We will continue to conduct in-depth research on how to select the operating area in the future to make the two achieve their optimal values. Another research direction is the integrated planning of demand responsive transport system and bike-sharing system, one of the fastest growing transportation modes [
33], to further improve non-motorized travel efficiency.