Demand Responsive Transit (DRT) responds to the dynamic users’ requests without any fixed routes and timetables and determines the stop and the start according to the demands. This study explores the optimization of dynamic vehicle scheduling and real-time route planning in urban public transportation systems, with a focus on bus services. It addresses the limitations of current shared mobility routing algorithms, which are primarily designed for simpler, single origin/destination scenarios, and do not meet the complex demands of bus transit systems. The research introduces an route planning algorithm designed to dynamically accommodate passenger travel needs and enable real-time route modifications. Unlike traditional methods, this algorithm leverages a queue-based, multi-objective heuristic A* approach, offering a solution to the inflexibility and limited coverage of suburban bus routes. Also, this study conducts a comparative analysis of the proposed algorithm with solutions based on Genetic Algorithm (GA) and Ant Colony Optimization Algorithm (ACO), focusing on calculation time, route length, passenger waiting time, boarding time, and detour rate. The findings demonstrate that the proposed algorithm significantly enhances route planning speed, achieving an 80–100-fold increase in efficiency over existing models, thereby supporting the real-time demands of Demand-Responsive Transportation (DRT) systems. The study concludes that this algorithm not only optimizes route planning in bus transit but also presents a scalable solution for improving urban mobility.

With the recent development of Internet/Internet of Things technology, more tasks can be performed through portable smartphones, and the emergence of shared bicycles, shared taxis, etc., has also brought revolutionary changes to the way people travel. As a result of these personal devices and the shared mobility, smartphones enable various services for public transportation, which include the schedule-checking, the routes-checking of bus, and the confirmation of the passenger numbers. On the other hands, Demand Responsive Transport (DRT, Demand Responsive Transit is a transit service operating in response to calls from passengers or their agents to the operator, who schedules a vehicle to pick up the passengers to transport them to their destinations) has been welcomed by many passengers for its economical, flexible, and environmentally friendly features, and has also greatly changed the way people travel [

DRT buses are different from the private cars or bicycles in the following aspects. First, the routes of DRT buses are undetermined and continuously vary according to user’s demand. Second, every passenger has a specific origin and destination. As passengers board and disembark, the composition of users is constantly changing, which gives DRT buses a notable multi-origin and multi-destination characteristic during transportation [

Nevertheless, due to the efforts of numerous scholars over the past several decades, various route planning algorithms have been developed for practical use in public transportation, such as those based on Genetic Algorithm (GA) and those based on Ant Colony Optimization (ACO) or Simulated Annealing (SA) [

To address these issues, this study aims to concretize the research question as follows: How can an optimal route for a bus be planned in a complex road network, given that the number and locations of origins and destinations change dynamically? The contributions of this study can be summarized as follows. First, this paper proposes a novel dynamic route planning algorithm that is real-time, efficient, and logically straightforward. Second, this paper compares the proposed algorithm with popular GA-based and ACO-based route planning schemes under equivalent conditions. Third, through experiment data, the high efficiency and superior performance of the proposed real-time dynamic route planning algorithm were demonstrated.

This paper is organized as follows: In

Bus route planning algorithms can be improved using algorithms for the Vehicle Routing Problem (VRP, Vehicle Routing Problem is a combinatorial optimization problem of finding a set of routes for a fleet of vehicles that minimizes travel time) and the Traveling Salesman Problem (TSP, Traveling Salesman Problem is the problem of finding the shortest path that visits a set of customers and returns to the first). The TSP is a special case of the VRP, and it has been proven by Gaery and others that the TSP is an NP-hard problem [

For example, in an article published by Asih et al., they compared GA, ACO, particle swarm optimization, and SA algorithms with two distinct sets of cases to verify their performance. The results indicated that both ACO and SA algorithms consistently found the shortest distances in the two different case scenarios [

After a detailed analysis of the characteristics of the DRT bus route planning problem, this study focuses on multiple origins, multiple destinations, dynamic changes in starting/ending points, and the need to balance user riding time and waiting time as research priorities. This study proposes a novel real-time dynamic route planning algorithm that addresses these issues efficiently while considering user experience. By designing comparative experiments, this paper scientifically compared and analyzed data with widely used GA and SA, thereby demonstrating the effectiveness of the proposed real-time dynamic route planning algorithm.

In this section, a real-time dynamic route planning algorithm suitable for DRT buses is proposed, and the principle of the algorithm is explained in detail. The algorithm is divided into three parts. First, bus stops are mapped based on road network nodes. Second, user-riding demands are dynamically managed through a simple queue design. Finally, starting from the current location of the DRT bus, the algorithm employs a real-time metaheuristic route search based on a multi-objective approach for the target bus stops contained in the queue, ultimately achieving dynamic route planning. The algorithm is illustrated in

The proposed dynamic route planning algorithm mainly consists of the following four steps:

Generate a target queue and place all received user starting stations in the target queue.

Use the multi-objective A* algorithm to search for routes in the stations within the target queue.

Obtain the current latitude and longitude of the bus to determine its road link node.

Calculate the heuristic function

Obtain the bus stop with the smallest heuristic value in the target queue as the next stop for the bus and generate the route.

Repeat steps A–C to generate the complete bus route between the bus stops.

After the bus arrives at the user’s bus stop, remove the user’s starting bus stop from the target queue and add the corresponding destination stop to the target queue collection.

Repeat steps 2 and 3 to generate/update routes in real-time.

In the above steps, note that all processing occurs during the bus’s journey. Therefore, the routes generated by the algorithm constantly change based on the received user riding demands. Whenever a new user riding request is received, the algorithm performs a real-time calculation to update the route, ensuring that the bus always travels according to the latest and most optimal route promptly.

The process of mapping bus stops in the road network is necessary before route finding can begin. According to the raw data obtained from the Korean standard node link database, a road in the real world is saved in a bidirectional and segmented manner in the computer database. In other words, a road in the real world is divided into multiple “links” in the positive and negative directions and “nodes” at both ends of the links in the computer world. In addition, bus stops are located adjacent to roads, but their positions are not exactly on the road link nodes. Therefore, the algorithm needs to map the bus stop locations in the road network before effectively planning the route.

In the process of mapping bus stops to the existing road network, as illustrated in

This method ensures that a bus stop is accurately mapped to the correct road link, allowing for a more precise representation of the road network structure and ultimately contributing to the efficiency of the proposed dynamic route planning algorithm.

Once the bus stops have been mapped to the road network, the next step is to generate a weighted network for route planning. The weights assigned to the network include travel time, distance, and other factors that may influence route selection, such as traffic conditions or road restrictions. By incorporating these weights into the network, the proposed algorithm can search for the most efficient and optimal routes based on various criteria. In this paper, this study uses the shortest travel time

As a result of the mapping of bus stops and the generation of a weighted network, a simple digital road connectivity network with the shortest travel time as weights is generated. Subsequent steps will then perform route planning based on the target queue using the weighted network. In summary, mapping bus stops to the road network and creating a weighted network are fundamental steps in constructing the proposed real-time dynamic route planning algorithm. These steps enable the algorithm to plan routes accurately based on the actual road network structure and various factors influencing route selection.

The multi-objective A* algorithm based on the target queue is the core component of the proposed real-time dynamic route planning algorithm. It is not a single process but rather a treatment throughout the implementation of the route planning algorithm. In particular, steps 1 and 3 involve dynamic modification of the target queue to meet dynamic user boarding demands.

For example, in the road network shown in

Add

Remove

After

In the real-time dynamic route planning algorithm, besides the real-time and dynamic processing of the target queue (

In this study, considering the characteristics of multiple target bus stops in the target queue, the multi-objective A* algorithm performs the following calculation processing to determine the driving order of bus stops. First, according to the bus stops saved in

As shown in

Because the heuristic function used by the original A* algorithm calculates the distance from the current node to the target node as the estimated cost [

The worst-case scenario for turns is an angle of 180°, i.e., a U-turn is required. In the case of a U-turn, the vehicle returns along the original route, and the estimated cost function becomes twice the original distance. The function

The time

To objectively evaluate the proposed real-time dynamic route planning algorithm, this study designed experiments based on the single-variable testing principle according to the requirements of the used scenarios. This study defined the tested scenarios as mixed scenarios. As the name suggests, this scenario includes users who have made reservations to use the vehicle in advance, as well as users who appear during the movement of the vehicle and issue real-time ride requests. In addition to the simulation test, this study also conducted a three-month real test of students riding the shuttle bus of Keimyung University in South Korea from November 2021 to February 2022. This study used real student travel data.

In this paper, this study selects the ride requests of 40 students as the test source. This study uses the ride requests of the first 20 students as reservation users, and the ride requests of the last 20 students are randomly issued after the vehicle operation starts. In this way, the data of 40 students can be used to not only test the algorithm’s response to the reservation scenario but also to test the algorithm’s processing capabilities during the real-time operation of the bus. Based on the ride requests of 40 students, this study provides the latitude and longitude distribution map as shown in

For the comparison object and evaluation standard of the algorithm, researchers frequently use different test standards. In their study, Lu et al. mainly focused on the travel distance in the tested items [

Combined with the description in the second section, this study selected route planning algorithms based on GA and ACO as the comparison objects. Through an objective comparison and analysis of the algorithm on test data, the proposed algorithm can be accurately evaluated. The algorithm calculation environment of this study was conducted in the Windows 10 Edu x64 version environment, with hardware consisting of an Intel Core i7-9700K CPU, 16 GB memory, and an NVIDIA RTX2080Ti graphics card.

As mentioned earlier, this study chose three sets of travel data from 20 students each, out of approximately 300 students’ travel data collected over three months, and organized the data according to travel time to satisfy the three test scenarios. As the proposed real-time dynamic route planning algorithm is based on the multi-objective A* algorithm, this paper referred to the algorithms as “MO A*,” “GA,” and “ACO” for ease of comparison in the experimental data.

For the GA and ACO used as comparative objects, this study directly implemented the GA by referring to the research on DRT bus planning by Jin et al. [

10000 | ||

Number of random tours to create before starting the algorithm. | ||

10000000 | ||

Number of times to perform the crossover operation before stopping. | ||

5 | ||

Number of tours to examine in each generation. The top two tours are chosen as the parent tours whose children replace the worst two tours in the group. | ||

3 | ||

Odds that a child tour will be mutated. | ||

1500 | ||

The number of ants that can be used when initializing the algorithm. | ||

600 | ||

The chemical traces left behind by simulated ants as they search for food are used to guide subsequent ants in their path selection. | ||

200 | ||

Threshold to stop finding routes. | ||

2 | ||

Determines the degree of influence of pheromone concentration on ants’ path selection decisions. | ||

3 | ||

It determines the degree of influence of heuristic information on the path chosen by ants. | ||

0.3 | ||

Controls the evaporation rate of pheromones. Gradually reduce the pheromone concentration along the path, thereby reducing the impact of past decisions on future decisions. |

During the testing process, since the purpose of this study is to propose a route planning algorithm that can satisfy DRT services in real time, the dynamic and real-time nature of the algorithm is crucial. Consequently, in the tests in mixed scenarios, this study primarily analyzed and evaluated the computation results within 10 s for each algorithm.

In the mixed scenario, this study divided the boarding data of 40 users into two parts: One part accounts for users who made reservations in advance, and the other part for users of boarding requests were received in real-time after the DRT bus departs. In such a test scenario, first, compare the total distance and time of routes planned by different algorithms. As shown in

In terms of specific data, as depicted in

In terms of passenger user experience, as shown in

In terms of the average detour rate of users, the ACO and MO A* algorithms have maintained consistently low detour rates of 3.17 and 2.97, respectively, showing a steady linear upward growth trend. In contrast, the GA has the characteristics of a disorderly rise. To explain in particular, the definition of the user’s average detour rate is defined as the ratio of the actual moving route distance of users taking mobility DRT to the moving route distance of users taking ordinary DRT buses to their destinations, that is:

From

In terms of the calculation performance of route planning, as depicted in

In addition, the algorithm goal is not only to be able to dynamically handle the user’s request to get on and off the vehicle, but also to meet the requirements of real-time calculation and real-time response. However, judging from the above measurement results, ACO and GA are unable to meet the immediacy of Mobility DRT bus route planning. In contrast, the algorithm proposed in this study can process all data within 0.2 s, fully satisfying the real-time requirements for Mobility DRT bus route planning. Therefore, considering the evaluation criteria from multiple perspectives, the proposed MO A* algorithm can sufficiently meet the needs of DRT bus route planning.

Finally, since the GA algorithm is at a disadvantage in each calculation result, it is necessary for us to analyze the reasons. As mentioned before, this may be because both the ACO algorithm and the GA algorithm are designed to find the optimal solution. In theory, the results generated by these algorithms should improve with the passage of computing time [

To confirm the aforementioned reasons, this study presents a trend chart of the algorithm results over time for 20 user transportation demands, as illustrated in

To summarize, the proposed real-time dynamic route planning algorithm is always satisfactory in mixed scenarios. Although its planned route is not always the “shortest route,” the distance difference within 3–5 km is acceptable, and it can exhibit excellent performance in other user experience aspects and provide a better user experience. In addition, the performance of the proposed algorithm is fast, 82.5 and 97.2 times faster than the ACO and GA algorithms and it can complete route planning for bus users within 1 s or even 0.2 s. Moreover, the algorithm shows stability of calculation in test scenarios, which is incomparable to GA- and ACO-based route planning algorithms. Based on this result, this study also believes that the MO A* algorithm will be able to handle it perfectly if it is a full reservation scenario or a full real-time request scenario.

Recently, on-demand mobility services have been developed, and it is expected that the demand for the services will further increase with the personal requirements in the future. The on-demand mobility service based on DRT buses will be more widely used due to its more economical and affordable characteristics. For DRT bus services to operate stably and efficiently, it is critical to reasonably allocate and dispatch vehicles, and to conduct real-time route planning according to passenger’s requirements.

In this study, the operating characteristics of DRT buses and the algorithm’s requirements can be summarized as follows: First, it needs to be able to update routes in real time; Second, it needs to be able to dynamically respond to users’ ride requests. Based on the characteristics of DRT buses, this study designed an algorithm (Real-time Dynamic Route Planning Algorithm) and explained its design in detail. Also, this study verified the suggested algorithm based on the real user travel data. To compare its results, a comparative test was conducted with the existing solutions based on the ACO algorithm and the GA algorithm, and both the total length and the generation time of the route, as well as the average travel time and average detour rate of users, were evaluated. The suggested algorithm can implement route planning and vehicle scheduling within 0.2 s. Based on the special structure this study proposed, the efficiency of route planning is improved by 82.5 times and 97.2 times compared with the ACO algorithm and GA algorithm, respectively. It can complete dynamic route planning for 40 passengers in 0.2 s. This calculation performance fully meets the real-time calculation requirements of on-demand DRT buses.

However, the suggested algorithm can be improved further. First, the working principle of the proposed algorithm is mainly based on the queue-based multi-objective A* algorithm. Therefore, with the increase in the number of passengers, the algorithm has to be rerun to plan a new route. This can result in heavy computation and increase more memory consumption when a new user takes public transportation. Second, in the actual operation of the bus, if the bus receives a passenger request from a bus stop less than 100 m ahead, the bus may be driving in the central lane because the bus driver has not made corresponding preparations in advance. Changing lanes to the bus stop can be difficult and dangerous, which may result in the user’s boarding request being ignored or assigned to the next bus. This results in a certain degree of resource waste and a negative user experience, as users may feel ignored when they see the bus drive away without stopping even though they sent a boarding request before the bus arrived. Third, although the algorithm can handle regional-level DRT bus operations, for broader practical operations, it still needs to expand the road network and add multiple DRT buses for joint operation testing to improve the algorithm to enhance the robustness of the algorithm. Besides the issues above, we plan to operate the algorithm in a wider urban transportation network and also plan to apply the algorithm to games in future work.

Not applicable.

Not applicable.

The authors confirm contribution to the paper as follows: Study concept and design: Hongle Li, SeongKi Kim; Algorithm development and testing: Hongle Li; Manuscript supervision: SeongKi Kim; All authors reviewed the results and approved the final version of the manuscript.

Road information data comes from the national standard node link database of the Korean National Transportation Information Center. The source data of the test comes from the travel records of students participating in the test. Under the premise of academic research, the data set can be obtained by contacting the corresponding author (

The authors declare that they have no conflicts of interest to report regarding the present study.