With the rapid development of the urban social economy, the travel demand of residents continues to increase, and the difficulty of getting a taxi is becoming challenging. Taxi is one of the important players in urban traffic, however, the transport capacity and demand at off-peak and peak hours do not always match. Due to the high operating cost, it is often in the empty-loaded state in the off-peak hours; in the peak hours, it is often difficult to take a taxi because a large number of taxis only carry one passenger. The traditional taxi ride-sharing behavior may cause excessive detour phenomenon, resulting in an increase in the passengers’ travel cost and time. For ride-sharing taxis, it has the advantages of intelligent scheduling and route selection, which can offer more reasonable costs and reduce the total operating costs, so as to improve the enthusiasm of the drivers and passengers, make reasonable use of traffic resources, reduce the emission of tail gas, protect the environment, and promote the sustainable development of urban traffic. Therefore, it is necessary to study the optimization model and algorithm of the ride-sharing route for ride hailing with the objective of the shortest ride-sharing route.
Normally, there is no sanitary situation concerns in ride-sharing. However, at present, protective measures need to be taken during the epidemic period, such as using plastic sheeting to isolate the interior of taxis and wearing masks for drivers and passengers. Even if there is no ride-sharing behavior, there are potential safety hazards in the case of an epidemic situation, and protective measures are still needed.
The study in this field evolved from simple ride-sharing feasibility to more sophisticated optimizations, such as the privacy of ride-sharing passengers, the design of ride hailing ride-sharing mechanism, the factors that affect the ride hailing service, and the characteristics of the usage behavior for ride-sharing [
1,
2,
3,
4]. Some mainly focused on ride-sharing, Altshuler et al. [
5] proposed a method for comprising a dynamically changing network using the taxi-rides, and analyzing the topological properties of this network. By analyzing the dynamics of these properties over time, they demonstrated their ability to accurately predict changes in the utilization of ride-sharing several hours in advance. Lee et al. [
6] presented a real-time taxi ride-sharing dispatching system for feeder buses. Chang et al. [
7] proposed a dynamic ride-sharing system with real-time vehicular information, including expounding its system architecture, message flows, and matching algorithms. Zhang et al. [
8] designed a taxi ride-sharing system consisting of a dispatch cloud server, passenger client and vehicle-mounted customized device. Daganzo and Ouyang [
9] presented a dispatching strategy, which only assigns the nearest suitable vehicle to a passenger along the shortest path. Shen et al. [
10] developed an online mechanism for ridesharing in autonomous mobility-on-demand systems. Amey et al. [
11] designed a mechanism for the on-demand first-mile ridesharing, a service that arranges real-time shared rides on very short notice to bring passengers to the nearby transit hub. In recent years, the research mainly focuses on the optimization algorithm of ride-sharing route. Among them, the leading idea was Genetic Algorithm. Zhou et al. [
12] considered the problem of ride-sharing route and cost sharing, constructed the optimization model with the minimum travel time cost as the objective function, and solved it by Genetic Algorithm. Zhang et al. [
13] built a multi-objective optimization model for solving the taxi ride-sharing with detour problem and designed a Genetic Algorithm to determine a fair pricing scheme for riders and drivers. In order to optimize the taxi ride-sharing route, Ma et al. [
14] built the taxi ride-sharing route optimization model with single objective and its extended model with multiple objectives respectively. Then, the model is solved based on the improved single objective Genetic Algorithm and the improved multiple-objective Genetic Algorithm. Rathod et al. [
15] described an improved ride-sharing system, and apply advanced Genetic Algorithm for finding optimal solution within a time. Although Genetic Algorithms have been widely used, there are still some other algorithms in use. Cheikh-Graiet et al. [
16] presented the so-called dynamic ride-sharing optimization system, which took decisions using a novel tabu search based metaheuristic. At the same time, they developed a simulation environment based on realistic ride-sharing demand data. Zhao et al. [
17] proposed a heuristic algorithm with the objective of minimizing the average arriving distance of all passengers in ride-sharing. Li et al. [
18] proposed a heuristic routing algorithm to identify the feasible routing paths for shared rides that interest both ride-sharing drivers and riders. The analysis of matching failure and ride-sharing ridership provided guidance on recommending stable matches and determining compensations in practice so as to maintain a balance between ride-sharing supply and demand. Tamannaei and Irandoost [
19] proposed an exact solution method based on Branch-and-Bound algorithm and a heuristic beam search algorithm which minimizes the costs of travel times, the vehicle use, and the vehicle delays. A bi-objective ride sharing matching model was proposed to maximize both the total generalized trip cost saving and the number of matches [
20]. The Monte Carlo Simulation (MCS) method was developed to evaluate the mean generalized trip cost. Additionally, they found a feasible ride-sharing match based on deterministic travel time can become infeasible in a stochastic ride-sharing system. Masoud and Jayakrishnan [
21] presented a real-time algorithm to optimally solve the ride-matching problem in a flexible ride-sharing system that maximizes the number of served riders in the system and minimized the number of transfers and waiting times for riders. At the same time, they found the proposed algorithm could solve matching problems in large-scale ride-sharing systems in a fraction of a second. Furthermore, allowing transfers could have a considerable impact on the number of served riders. Filcek et al. [
22] used dynamic programming and Dijkstra algorithm to solve the problem, and obtained the matching ride-sharing car and ride-sharing route. Ma [
23] proposed a solution algorithm based on optimal request-vehicle assignments for solving dynamic bi-/multi-modal ridesharing problems. After testing, this study provided a useful tool for real-time mobility-on-demand service planning and designed in a multimodal transportation network. Naoum-Sawaya et al. [
24] presented a stochastic mixed integer programming model and took into account the unforeseen event of vehicle unavailability, solved by heuristic algorithm. Lee and Savelsbergh [
25] started by formulating the matching problem as an integer program and designed a heuristic to solve. In addition, some scholars studied the pricing of ride-sharing taxis. For example, Zhang et al. [
26] mainly studied the taxi sharing routes and constructed the sharing expense model. Ma et al. [
27] discussed ride-sharing user equilibrium problem under OD-based surge pricing strategy. They discovered the ride-sharing under this strategy reduces not only the travel cost for travelers but also the deliberate detours. Di et al. [
28] introduced average vehicle occupancy ratio into cost calculation to represent more realistic aspects of ride-sharing costs subdued by ride-sharing drivers and passengers. Lei et al. [
29] proposed a multi-period game-theoretic model that addresses dynamic pricing and idling vehicle dispatching problems in the on-demand ride-sharing systems with fully compliant drivers and vehicles. It could help ride-sharing service providers achieve better system performance while facing spatial and temporal variations in ride-sharing demand.
In terms of the research on the ride-sharing optimization problem, many literatures focus on the system optimization. The consideration of the ride-sharing cost directly determines the interests of both drivers and passengers, but there is a game between them, so the simple cost-sharing method is usually adopted, which is controversial about fairness. However, it is a challenge to establish a fair ride-sharing route optimization model for the ride hailing, taking into account both system optimization and user fairness, and enhancing the rationality of ride-sharing. Therefore, although researchers have done some studies on taxi ride-sharing route optimization, they mainly focus on the algorithm itself. Different algorithms or operators are designed to solve the problem efficiently. The principle of system optimization and user fairness is rarely considered in the modeling. In addition, there is also a lack of constraints on the benefit of drivers and ride-sharing passengers. In view of the above gaps, this paper contributes to the existing literature on ride-sharing for ride hailing in threefold:
The research results show that the implementation of ride-sharing ride hailing mode can reduce the empty-loaded rate of vehicles and improve the occupancy rate of passengers. It can not only create more benefits for passengers and drivers, but also realize the reasonable allocation of resources. At the same time, it is conducive to moderate control of taxi scale, relieve urban traffic pressure and energy consumption, environmental pollution and so on, which promotes the sound and stable development of urban economy and the green sustainable development of urban traffic.