## 1 Introduction  
Giving priority to the development of public transport is an indispensable way to enhance resource utilization and promote sustainable transport development. However, current conventional buses are seriously uncompetitive due to various problems such as overcrowded carriages, long waiting times for passengers, and low levels of traveling comfort. To solve the above problems, demand-responsive transit (DRT) has emerged. DRT is a mode of public transportation to pick up and drop off passengers according to their travel requests at specific locations and does not have fixed routes and stops. It is flexible in terms of arrival time and operating routes and can help to improve the competitiveness of public transport, ease urban traffic congestion, and reduce traffic pollution. In the 1970s, [PERSON] [1] first proposed the concept of DRT and successfully conducted it in a small city. The Transit Cooperative Research Program (TCRP) documents six types of DRT service: request stops, flexible route segments, route deviation, point deviation, zone routes, and demand-responsive connector service [2]. Entering the 21 st century, the rapid development of emerging technologies such as artificial intelligence (AI) and big data provides a technological foundation for the realization of DRT. Therefore, how to efficiently and stably carry out the operation of DRT has become an urgent task in the study of urban public transport. Now, there has been a proliferation of research and practice on DRT. As an important part of the research on DRT, the DRT scheduling problem has achieved many results after years of development. The latest research progress is introduced from three aspects of optimization objectives, constraints, and solution algorithms as follows. 1. Optimization Objectives
2. Optimization objectives mainly include considering the costs of passengers and operators, energy consumption, and so on. Among them, the comprehensive consideration of the costs of passengers and operators is the mainstream research direction. [PERSON] et al. established a DRT scheduling equivalent decomposition model with minimum vehicle operating mileage and minimum use of vehicles as the objective function. They designed a distributed column generation algorithm to solve the problem [3]. [PERSON] et al. researched the dynamic path optimization problem with a fuzzy time window, established a multi-objective model intending to minimize the operating cost, and used a genetic algorithm to solve the problem [4]. [PERSON] et al. combined demand-responsive buses with conventional buses and used the average waiting time of passengers as the optimization objective, and finally found that the average waiting time of users was lower than that of the two modes alone [5]. [PERSON] et al. proposed a bus route optimization method based on the reliability of shortest paths to efficiently and quickly complete the passenger route optimization problem in a complex and changeable traffic environment. The method takes the minimization of total passenger and operating costs as the objective function and adopts the forbidden search algorithm to solve the problem [6]. [PERSON] established a VRP model based on a single-vehicle DRT path optimization problem to minimize the total fleet operating time and the passenger service level reduced by early or delayed vehicle arrivals [7]. [PERSON] et al. proposed a mixed integer linear model for DRT service that simultaneously minimizes the total mileage operating cost and maximizes passenger satisfaction [8]. [PERSON] et al. considered both operator and passenger benefits to construct a multi-objective route optimization model with the minimum operating and passenger costs [9]. In the study considering minimum energy consumption, [PERSON] et al. embedded the eco-path strategy into the DRT service and integrated the vehicle dynamics module and the fuel consumption module for different traffic conditions and road types, which can significantly reduce energy consumption and emissions [10]. [PERSON] et al.