## 1 Introduction  
A smart factory usually has a series of machining centers, industrial robots, storage cracks, and mobile robots. The mobile robots can assist the industrial robots and machining centers with complex manufacturing jobs by delivering raw materials and parts and inspecting the status of production lines [1, 2, 3]. As the number of robots and tasks grows, the scheduling and planning of these robots can become complicated. Therefore, it is necessary to investigate how to efficiently assign and schedule mobile robots to transport materials between machining centers and storage racks with the goal of minimizing the makespan (i.e., the time consumed in transportation and processing) and/or the amount of consumed energy. Moreover, constraints of temporal precedence usually exist between sequential manufacturing processes and material delivery operations (e.g., picking up, delivering, processing, and storing). This type of scheduling and planning problem can be defined as a precedence-constrained multi-agent task assignment and path finding (PC-TAPF) problem [4]. In a PC-TAPF problem, a set of tasks and a team of mobile robots are usually given at the beginning. We first need to assign each task to a suitable robot [5], then a set of conflict-free paths for robots needs to be generated to ensure the assigned tasks can be successfully completed [6, 7]. Note that precedence constraints can exist between tasks in a PC-TAPF problem [8]. For example, suppose that A, B, and C are three transportation tasks, and tasks A and task B must be completed before task C is started. Then, the initial position of task C can only be determined once the target positions of task A and task B have been determined in a scenario of flowline production [4]. Therefore, considering that the precedence constraints of transportation tasks are different between these environments, it is not appropriate to simply apply the task assignment and path-planning algorithms developed for warehousing in smart manufacturing. Various approaches have been developed to solve PC-TAPF problems [9; 10; 11; 12]. These approaches often solve task assignment and path finding separately. The common procedure is to generate all possible assignments, and then, find a feasible path for each assigned task. However, many of these approaches either suffer from high complexity in computation, which leads to difficult deployment in practice, or simply assume the solved paths will not conflict with each other no matter how the tasks are assigned [13; 14; 15]. For example, [PERSON] [16] proposes a novel application of constraint programming for the job-shop scheduling problem (JSP) with transbots. [PERSON] et al. [17] propose mixed-integer linear programming and constraint programming approaches for the scheduling of multi-robot job-shop systems in dynamic environments. These approaches focus on solving task scheduling problems and may not directly apply to those problems where task assignment and path finding are coupled. In recent years, approaches that jointly solve task assignment and path finding have been emerging. For instance, the CBM (Conflict-Based Min-Cost-Flow) and CBS-TA (Conflict-Based Search with Optimal Task Assignment) algorithms [18; 19] can find makespan-optimal solutions to task assignment and path finding. [PERSON] et al. [4] proposed a four-level hierarchical algorithm for computing makespan-optimal solutions to PC-TAPF problems. However, many of these algorithms are limited by poor scalability, and timeout failures can happen when the numbers of agents and tasks become relatively large. In addition, they usually only consider makespan as the single optimization objective. To tackle these issues, some new methods have been proposed to solve task assignment and path finding problems in an integrated way [20; 21; 22]. For instance, [PERSON] et al. [20] developed a combined method to generate task sequences by dynamically updating path costs.