## 1 Introduction  
With the development of the e-commerce and logistics industries, the advantages of the intelligent warehouse have begun to emerge [1]. The intelligent warehouse is mainly deployed by the multi-robot system [2], which can significantly improve efficiency and reduce cost. Amazon's order fulfillment center is the most mature intelligent warehouse globally [3]. As shown in Figure 1, the intelligent warehouse comprises three parts: robots, inventory pods, and inventory stations. The robots can operate autonomously in narrow passages. All robots are homogeneous, where every robot has the same ability to move the inventory pod. Robots are sometimes referred to as automated guided vehicles (AGVs). The inventory pods are containers that can hold one or more kinds of goods and can be transported by robots. The inventory stations have two types: picking stations and replenishment stations. Picking or replenishing goods from inventory pods is primarily done by workers. The workflow of an intelligent warehouse mainly includes multi-robot task assignment [4] and path-finding [5]. The two processes interact with each other [6]. Practical task assignments can reduce costs and avoid path conflicts. There are many methods for solving multi-robot task assignment problems, including combinatorial optimization methods, market-based methods, swarm intelligence methods, clustering, and so on [7]. Multi-robot task assignment also has many applications in industrial manufacturing, especially flexible manufacturing systems [8]. In [9], the scholars explored the task assignment of material handling by multiple AGVs in complex random production lines. In [10], the scholars use the tabu search algorithm to solve the problem of simultaneous task assignments between machines and multiple AGVs in flexible manufacturing systems. In [11], the scholars discuss multi-objective multi-AGV task assignment in flexible manufacturing systems using evolutionary algorithms. However, few studies are about multi-robot task assignment in an intelligent warehouse. According to the number of tasks assigned during every time window, task assignment can be divided into single-task assignment (STA) and multi-task assignment (MTA) [12]. Single-task assignment (STA) is deployed quickly, but multi-task assignment (MTA) is more helpful in reducing costs and increasing efficiency. Single-task assignment (STA) is also known as online task assignment. When a task arrives, the system assigns it to an idle robot based on some heuristics, such as the task order (first come and first served, FCFS) [13], the task priority [14], the distance between the task and the idle robot, the utilization of toes, the age of the tasks [15], and so on. The system assigns multiple associated tasks to each robot through an optimization model during each time window in multi-task assignment (MTA). The scholars study multi-task assignment (MTA) in intelligent warehousing using the genetic algorithms in [8; 16; 17]. However, the above studies only analyze one kind of task, such as the picking task. They do not include all kinds of warehouse tasks, which simplifies the actual task assignment in an intelligent warehouse. This paper's task assignment method belongs to multi-task assignment (MTA) and can assign three different kinds of tasks. As shown in Figure 2, during a specific time window, each robot starts from an initial position to complete a series of tasks and does not return. There are three kinds of tasks: replenishment, moving, and picking. The replenishment task means the robots carry the inventory pod to the replenishment station and return. The moving task means the robots carry the inventory pods from their initial position to another location. The picking task means the robots carry the inventory pods to the picking stations and return. We assume that the robots carry the inventory pods to the initial position when the robots complete the replenishment and picking task. The replenishment and picking tasks are considered to be node tasks.