## 2 Related Work
### RMFS Orders Batch-Picking Scheduling  
RMFS has been a popular picking system in recent years, which decomposes traditional warehouse picking activities into two sub-activities: handling by robots and picking by humans. This allows robots and manual pickers to complement each other's advantages, freeing manual pickers from heavy handling activities while fully retaining and leveraging the experiential advantages of manual pickers in picking activities.  
[PERSON] et al. [24] and [PERSON] et al. [25] found that the order-picking problem in RMFS has not been fully resolved. [PERSON] et al. [26] paid attention to the coupling relationship between order sorting and mobile shelf scheduling. They established an integer programming model to describe the problem and proposed a two-stage solution method to solve the joint optimization of order sequencing and mobile shelves scheduling. [PERSON], [PERSON] et al. [27] innovatively transformed the robot task scheduling problem into a resource-constrained project scheduling problem with transfer time and proposed a genetic algorithm using a building-block-based crossover (BBX) operator to solve this problem. [PERSON] et al. [28] also recognized the correlation between order sorting and shelf scheduling and proposed a new mixed integer programming formula based on original preprocessing techniques to solve the order and shelf sorting problem with a single picking station, which provided a reference example for the optimization problem of RMFS orders at a medium scale. [PERSON] and [PERSON] [29] established an integrated order scheduling model that differs from the commonly used phased decision-making model in other literature and proposed a heuristic solution method called a bi-level psychological memetic algorithm, which further extended the two problems of order sorting and shelf scheduling. In addition, [PERSON] et al. [30] first incorporated the recycling of pods into the RMFS order-picking model. The process of pod picking and recycling described in the model is like the order recycling in the SACOP problem. However, the model proposed in that paper was limited by a single picking station and considered the single optimization objective, which was unsuitable for the SACOP problem.  
By reviewing the literature mentioned above, although there are certain differences in the order-picking system (OPS) between RMFS and SACOP, based on similar behavior patterns and related constraints, the mobile shelves in RMFS can be considered AGVs to some extent in the SACOP problem. Therefore, summarizing the above literature can further clarify the strong coupling between order batch picking and AGV scheduling in the SACOP problem. The relevant ideas, mathematical models, and optimization algorithms design have significant inspiration for the study in this paper. In addition, the literature [31] on the labor intensity of picking workers provides useful insights for this paper, and the literature [32; 33] provided useful optimization method design ideas for this paper.  
By the literature review in this section, the limitations of existing research have been clarified: (1) There is a lack of research on collaborate picking systems' concluding stackers, AGVs, and picking stations. (2) Existing research has overlooked other important optimization objectives, such as machine energy consumption and worker load, or subjectively weighted multiple optimization objectives into a single objective, which resulted in the results deviating from reality. On the other hand, this also demonstrates the complexity of the SACOP problem.  
As a result, this paper dictates the multi-objective scheduling optimization model and method for the SACOP problem, firstly, which takes the overall energy consumption and operational efficiency into account. With our work, a Pareto optimal solution set can be generated within a reasonable time range for a batch outbound task of orders and transformed into corresponding stacker scheduling schemes, AGV scheduling schemes, and pick station task schemes.