## 1 Introduction  
With the intensification of market competition and the acceleration of product updates, the modern manufacturing industry is facing challenges such as single-piece, small-batch, and personalized production [1]. In order to adapt to market changes, companies need to quickly adjust workshop layout and production plans to meet demand [2]. Therefore, the production mode of make-to-order (MTO) with multi-variety and small-batch demand is increasingly popular, and flexible job shop scheduling has become the focus of current research, especially for intelligent manufacturing systems with MTO requirements. The production systems of MTO with multi-variety and small-batch demand often employ multi-equipment work centers to maintain process flexibility and separate operation time for fine management. These are difficult and complicated to schedule and optimize for the production system with multi-equipment work centers due to external factors such as the various types of products ordered by customers, small batches, short lead times, and internal factors such as limited production resources. The scheduling problem of the production system with multi-equipment work centers introduces two different types of work centers, the processing equipment work center and the handling work center, and configures multiple pieces of processing equipment and handling equipment with the same function for them, respectively, so as to complete the production tasks of the MTO system faster and more efficiently to adapt to changes in market demand. This kind of problem is an extension problem based on the FJSP, and it is also an NP-hard problem. Therefore, it can be extended on the basis of the FJSP, using the advantages of multi-equipment work centers and the mutual cooperation and resource sharing in each multi-equipment work center to adapt to the production needs of different products or orders, so as to improve the response speed and flexibility of the MTO system. FJSPs for intelligent manufacturing and MTO have great application value in actual production. In industries like aerospace, airframe, shipbuilding, and machinery, orders are often unique and low in quantity, requiring customization based on specific customer needs and specifications [3]. Many scholars have researched the FJSP from two aspects. Some scholars have built different mathematical models to study the actual production problems of enterprises, while others have improved the algorithm, aiming to obtain an effective solution. The early workshop scheduling theory only considered the machine processing time factor and only took makespan as the optimization goal, but recently, various multi-objective scheduling optimization studies that are more in line with actual factory needs have been developed. [PERSON] et al. [4] established a flexible job shop scheduling model with the optimization objectives of minimizing the maximum completion time, minimizing total carbon emissions, and minimizing the machine load. [PERSON] et al. [5] developed a flexible job shop scheduling problem with the goals of minimizing non-processing energy consumption, total weighted delay, delivery time, and maximum completion time. Nevertheless, the scheduling schemes formulated in the literature only take into account the machine processing time factor and overlook the impact of auxiliary time on scheduling. With the in-depth study of the theory of shop scheduling, the FJSP should not only consider the workpiece processing time but also incorporate some necessary auxiliary time factors such as the workpiece handling time and the adjustment time of the processing machine. In this regard, some studies have been carried out. [PERSON] et al. [6] considered an FJSP with shipping and setup times while optimizing the maximum completion time, total energy consumption, critical machine workload, and early/late penalties, and established a multi-objective optimization mathematical model. [PERSON] et al.