## 1 Introduction  
### Background and Motivation  
The Fourth Industrial Revolution (intelligent era) has opened the curtain, and the production mode of the manufacturing industry has begun to shift to automation and intelligence [1]. The transformation and innovation of the manufacturing production mode have led to the traditional large-scale standardized manufacturing mode being replaced by the multi-variety, small batch, short cycle, and personalized manufacturing mode, which also puts forward higher requirements for workshop production flexibility and processes [2]. Therefore, it is an urgent need for manufacturing enterprises to solve the scheduling problem before processing or assembly to optimize their manufacturing resource allocation strategy and improve the utilization rate of manufacturing resources. It should be emphasized that shop floor scheduling has become a bottleneck and key problem faced by manufacturing enterprises [3;4]. A reasonable flexible shop floor scheduling scheme is key to improving efficiency, reducing costs and allocating resources reasonably for manufacturing enterprises.  
In recent years, manufacturing enterprises have actively promoted the concept of advanced intelligent manufacturing. In order to realize the transformation from a traditional manufacturing shop to intelligent shop, many manufacturing enterprises have introduced automated logistics equipment such as automatic guided vehicles (AGVs). This has made the traditional optimal allocation of manufacturing tasks, machines, and personnel gradually expand to the integrated optimization of multi-types of manufacturing resources [5]. In the actual job shop, different path choices of AGVs cause different time consumption. It will also affect the processing time, scheduling planning, and completion time of the entire production task. Therefore, flexible shop floor integrated scheduling with an AGV has gradually become one of the key research problems in the field of production scheduling optimization.  
In flexible job shop scheduling (FJS), AGVs are used for material transportation, which breaks the constraint of machine uniqueness in traditional shop floor production. In the flexible job shop scheduling problem (FJSP), the number of alternative AGV sets to transport materials to any machine meeting the production requirements for processing in the alternative machine sets, so that the workshop production scheduling problem can be flexibly scheduled according to the different actual needs. FJSP includes operations such as machine loading and unloading, production activity programming, machine planning and allocation, AGV allocation, and AGV path selection [6; 7; 8], which also makes the optimal allocation of production resources more complex. Therefore, FJSP using AGV transportation is an extension of FSSP and the traditional shop scheduling problem, which is a more complex and difficult NP-hard problem [9]. It is well-known that accurate algorithms can find it difficult to obtain excellent exact solutions of NP-hard problems in limited time, and their solving speed and accuracy are far less than that of intelligent optimization algorithms [10; 11; 12; 13]. Furthermore, the FJSP may necessitate the simultaneous consideration of multiple objectives, some of which might exhibit conflicting interests. This not only leads to an expansive search space, but also makes it challenging to attain optimality within a short timeframe. Therefore, it is very challenging to solve the flexible job-shop scheduling problem with large-scale and multi-objectives.