## 1 Introduction  
With the advent of the fourth industrial revolution in the context of industrial 4.0, intelligent manufacturing has become a symbol of the new information age. The semiconductor industry, as the cornerstone of the information age, belongs to the high-tech industry and faces many opportunities and challenges. While it brings high profits, fierce industry competition also forces semiconductor manufacturers to continuously improve production efficiency and resource utilization [1]. In a semiconductor manufacturing process, wafer manufacturing is called the front-end process while wafer testing and packaging is called the back-end process. Because the equipment used in wafer manufacturing are expensive and the processing process is complex, it has attracted wide attention of scholars at home and abroad. Re-entrant is a remarkable feature of semiconductor wafer fabrication [2; 3; 4], which means that the jobs may repeatedly access certain devices at different stages of the processing process. More than one machine with at least one stage is used for processing. In addition, during the processing of the wafer, various physical and chemical processing steps are needed to form a required circuit layer on the surface of the wafer, and the processing steps involved mainly include oxidation,deposition, implantation, sputtering, photolithography, etching, and cleaning, etc. There are strict order constraints between operations. The manufacturing process can be reduced to the reentrant hybrid flow shop (RHFS) problem, which has been proven to be an NP-hard (Non-deterministic polynomial hard) problem [5]. Because of its large scale and high complexity, the RHFS problem is difficult to solve effectively in an acceptable time using traditional mathematical modeling methods. In addition, according to the \"no free lunch\" theorem [6], no algorithm can achieve better results for all application problems, so it is of great significance and value to design and develop new intelligent optimization algorithms. [PERSON] et al. [7] proposed an integer linear programming formulation of the hybrid flow shop with recirculation, and minimizing the weighted number of tardy jobs was regarded as the optimization goal. Then a lower bound, a greedy algorithm, and a genetic algorithm were described as approximate methods. [PERSON] et al. [8] proposed a Pareto genetic algorithm based on the Minkowski crossover operator to solve the RHFS problem, and is also designed as corresponding benchmark data sets for simulation experiments. [PERSON] et al. [9] proposed an adaptive hybrid incremental learning algorithm to solve the reentrant permutation flow shop scheduling problem with make span as the optimization objective. The degree of population evolution was evaluated by using the information entropy of the probability matrix. The mutation mechanism of the probability model and the local search method of the critical path were designed to expand the search area of the population. [PERSON] et al. [10] designed an improved particle swarm optimization (PSO) algorithm to solve the two-stage reentrant multi-machine flow shop scheduling problem with a due window. Taking the wafer testing process as an example, aiming at minimizing the lead time or delay time, effectiveness, and robustness of the proposed algorithm were verified by large-scale test experiments. [PERSON] et al. [11] proposed a two-level optimization algorithm to solve the reentrant flow shop problem, which satisfied the maximization of total product quantity and minimization of the customer demand delay, and applied it to real TFT-LCD (Thin Film Transistor-Liquid Crystal Display) production. To sum up, up to now, the research on the reentrant scheduling problem in domestic and foreign literature is basically based on a single production line. However, in actual production, multi-factory manufacturing and collaborative production play a key role.