## 1 Introduction
Multi-factory manufacturing, including distributed manufacturing, through the cooperation of different factories distributed in different geographical locations to complete the production of products, which can rationally allocate the resources of each factory, realize the optimal combination and sharing of resources, reduce the production cost of products, and improve the satisfaction of customers, meet the diversification of customer needs. [PERSON] et al. [12] proposed an event-driven framework, which could realize the interaction of heterogeneous distributed resources. In particular, this research provided new mechanisms combining many technologies such as IIOT and Semantic Web, to notify significant information produced within the factory toward enabled and interested production resources. [PERSON] et al. [13] developed a distributed approach and also used the Nash bargaining solution based on game theory, for a network of independent enterprises, which could facilitate the capacity process by using a multiagent architecture and a cooperative protocol. The simulation results demonstrated that the proposed method had a better performance when the dynamicity of the environment grows. [PERSON] et al. [14] designed a framework based on a cooperative game algorithm and a fuzzy engine for capacity sharing in cloud manufacturing. The utility functions of the involved firms were taken into account in the capacity allocation policy. [PERSON] et al. [15] proposed an effective hybrid immune algorithm to solve the distributed permutation flow shop scheduling problem by designing a new cross mutation inoculation and local search operator. Experiments showed that the algorithm was particularly effective for large-scale test problems. [PERSON] et al. [16] designed a distributed optimization method to solve distributed flow shop scheduling problems by reducing the power cost of manufacturing factories. [PERSON] et al. [17] proposed a two-stage heuristic search algorithm to solve the distributed flow shop scheduling problem with flexible assembly and installation time, with the objective of minimizing make span. [PERSON] et al. [18] designed an improved genetic algorithm based on 3D-1D encoding and 1D-3D decoding to solve the distributed flexible job shop scheduling problem. It also introduced the allocation strategy of jobs to factories in detail. [PERSON] et al. [19] established a stochastic multi-objective distributed permutation flow shop scheduling model considering total tardiness, make span, and total energy consumption, which also designed a new multi-objective brainstorming optimization algorithm to solve the problem. [PERSON] et al. [20] used the improved adaptive large neighborhood search algorithm to solve the distributed re-entrant permutation flow shop scheduling problem. It was the first time that the distributed re-entrant flow shop (DRFS) scheduling problem was studied, and it pointed out that DRFS problem was NP-Hard. To sum up, up to now, the studies on distributed scheduling problem in domestic and foreign literature is mostly confined to homogeneous factory, and most of them are research on flow shop, permutation flow shop, and flexible job shop. To the best of my knowledge, there is little research on a distributed reentrant hybrid flow shop. Distributed manufacturing of semiconductor wafers can be attributed to the distributed reentrant hybrid flow shop (DRHFS) problem, which has similar properties to the RHFS problem, but extends to multi-factory issues. Therefore, it is clear that it also belongs to the NP-Hard problem. Environmental issues are the focus of global attention, and sustainable green manufacturing is a serious challenge for today's manufacturing industry. Noises and CO\({}_{2}\) emissions from the manufacturing industry are the main sources of pollution. For semiconductor wafer factories, because they are usually equipped with hundreds of precision equipment, and the wafer manufacturing process is very complex, there may be hundreds of products flowing simultaneously on the production line.