**1. Introduction**

A hybrid flow shop is a kind of flow shop containing more than two stages and at least one stage with multiple parallel machines, also known as a flexible flow shop. The hybrid flow shop scheduling problem (HFSP) is of great theoretical significance and practical value, as it is widely applied in the chemical, textile, steel and semiconductor industries. In the context of intelligent manufacturing, dynamic scheduling based on reinforcement learning has become a research trend. Many research studies have been conducted in the literature. Han et al. first proposed a reinforcement learning method for HFSP [1]. Gil and Lee studied the use of the deep reinforcement learning approach to solve the material scheduling problem of many machines in a hybrid flow shop environment [2]. Cai et al. proposed a new shuffle frog-learning algorithm with Q-learning to solve a distributed assembly hybrid flow shop scheduling problem with fabrication, transportation and assembly [3]. Wang, J.J. and Wang, L. studied an energy-aware distributed hybrid flow shop scheduling method based on reinforcement learning [4]. Lang et al. presented a dynamic scheduling method based on the NEAT algorithm for a two-stage hybrid flow shop scheduling problem with family setup times [5].

The problem of dynamic scheduling in hybrid flow shops where machines require flexible preventive maintenance and where jobs arrive randomly and processing times are uncertain has not yet been identified, so this paper studies the HFSP scheduling problem with the objective of minimizing the makespan and designs a dynamic scheduling method based on NEAT reinforcement learning and compares it with scheduling rules.
