# Multi-Scenario Robust Distributed Permutation Flow Shop Scheduling Based on DDQN
## 1 Introduction
However, in real manufacturing environments, numerous uncontrollable and uncertain factors--such as machine aging and failure, variations in operator skill levels, unstable material supply, and external environmental changes--can significantly affect system stability and scheduling effectiveness. These uncertainties are often challenging to predict during the planning phase, resulting in deviations between deterministic scheduling models and actual production. Consequently, this affects the feasibility and robustness of solutions. Therefore, research on the MSRDPFSP is of great significance. It not only improves scheduling stability in complex and dynamic manufacturing environments but also holds substantial economic value and practical application potential [14]. [PERSON] and [PERSON] [15] proposed a collaborative optimization framework integrating dual population genetic algorithm and Q-learning for multi-objective DPFSP. [PERSON] et al. [16] proposed a bio-inspired reinforcement learning method to tackle the robustness challenges in replacement flow shop scheduling, offering a bio-inspired solution for adaptive scheduling in smart manufacturing environments. [PERSON] et al. [17] conducted a comprehensive survey of reinforcement learning-based production scheduling systems, highlighting the challenges in applying such methods to industrial environments, such as high training costs and limited model stability. [PERSON] et al. [18] addressed machine unavailability due to preventive and corrective maintenance in job shop scheduling by proposing a robust scheduling method that incorporates both deterministic and stochastic unavailability constraints. This method enhances system stability and execution reliability amid uncertainty. [PERSON] et al. [19] proposed a hybrid optimization approach combining Estimation of Distribution Algorithm and Proximal Policy Optimization. [PERSON] et al. [20] devised a DQN approach within a multi-agent system architecture to tackle dynamic disturbances, including uncertain processing times, order changes, and machine failures. This framework provides a novel strategy for real-time scheduling in intelligent manufacturing environments, enabling adaptive response to runtime uncertainties. However, solving the MSRDPFSP using traditional algorithms is extremely time-consuming, particularly in simulation-based environments. Against this backdrop, digital transformation has provided strong support for technological innovation and industrial upgrading in intelligent manufacturing. By using Plant Simulation to establish digital twin models of existing workflows, [PERSON] et al. [21] improved resource allocation efficiency. [PERSON] et al. [22] innovatively applied Plant Simulation to traffic node modeling and optimization, achieving dynamic simulation and 3D visualization of vehicle operation, congestion formation, and delay situations. [PERSON] et al. [23] simulated the logic verification of manufacturing systems using Plant Simulation, enabling rapid verification and optimization of control logic in manufacturing systems, thereby significantly reducing costs and risks during the actual debugging phase. [PERSON] et al. [24] proposed an assembly flow shop scheduling optimization method integrating virtual simulation and a migratory bird optimization algorithm. They established a virtual simulation environment incorporating digital twin technology and enabled real-time performance evaluation of scheduling schemes. Recent studies have demonstrated Plant Simulation as a discrete event simulation tool--a tool boasting significant advantages in modeling complex systems in the manufacturing industry [25; 26; 27]. Digital modeling enables real-time access to production environment data while supporting efficient simulation, which significantly improves the accuracy and feasibility of solving complex scheduling problems under MSRDPFSP scenarios. Despite these advantages, most existing digital simulation platforms still rely on exhaustive search strategies for scheduling.