# Multi-Scenario Robust Distributed Permutation Flow Shop Scheduling Based on DDQN
## 1 Introduction
As the problem scale expands, this leads to a dramatic increase in computational complexity, making the optimization of scheduling sequences increasingly time-consuming and less efficient. This paper presents a hybrid simulation system that models the MSRDPFSP using Plant Simulation to address scheduling sequence simulation time. The system more accurately replicates complex real-world production environments compared to traditional methods. The DDQN algorithm retrieves model simulation results via the COM interface or DLL, enabling iterative learning from initial populations generated by the NEH algorithm to rapidly balance maximum completion times across workshops. The main contributions of this work are summarized as follows:  
* Siemens Plant Simulation is employed to digitally model the distributed workshop through the definition of operational processes, dynamic events, scheduling rules, and optimization goals. To simulate the complexity of real-world production environments, seven distinct factory types are designed to quantitatively analyze the workshop layout, assembly line design, the state of the workers, robotic arms, AGV vehicles, and other production system parameters. Fault rates are incorporated into the production system to maximize the reproduction of the real production environment. Moreover, GA components are employed to optimize the production process, greatly improving production efficiency. * An approximate optimal solution is generated for the DPFSP using the NEH algorithm and used as the initial solution for MSRDPFSP. Four search strategies are designed, with DQN introduced to minimize the processing time as the target for evaluating Q values. Greedy selection is performed among the four search strategies. The DDQN approach separates the Target Network and the Evaluation Network to mitigate the overestimation of Q-values. Additionally, the allocation information of the workpieces is replaced with the makespan of each workshop as the state information, reducing the training difficulty of the neural network. * Using the COM interface of Plant Simulation, the models in Plant Simulation are controlled through Pytharm to retrieve simulation results, while calculation and analysis functions in Pytharm are invoked through Plant Simulation. The hybrid DDQN-NEH algorithm is directly integrated into the MSRDPFSP simulation model via DLL, thus completing the entire link from modeling, optimization, to simulation. The remaining chapters of this paper are structured as follows: Section 2 introduces some basic concepts of the research content; Section 3 constructs a digital simulation model of DPFSP using Plant Simulation reference Taillard dataset and thus builds a MSRDPFSP simulation model by increasing the scenario complexity as well as the robustness; Section 4 elaborates on the design of the hybrid DDQN-NEH algorithm proposed in this paper and its interaction with the simulation model established in Section 3; Section 5 evaluates the performance of this joint simulation system; Section 6 delineates the experimental protocol and engages in a comprehensive discourse on the findings; and Section 7 furnishes the conclusions, highlights the study's limitations, and illuminates avenues for future exploration.