The permutation flow shop scheduling problem (PFSP) stands as a classic conundrum within the realm of combinatorial optimization, serving as a prevalent organizational structure in authentic production settings. Given that conventional scheduling approaches fall short of effectively addressing the intricate and ever-shifting production landscape of PFSP, this study proposes an end-to-end deep reinforcement learning methodology with the objective of minimizing the maximum completion time. To tackle PFSP, we initially model it as a Markov decision process, delineating pertinent states, actions, and reward functions. A notably innovative facet of our approach involves leveraging disjunctive graphs to represent PFSP state information. To glean the intrinsic topological data embedded within the disjunctive graph’s underpinning, we architect a policy network based on a graph isomorphism network, subsequently trained through proximal policy optimization. Our devised methodology is compared with six baseline methods on randomly generated instances and the Taillard benchmark, respectively. The experimental results unequivocally underscore the superiority of our proposed approach in terms of $makespan$ and computation time. Notably, the $makespan$ can save up to 183.2 h in randomly generated instances and 188.4 h in the Taillard benchmark. The calculation time can be reduced by up to 18.70 s for randomly generated instances and up to 18.16 s for the Taillard benchmark.

The panel block is a quite important “intermediate product” in the shipbuilding process. However, the assembly efficiency of the panel block assembly line is not high. Therefore, rational scheduling optimization is of great significance for improving shipbuilding efficiency. Currently, the processing sequence of the panel blocks in the panel block assembly line is mainly determined using heuristic and metaheuristic algorithms. However, these algorithms have limitations, such as small problem-solving capacity and low computational efficiency. To address these issues, this study proposes an end-to-end approach based on deep reinforcement learning to solve the scheduling problem of the ship’s panel block assembly line. First, a Markov decision model is established, and a disjunctive graph is creatively used to represent the current scheduling status of the panel block assembly line. Then, a policy function based on a graph isomorphism network is designed to extract information from the disjunctive graph’s state and train it using Proximal Policy Optimization algorithms. To validate the effectiveness of our method, tests on both real shipbuilding data and publicly available benchmark datasets are conducted. We compared our proposed end-to-end deep reinforcement learning algorithm with heuristic algorithms, metaheuristic algorithms, and the unimproved reinforcement learning algorithm. The experimental results demonstrate that our algorithm outperforms other baseline methods in terms of model performance and computation time. Moreover, our model exhibits strong generalization capabilities for larger instances.