A Hopfield neural network-based approach for parallel additive machine scheduling problems with due dates

In this study, we investigate a parallel additive manufacturing batch scheduling problem with unrelated parallel machines operating under powder bed fusion technology. The objective is to minimize the makespan and the total weighted earliness and tardiness. We propose a constructive heuristic that accounts for problem-specific characteristics such as due dates, earliness/tardiness penalties, and machine batch availability. To further enhance solution quality, we develop a Hopfield neural network (HNN)-based improvement scheme specifically tailored to this problem. The performance of the proposed approach is evaluated against an integrated mixed integer linear programming formulation, as well as a Genetic Algorithm (GA). Computational experiments based on adapted benchmark instances demonstrate that the HNN-based solution approach outperforms the solver and the GA on larger instances with limited machines, while it remains competitive with the GA for smaller instances.