Additive manufacturing – also known as 3D printing – is a manufacturing process that is attracting more and more interest due to high production rates and reduced costs. This paper focuses on the scheduling problem of multiple additive manufacturing machines, recently proposed in the scientific literature. Given its intractability, instances of relevant size of additive manufacturing (AM) machine scheduling problem cannot be solved in reasonable computational times through mathematical models. For this reason, this paper proposes a Reinforcement Learning Iterated Local Search meta-heuristic, based on the implementation of a Q-Learning Variable Neighborhood Search, to provide heuristically good solutions at the cost of low computational expenses. A comprehensive computational study is conducted, comparing the proposed methodology with the results achieved by the CPLEX solver and to the performance of an Evolutionary Algorithm recently proposed for a similar problem, and adapted for the AM machine scheduling problem. Additionally, to explore the trade-off between efficiency and effectiveness more deeply, we present a further set of experiments that test the potential inclusion of a probabilistic stopping rule. The numerical results evidence that the proposed Reinforcement Learning Iterated Local Search is able to obtain statistically significant improvements compared to the other solution approaches featured in the computational experiments.

增材制造（也称为3D打印）是一种由于高生产率和降低成本而引起越来越多兴趣的制造过程。本文关注的是最近在科学文献中提出的多种增材制造机器的调度问题。鉴于其难处理性，无法通过数学模型在合理的计算时间内解决增材制造（AM）机器调度问题相关大小的情况。因此，本文基于Q学习可变邻域搜索的实现，提出了一种强化学习迭代局部搜索元启发式算法，以较低的计算费用为代价提供启发式良好的解决方案。进行了全面的计算研究，将提出的方法与CPLEX求解器获得的结果进行比较，并与最近针对类似问题提出的进化算法的性能进行比较，并适用于AM机器调度问题。此外，为了更深入地探讨效率与有效性之间的取舍，我们提出了另一组实验，以测试可能包含概率停止规则。数值结果表明，与计算实验中的其他解决方案相比，本文提出的增强学习迭代局部搜索能够获得统计上显着的改进。为了更深入地探索效率与有效性之间的取舍，我们提出了另一组实验，以测试可能包含的概率停止规则。数值结果表明，与计算实验中的其他解决方案相比，本文提出的增强学习迭代局部搜索能够获得统计上显着的改进。为了更深入地探索效率与有效性之间的取舍，我们提出了另一组实验，以测试可能包含的概率停止规则。数值结果表明，与计算实验中的其他解决方案相比，本文提出的增强学习迭代局部搜索能够获得统计上显着的改进。