Learning to solve single-batch-processing machine scheduling problem with two-dimensional packing constraints

Machines that simultaneously process jobs in a batch and sequentially handle batches are widely used in additive manufacturing such as three-dimensional (3D) printing. This paper is concerned with the job packing and batch scheduling problem of single-batch-processing machine under two-dimensional geometric constraints (2D-SBPM). Existing approaches for 2D-SBPM predominantly rely on heuristic methods, which often yield suboptimal solutions due to repetitive evaluation cycles during scheduling and the persistent dependence on conventional heuristic rules for packing. To improve computational efficiency and solution quality, this paper proposes a two-stage solution scheme based on deep reinforcement learning (DRL). Specifically, we introduce a packing method, called Packing-Net, that significantly enhances the conventional packing scheme by the attention mechanism. Furthermore, we propose a sequence generator with multiple policy optimization to make the training process fast and stable. Directly generating job sequences avoids invalid evaluations. Experimental results show that our method outperforms the conventional heuristics with various sizes.