The Bin Packing Problem (BPP) has attracted enthusiastic research interest recently, owing to widespread applications in logistics and warehousing environments. It is truly essential to optimize the bin packing to enable more objects to be packed into boxes. Object packing order and placement strategy are the two crucial optimization objectives of the BPP. However, existing optimization methods for BPP, such as the genetic algorithm (GA), emerge as the main issues in highly computational cost and relatively low accuracy, making it difficult to implement in realistic scenarios. To well relieve the research gaps, we present a novel optimization methodology of two-dimensional (2D)-BPP and three-dimensional (3D)-BPP for objects with regular shapes via deep reinforcement learning (DRL), maximizing the space utilization and minimizing the usage number of boxes. First, an end-to-end DRL neural network constructed by a modified Pointer Network consisting of an encoder, a decoder and an attention module is proposed to achieve the optimal object packing order. Second, conforming to the top-down operation mode, the placement strategy based on a height map is used to arrange the ordered objects in the boxes, preventing the objects from colliding with boxes and other objects in boxes. Third, the reward and loss functions are defined as the indicators of the compactness, pyramid, and usage number of boxes to conduct the training of the DRL neural network based on an on-policy actor-critic framework.Finally, a series of experiments are implemented to compare our method with conventional packing methods, from which we conclude that our method outperforms these packing methods in both packing accuracy and efficiency.
Recent deep models for solving routing problems always assume a single distribution of nodes for training, which severely impairs their cross-distribution generalization ability. In this paper, we exploit group distributionally robust optimization (group DRO) to tackle this issue, where we jointly optimize the weights for different groups of distributions and the parameters for the deep model in an interleaved manner during training. We also design a module based on convolutional neural network, which allows the deep model to learn more informative latent pattern among the nodes. We evaluate the proposed approach on two types of well-known deep models including GCN and POMO. The experimental results on the randomly synthesized instances and the ones from two benchmark dataset (i.e., TSPLib and CVRPLib) demonstrate that our approach could significantly improve the cross-distribution generalization performance over the original models.
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