Attention-based Reinforcement Learning for Combinatorial Optimization: Application to Job Shop Scheduling Problem

Job shop scheduling problems are one of the most important and challenging combinatorial optimization problems that have been tackled mainly by exact or approximate solution approaches. However, finding an exact solution can be infeasible for real-world problems, and even with an approximate solution approach, it can require a prohibitive amount of time to find a near-optimal solution, and the found solutions are not applicable to new problems in general. To address these challenges, we propose an attention-based reinforcement learning method for the class of job shop scheduling problems by integrating policy gradient reinforcement learning with a modified transformer architecture. An important result is that our trained learners in the proposed method can be reused to solve large-scale problems not used in training and demonstrate that our approach outperforms the results of recent studies and widely adopted heuristic rules.

CyCNN: A Rotation Invariant CNN using Polar Mapping and Cylindrical Convolution Layers

Deep Convolutional Neural Networks (CNNs) are empirically known to be invariant to moderate translation but not to rotation in image classification. This paper proposes a deep CNN model, called CyCNN, which exploits polar mapping of input images to convert rotation to translation. To deal with the cylindrical property of the polar coordinates, we replace convolution layers in conventional CNNs to cylindrical convolutional (CyConv) layers. A CyConv layer exploits the cylindrically sliding windows (CSW) mechanism that vertically extends the input-image receptive fields of boundary units in a convolutional layer. We evaluate CyCNN and conventional CNN models for classification tasks on rotated MNIST, CIFAR-10, and SVHN datasets. We show that if there is no data augmentation during training, CyCNN significantly improves classification accuracies when compared to conventional CNN models. Our implementation of CyCNN is publicly available on https://github.com/mcrl/CyCNN.