  We introduce the transport-and-pack(TAP) problem, a frequently encountered
instance of real-world packing, and develop a neural optimization solution
based on reinforcement learning. Given an initial spatial configuration of
boxes, we seek an efficient method to iteratively transport and pack the boxes
compactly into a target container. Due to obstruction and accessibility
constraints, our problem has to add a new search dimension, i.e., finding an
optimal transport sequence, to the already immense search space for packing
alone. Using a learning-based approach, a trained network can learn and encode
solution patterns to guide the solution of new problem instances instead of
executing an expensive online search. In our work, we represent the transport
constraints using a precedence graph and train a neural network, coined
TAP-Net, using reinforcement learning to reward efficient and stable packing.
The network is built on an encoder-decoder architecture, where the encoder
employs convolution layers to encode the box geometry and precedence graph and
the decoder is a recurrent neural network (RNN) which inputs the current
encoder output, as well as the current box packing state of the target
container, and outputs the next box to pack, as well as its orientation. We
train our network on randomly generated initial box configurations, without
supervision, via policy gradients to learn optimal TAP policies to maximize
packing efficiency and stability. We demonstrate the performance of TAP-Net on
a variety of examples, evaluating the network through ablation studies and
comparisons to baselines and alternative network designs. We also show that our
network generalizes well to larger problem instances, when trained on
small-sized inputs.
