Reinforcement learning has recently shown promise in learning quality solutions in many combinatorial optimization problems. In particular, the attention-based encoder-decoder models show high effectiveness on various routing problems, including the Traveling Salesman Problem (TSP). Unfortunately, they perform poorly for the TSP with Drone (TSP-D), requiring routing a heterogeneous fleet of vehicles in coordination -- a truck and a drone. In TSP-D, the two vehicles are moving in tandem and may need to wait at a node for the other vehicle to join. State-less attention-based decoder fails to make such coordination between vehicles. We propose a hybrid model that uses an attention encoder and a Long Short-Term Memory (LSTM) network decoder, in which the decoder's hidden state can represent the sequence of actions made. We empirically demonstrate that such a hybrid model improves upon a purely attention-based model for both solution quality and computational efficiency. Our experiments on the min-max Capacitated Vehicle Routing Problem (mmCVRP) also confirm that the hybrid model is more suitable for the coordinated routing of multiple vehicles than the attention-based model. The proposed model demonstrates comparable results as the operations research baseline methods.
@article{arxiv.2112.12545,
title = {A Deep Reinforcement Learning Approach for Solving the Traveling Salesman Problem with Drone},
author = {Aigerim Bogyrbayeva and Taehyun Yoon and Hanbum Ko and Sungbin Lim and Hyokun Yun and Changhyun Kwon},
journal= {arXiv preprint arXiv:2112.12545},
year = {2022}
}