A deep reinforcement learning approach for solving the Traveling Salesman Problem with Drone

• DOI: 10.1016/j.trc.2022.103981
• Publication Date: 2023-01-07T12:26:04Z
• Authors: Aigerim Bogyrbayeva; Taehyun Yoon; Hanbum Ko; Sungbin Lim; Hyokun Yun; Changhyun Kwon
• Keywords: 629; FOS: Computer and information sciences; Computer Science - Machine Learning; Artificial Intelligence (cs.AI); Computer Science - Artificial Intelligence; Optimization and Control (math.OC); 0502 economics and business; 05 social sciences; FOS: Mathematics; 0211 other engineering and technologies; 02 engineering and technology; Mathematics - Optimization and Control; Machine Learning (cs.LG)

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.