A Scalable Graph Learning Approach to Capacitated Vehicle Routing Problem Using Capsule Networks and Attention Mechanism

Abstract

Abstract This paper introduces a new graph neural network architecture for learning solutions of Capacitated Vehicle Routing Problems (CVRP) as policies over graphs. CVRP serves as an important benchmark for a wide range of combinatorial planning problems, which can be adapted to manufacturing, robotics and fleet planning applications. Here, the specific aim is to demonstrate the significant real-time executability and (beyond training) scalability advantages of the new graph learning approach over existing solution methods. While partly drawing motivation from recent graph learning methods that learn to solve CO problems such as multi-Traveling Salesman Problem (mTSP) and VRP, the proposed neural architecture presents a novel encoder-decoder architecture. Here the encoder is based on Capsule networks, which enables better representation of local and global information with permutation invariant node embeddings; and the decoder is based on the Multi-head attention (MHA) mechanism allowing sequential decisions. This architecture is trained using a policy gradient Reinforcement Learning process. The performance of our approach is favorably compared with state-of-the-art learning and non-learning methods for a benchmark suite of Capacitated-VRP (CVRP) problems. A further study on the CVRP with demand uncertainties is conducted to explore how this Capsule-Attention Mechanism architecture can be extended to handle real-world uncertainties by embedding them through the encoder.