Reinforcement Learning for Routing Problems with Hybrid Edge-Embedded Networks

Abstract

The routing problem poses a significant combinatorial optimization (COP) challenge that cannot be effectively solved by using traditional methods due to its NP-hardness. Recent studies have shown that Graph Attention Networks (GAT) [1] hold promise in addressing this problem. However, existing models have neglected the importance of distance matrix information between nodes, rendering the trained model less effective. Furthermore, the ability of existing models to solve asymmetric routing problems on real road networks is limited, as these models solely rely on the coordinates of the nodes. In this paper, we propose a novel model that incorporates a hybrid structure of edge-graph attention network (E-GAT) and edge-embedded multi-head attention (E-MHA) as the encoder. Besides, the edges are embedded to obtain graph structure information directly, and it allows us to capture the correlation between different nodes and avoid potential noise. Experimental results demonstrate that our proposed method outperforms existing methods in routing problems of varying scales while maintaining good compatibility and generalization ability. In addition, our method effectively addresses the Travelling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) under both symmetric and asymmetric distance matrix.