Combinatorial Optimization by Graph Pointer Networks and Hierarchical Reinforcement Learning
This work addresses combinatorial optimization problems like TSP for applications in logistics and scheduling, presenting an incremental improvement over existing methods.
The paper tackled the traveling salesman problem (TSP) and its constrained variants by introducing Graph Pointer Networks trained with reinforcement learning, achieving shorter tour lengths and faster computational times on larger-scale problems and outperforming previous baselines for constrained TSP.
In this work, we introduce Graph Pointer Networks (GPNs) trained using reinforcement learning (RL) for tackling the traveling salesman problem (TSP). GPNs build upon Pointer Networks by introducing a graph embedding layer on the input, which captures relationships between nodes. Furthermore, to approximate solutions to constrained combinatorial optimization problems such as the TSP with time windows, we train hierarchical GPNs (HGPNs) using RL, which learns a hierarchical policy to find an optimal city permutation under constraints. Each layer of the hierarchy is designed with a separate reward function, resulting in stable training. Our results demonstrate that GPNs trained on small-scale TSP50/100 problems generalize well to larger-scale TSP500/1000 problems, with shorter tour lengths and faster computational times. We verify that for constrained TSP problems such as the TSP with time windows, the feasible solutions found via hierarchical RL training outperform previous baselines. In the spirit of reproducible research we make our data, models, and code publicly available.