Combinatorial Optimization by Graph Pointer Networks and Hierarchical Reinforcement Learning

TL;DR

This paper introduces Graph Pointer Networks and hierarchical reinforcement learning to efficiently solve large-scale and constrained traveling salesman problems, demonstrating superior performance and generalization.

Contribution

It presents novel graph embedding-based pointer networks and hierarchical RL methods for combinatorial optimization, improving solution quality and scalability.

Findings

GPNs generalize well from small to large TSP instances.

Hierarchical RL with separate reward functions stabilizes training.

Proposed methods outperform existing baselines on constrained TSPs.

Abstract

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.