Learning to Solve Multiple-TSP with Time Window and Rejections via Deep Reinforcement Learning

TL;DR

This paper introduces a deep reinforcement learning framework with manager and worker agents to efficiently solve a complex variant of the TSP involving multiple vehicles, time windows, and rejections, outperforming existing methods.

Contribution

It presents a novel manager-worker RL framework using GIN-based policies for dividing and solving mTSPTWR, improving solution quality and generalization to larger instances.

Findings

Outperforms strong baselines in solution quality and speed

Achieves competitive results on unseen larger instances

Demonstrates effectiveness of RL in complex routing problems

Abstract

We propose a manager-worker framework based on deep reinforcement learning to tackle a hard yet nontrivial variant of Travelling Salesman Problem (TSP), \ie~multiple-vehicle TSP with time window and rejections (mTSPTWR), where customers who cannot be served before the deadline are subject to rejections. Particularly, in the proposed framework, a manager agent learns to divide mTSPTWR into sub-routing tasks by assigning customers to each vehicle via a Graph Isomorphism Network (GIN) based policy network. A worker agent learns to solve sub-routing tasks by minimizing the cost in terms of both tour length and rejection rate for each vehicle, the maximum of which is then fed back to the manager agent to learn better assignments. Experimental results demonstrate that the proposed framework outperforms strong baselines in terms of higher solution quality and shorter computation time. More importantly, the trained agents also achieve competitive performance for solving unseen larger instances.