Learning the Partially Dynamic Travelling Salesman Problem

Jack Trainer, David S. Leslie, Anthony Nixon

Keywords: Reinforcement Learning, Graph Neural Networks, Dynamic Graphs, Dynamic Graph Neural Networks, Travelling Salesman Problem, Combinatorial Optimisation

TL;DR: Using Deep Reinforcement Learning with Graph Neural Networks to solve a dynamic variant of the Travelling Salesman Problem.

Abstract: Learning to solve the Travelling Salesman Problem (TSP) using Deep Reinforcement Learning (Deep RL) and Graph Neural Networks (GNNs) has shown promising results for small instances of the problem. We demonstrate that these methods can be extended to solve instances of a partially dynamic variant of the TSP. Solving this partially dynamic variant more effectively exploits the strengths of reinforcement learning and also presents challenges for more established methods of solving the TSP. We show the policies trained using Deep RL outperform modified versions of TSP solvers and heuristics for different distributions of dynamic vertices, including on larger instances than the policies were trained on. This shows the promise of Deep RL for solving this type of dynamic routing problem which is predicted to become of great importance as logistical services become more flexible and responsive to customer demand. Furthermore, our method is a general purpose approach to Deep RL where the problem consists of selecting items from a dynamically-evolving and arbitrarily-sized set.

Primary Area: reinforcement learning

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Submission Number: 10811