# Graph Reinforcement Learning for Operator Selection in the ALNS Metaheuristic

## TL;DR

This paper introduces a deep reinforcement learning approach using graph neural networks to enhance operator selection in ALNS, leading to improved performance and reduced manual effort in solving combinatorial optimization problems.

## Contribution

It formulates operator selection as a Markov Decision Process and applies deep RL with GNNs, outperforming classic ALNS adaptive methods and reducing manual tuning.

## Key findings

- Proposed method outperforms classic ALNS adaptive layer
- Conditioning operator choice on current solution improves results
- Significant reduction in manual effort for operator portfolio design

## Abstract

ALNS is a popular metaheuristic with renowned efficiency in solving combinatorial optimisation problems. However, despite 16 years of intensive research into ALNS, whether the embedded adaptive layer can efficiently select operators to improve the incumbent remains an open question. In this work, we formulate the choice of operators as a Markov Decision Process, and propose a practical approach based on Deep Reinforcement Learning and Graph Neural Networks. The results show that our proposed method achieves better performance than the classic ALNS adaptive layer due to the choice of operator being conditioned on the current solution. We also discuss important considerations such as the size of the operator portfolio and the impact of the choice of operator scales. Notably, our approach can also save significant time and labour costs for handcrafting problem-specific operator portfolios.