Neural Algorithmic Reasoning for Combinatorial Optimisation

Abstract

Solving NP-hard/complete combinatorial problems with neural networks is a challenging research area that aims to surpass classical approximate algorithms. The long-term objective is to outperform hand-designed heuristics for NP-hard/complete problems by learning to generate superior solutions solely from training data. The Travelling Salesman Problem (TSP) is a prominent combinatorial optimisation problem often targeted by such approaches. However, current neural-based methods for solving TSP often overlook the inherent "algorithmic" nature of the problem. In contrast, heuristics designed for TSP frequently leverage well-established algorithms, such as those for finding the minimum spanning tree. In this paper, we propose leveraging recent advancements in neural algorithmic reasoning to improve the learning of TSP problems. Specifically, we suggest pre-training our neural model on relevant algorithms before training it on TSP instances. Our results demonstrate that, using this learning setup, we achieve superior performance compared to non-algorithmically informed deep learning models