Neural Algorithmic Reasoning for Combinatorial Optimisation
About
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. Current neural-based methods for solving CO problems often overlook the inherent "algorithmic" nature of the problems. In contrast, heuristics designed for CO problems, e.g. 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 CO problems. Specifically, we suggest pre-training our neural model on relevant algorithms before training it on CO instances. Our results demonstrate that by using this learning setup, we achieve superior performance compared to non-algorithmically informed deep learning models.
Related benchmarks
| Task | Dataset | Result | Rank | |
|---|---|---|---|---|
| Traveling Salesman Problem | TSP-200 | Optimality Gap33.6 | 46 | |
| Traveling Salesperson Problem | TSP (test) | Inference Time (Total)1.17 | 12 | |
| Traveling Salesperson Problem | TSP 40 nodes | Optimality Gap7.5 | 5 | |
| Traveling Salesperson Problem | TSP 1000 nodes | Deviation from Optimal (%)38.5 | 5 | |
| Traveling Salesperson Problem | TSP 60 nodes | Relative Gap (%)13.3 | 5 | |
| Traveling Salesperson Problem | TSP 80 nodes | Gap to Optimal (%)19 | 5 | |
| Traveling Salesperson Problem | TSP 100 nodes | Relative Gap (%)23.8 | 5 | |
| Minimum Vertex Cover | MVC size 16 | J/Japprox Ratio0.943 | 4 | |
| Minimum Vertex Cover | MVC size 32 | J/J Approximation Ratio0.957 | 4 | |
| Minimum Vertex Cover | MVC size 64 | J/Japprox Score0.966 | 4 |