# ASP: Learn a Universal Neural Solver!

## TL;DR

This paper introduces ASP, a universal neural solver for combinatorial optimization that enhances generalization across distributions and scales through exploration and curriculum learning, outperforming standard methods.

## Contribution

ASP is a novel approach combining distributional exploration and scale adaptation to create a universal neural solver for various COPs.

## Key findings

- ASP achieves significant reductions in optimality gap on TSP and CVRP.
- ASP generalizes well to unseen distributions and scales.
- ASP outperforms standard training pipelines in multiple benchmarks.

## Abstract

Applying machine learning to combinatorial optimization problems has the potential to improve both efficiency and accuracy. However, existing learning-based solvers often struggle with generalization when faced with changes in problem distributions and scales. In this paper, we propose a new approach called ASP: Adaptive Staircase Policy Space Response Oracle to address these generalization issues and learn a universal neural solver. ASP consists of two components: Distributional Exploration, which enhances the solver's ability to handle unknown distributions using Policy Space Response Oracles, and Persistent Scale Adaption, which improves scalability through curriculum learning. We have tested ASP on several challenging COPs, including the traveling salesman problem, the vehicle routing problem, and the prize collecting TSP, as well as the real-world instances from TSPLib and CVRPLib. Our results show that even with the same model size and weak training signal, ASP can help neural solvers explore and adapt to unseen distributions and varying scales, achieving superior performance. In particular, compared with the same neural solvers under a standard training pipeline, ASP produces a remarkable decrease in terms of the optimality gap with 90.9% and 47.43% on generated instances and real-world instances for TSP, and a decrease of 19% and 45.57% for CVRP.