Yaohui Jin

Wenxuan Guo, Junchi Yan, Hui-Ling Zhen et al.

This paper reviews the recent literature on solving the Boolean satisfiability problem (SAT), an archetypal NP-complete problem, with the help of machine learning techniques. Despite the great success of modern SAT solvers to solve large industrial instances, the design of handcrafted heuristics is time-consuming and empirical. Under the circumstances, the flexible and expressive machine learning methods provide a proper alternative to solve this long-standing problem. We examine the evolving ML-SAT solvers from naive classifiers with handcrafted features to the emerging end-to-end SAT solvers such as NeuroSAT, as well as recent progress on combinations of existing CDCL and local search solvers with machine learning methods. Overall, solving SAT with machine learning is a promising yet challenging research topic. We conclude the limitations of current works and suggest possible future directions.

Wenxuan Guo, Yanyan Xu, Yaohui Jin

Facility location problems on graphs are ubiquitous in real world and hold significant importance, yet their resolution is often impeded by NP-hardness. Recently, machine learning methods have been proposed to tackle such classical problems, but they are limited to the myopic constructive pattern and only consider the problems in Euclidean space. To overcome these limitations, we propose a general swap-based framework that addresses the p-median problem and the facility relocation problem on graphs and a novel reinforcement learning model demonstrating a keen awareness of complex graph structures. Striking a harmonious balance between solution quality and running time, our method surpasses handcrafted heuristics on intricate graph datasets. Additionally, we introduce a graph generation process to simulate real-world urban road networks with demand, facilitating the construction of large datasets for the classic problem. For the initialization of the locations of facilities, we introduce a physics-inspired strategy for the p-median problem, reaching more stable solutions than the random strategy. The proposed pipeline coupling the classic swap-based method with deep reinforcement learning marks a significant step forward in addressing the practical challenges associated with facility location on graphs.