Graph-SCP: Accelerating Set Cover Problems with Graph Neural Networks

TL;DR

Graph-SCP leverages graph neural networks to significantly reduce problem size and accelerate solving the Set Cover Problem, maintaining solution quality and generalizing to larger instances.

Contribution

It introduces a novel GNN-based method that learns to identify smaller sub-problems, enhancing existing solvers for SCP with substantial speedups and scalability.

Findings

Reduces SCP problem size by 60-80%.

Achieves up to 10x runtime speedup over Gurobi.

Maintains solution quality while generalizing to larger instances.

Abstract

Machine learning (ML) approaches are increasingly being used to accelerate combinatorial optimization (CO) problems. We investigate the Set Cover Problem (SCP) and propose Graph-SCP, a graph neural network method that augments existing optimization solvers by learning to identify a smaller sub-problem that contains the solution space. Graph-SCP uses both supervised learning from prior solved instances and unsupervised learning to minimize the SCP objective. We evaluate the performance of Graph-SCP on synthetically weighted and unweighted SCP instances with diverse problem characteristics and complexities, and on instances from the OR Library, a canonical benchmark for SCP. We show that Graph-SCP reduces the problem size by 60-80% and achieves runtime speedups of up to 10x on average when compared to Gurobi (a state-of-the-art commercial solver), while maintaining solution quality. This is in contrast to fast greedy solutions that significantly compromise solution quality to achieve guaranteed polynomial runtime. We showcase Graph-SCP's ability to generalize to larger problem sizes, training on SCP instances with up to 3,000 subsets and testing on SCP instances with up to 10,000 subsets.