🤖 AI Summary
To address the challenge of balancing computational efficiency and solution quality in the Set Cover Problem (SCP), this paper proposes Graph-SCP: a graph neural network-based preprocessing method that models SCP as a set-element bipartite graph. Graph-SCP is the first approach to jointly train via supervised learning—leveraging historical optimal solutions—and unsupervised learning—minimizing the SCP objective—to automatically identify and compress the original instance into a high-quality subproblem of 20–40% its original size. Evaluated on OR Library and synthetic benchmarks, Graph-SCP achieves an average 10× speedup over Gurobi without sacrificing solution quality; it also significantly outperforms greedy heuristics in accuracy. Crucially, it exhibits strong cross-scale generalization—trained on instances with ≤3k subsets and tested on up to 10k—thereby breaking the classical trade-off between precision and efficiency inherent in traditional exact and heuristic methods.
📝 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 much smaller sub-problem that contains the solution space. Graph-SCP uses both supervised learning from prior solved instances and unsupervised learning aimed at minimizing 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.
