Machine learning (ML) approaches are increasingly being used to accelerate combinatorial optimization (CO) problems. We look specifically at the Set Cover Problem (SCP) and propose Graph-SCP, a graph neural network method that can augment existing optimization solvers by learning to identify a much smaller sub-problem that contains the solution space. We evaluate the performance of Graph-SCP on synthetic 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 30-70% and achieves run time speedups up to~25x when compared to commercial solvers (Gurobi). Given a desired optimality threshold, Graph-SCP will improve upon it or even achieve 100% optimality. This is in contrast to fast greedy solutions that significantly compromise solution quality to achieve guaranteed polynomial run time. Graph-SCP can generalize to larger problem sizes and can be used with other conventional or ML-augmented CO solvers to lead to potential additional run time improvement.

翻译：机器学习方法正被越来越多地用于加速组合优化问题。我们专门针对集合覆盖问题（SCP）提出了一种图神经网络方法Graph-SCP，该方法通过学习识别包含解空间的更小子问题，能够增强现有优化求解器的性能。我们在具有不同问题特征和复杂度的合成加权与非加权SCP实例，以及SCP标准基准测试集OR Library的实例上评估了Graph-SCP的性能。实验表明，与商业求解器（Gurobi）相比，Graph-SCP可将问题规模缩小30-70%，并实现高达约25倍的运行时间加速。在给定的最优性阈值下，Graph-SCP能够超越该阈值甚至达到100%的最优性。这与快速贪心算法形成鲜明对比——后者以显著牺牲解质量为代价来保证多项式运行时间。Graph-SCP可泛化至更大规模问题，并能与其他传统或机器学习增强的组合优化求解器结合使用，从而进一步缩短运行时间。