Combinatorial optimization problems arise naturally in a wide range of applications from diverse domains. Many of these problems are NP-hard and designing efficient heuristics for them requires considerable time, effort and experimentation. On the other hand, the number of optimization problems in the industry continues to grow. In recent years, machine learning techniques have been explored to address this gap. In this paper, we propose a novel framework for leveraging machine learning techniques to scale-up exact combinatorial optimization algorithms. In contrast to the existing approaches based on deep-learning, reinforcement learning and restricted Boltzmann machines that attempt to directly learn the output of the optimization problem from its input (with limited success), our framework learns the relatively simpler task of pruning the elements in order to reduce the size of the problem instances. In addition, our framework uses only interpretable learning models based on intuitive local features and thus the learning process provides deeper insights into the optimization problem and the instance class, that can be used for designing better heuristics. For the classical maximum clique enumeration problem, we show that our framework can prune a large fraction of the input graph (around 99% of nodes in case of sparse graphs) and still detect almost all of the maximum cliques. Overall, this results in several fold speedups of state-of-the-art algorithms. Furthermore, the classification model used in our framework highlights that the chi-squared value of neighborhood degree has a statistically significant correlation with the presence of a node in a maximum clique, particularly in dense graphs which constitute a significant challenge for modern solvers. We leverage this insight to design a novel heuristic we call ALTHEA for the maximum clique detection problem, outperforming the state-of-the-art for dense graphs.

组合优化问题自然出现在来自不同领域的广泛应用中。其中许多问题都是 NP-hard 问题，为它们设计有效的启发式方法需要大量的时间、精力和实验。另一方面，行业优化问题数量持续增长。近年来，人们探索了机器学习技术来解决这一差距。在本文中，我们提出了一种利用机器学习技术扩展精确度的新框架组合优化算法。与基于深度学习、强化学习和受限玻尔兹曼机的现有方法不同，这些方法试图直接从输入中学习优化问题的输出（成功率有限），我们的框架学习了相对简单的任务，即修剪元素为了减少问题实例的大小。此外，我们的框架仅使用基于直观局部特征的可解释学习模型，因此学习过程提供了对优化问题和实例类的更深入洞察，可用于设计更好的启发式方法。对于经典的最大团枚举问题，我们表明我们的框架可以修剪大部分输入图（在稀疏图的情况下大约 99% 的节点）并且仍然检测到几乎所有的最大派系。总的来说，这导致最先进算法的数倍加速。此外，我们框架中使用的分类模型强调，邻域度的卡方值与最大团中节点的存在具有统计上显着的相关性，特别是在密集图中，这对现代求解器构成了重大挑战。我们利用这种洞察力设计了一种新的启发式算法，我们称之为 ALTHEA 来解决最大的集团检测问题，优于最先进的密集图。我们框架中使用的分类模型强调，邻域度的卡方值与最大团中节点的存在具有统计上显着的相关性，特别是在密集图中，这对现代求解器构成了重大挑战。我们利用这种洞察力设计了一种新的启发式算法，我们称之为 ALTHEA 来解决最大的集团检测问题，优于最先进的密集图。我们框架中使用的分类模型强调，邻域度的卡方值与最大团中节点的存在具有统计上显着的相关性，特别是在密集图中，这对现代求解器构成了重大挑战。我们利用这种洞察力设计了一种新的启发式算法，我们称之为 ALTHEA 来解决最大的集团检测问题，优于最先进的密集图。