Combinatorial Optimization (CO) has been a long-standing challenging research topic featured by its NP-hard nature. Traditionally such problems are approximately solved with heuristic algorithms which are usually fast but may sacrifice the solution quality. Currently, machine learning for combinatorial optimization (MLCO) has become a trending research topic, but most existing MLCO methods treat CO as a single-level optimization by directly learning the end-to-end solutions, which are hard to scale up and mostly limited by the capacity of ML models given the high complexity of CO. In this paper, we propose a hybrid approach to combine the best of the two worlds, in which a bi-level framework is developed with an upper-level learning method to optimize the graph (e.g. add, delete or modify edges in a graph), fused with a lower-level heuristic algorithm solving on the optimized graph. Such a bi-level approach simplifies the learning on the original hard CO and can effectively mitigate the demand for model capacity. The experiments and results on several popular CO problems like Directed Acyclic Graph scheduling, Graph Edit Distance and Hamiltonian Cycle Problem show its effectiveness over manually designed heuristics and single-level learning methods.

翻译：混合优化(MLCO)是长期具有挑战性的研究课题,其特点是NP-硬性(CO)性质。这类问题通常由通常快速但可能牺牲解决方案质量的超光速算法来解决。目前,组合优化(MLCO)的机器学习已成为趋势式研究课题,但大多数现有的刚果解放运动组织方法将CO视为单一优化,直接学习端对端解决方案,这很难扩大,而且主要受ML模型能力的制约,因为CO的高度复杂性很大。在本文中,我们提出一种混合方法,将两个世界中最优秀的混合起来,其中双层框架与高层学习方法一起开发,以优化图表(例如,在图表中添加、删除或修改边缘),与在优化图形上的较低层超层超层超层超层超层超层超层超层超层超度算法。这种双层方法简化了原始硬CO的学习,可以有效缓解对模型能力的需求。在本文中,我们建议采用两种通用的共产问题实验和结果,如直接循环图表列表、图表编辑距离和汉密尔顿周期性单一周期方法。