Combinatorial Optimization (CO) problems over graphs appear routinely in many applications such as in optimizing traffic, viral marketing in social networks, and matching for job allocation. Due to their combinatorial nature, these problems are often NP-hard. Existing approximation algorithms and heuristics rely on the search space to find the solutions and become time-consuming when this space is large. In this paper, we design a neural method called COMBHelper to reduce this space and thus improve the efficiency of the traditional CO algorithms based on node selection. Specifically, it employs a Graph Neural Network (GNN) to identify promising nodes for the solution set. This pruned search space is then fed to the traditional CO algorithms. COMBHelper also uses a Knowledge Distillation (KD) module and a problem-specific boosting module to bring further efficiency and efficacy. Our extensive experiments show that the traditional CO algorithms with COMBHelper are at least 2 times faster than their original versions.

翻译：组合优化问题在图结构中的应用广泛存在于交通流量优化、社交网络病毒式营销以及岗位分配匹配等场景中。由于问题的组合特性，这类问题通常属于NP难问题。现有近似算法和启发式方法依赖搜索空间来求解，当搜索空间规模较大时计算耗时显著增长。本文设计了一种名为COMBHelper的神经方法，通过缩减搜索空间提升基于节点选择的传统组合优化算法的效率。具体而言，该方法采用图神经网络识别解集中的潜在优质节点，将剪枝后的搜索空间输入传统组合优化算法。COMBHelper还引入知识蒸馏模块和问题特定增强模块以进一步提升效率与有效性。大量实验表明，集成COMBHelper的传统组合优化算法运行速度至少比原始版本快两倍。