The distance-based critical node problem involves identifying a subset of nodes in a graph such that the removal of these nodes leads to a residual graph with the minimum distance-based connectivity. Due to its NP-hard nature, solving this problem using exact algorithms has proved to be highly challenging. Moreover, existing heuristic algorithms are typically time-consuming. In this work, we introduce a fast tri-individual memetic search approach to solve the problem. The proposed approach maintains a small population of only three individuals during the whole search. At each generation, it sequentially executes an inherit-repair recombination operator to generate a promising offspring solution, a fast betweenness centrality-based late-acceptance search to find high-quality local optima, and a simple population updating strategy to maintain a healthy population. Extensive experiments on both real-world and synthetic benchmarks show our method significantly outperforms state-of-the-art algorithms. In particular, it can steadily find the known optimal solutions for all 22 real-world instances with known optima in only one minute, and new upper bounds on the remaining 22 large real-world instances. For 54 synthetic instances, it finds new upper bounds on 36 instances, and matches the previous best-known upper bounds on 15 other instances in ten minutes. Finally, we investigate the usefulness of each key algorithmic ingredient.

基于距离的关键节点问题涉及识别图中的节点子集，以便删除这些节点导致具有最小基于距离的连通性的残差图。由于其 NP-hard 性质，使用精确算法解决此问题已被证明是极具挑战性的。此外，现有的启发式算法通常很耗时。在这项工作中，我们引入了一种快速的三个体模因搜索方法来解决这个问题。所提出的方法在整个搜索过程中保持只有三个人的小群体。在每一代，它依次执行一个继承修复重组算子来生成一个有前途的后代解决方案，一个快速的基于介数中心性的后期接受搜索来找到高质量的局部最优，和一个简单的种群更新策略来维持健康的种群。在现实世界和合成基准上进行的大量实验表明，我们的方法明显优于最先进的算法。特别是，它可以在一分钟内稳定地找到所有 22 个已知最优的真实世界实例的已知最优解，并在其余 22 个大型真实世界实例上找到新的上界。对于 54 个合成实例，它在 36 个实例上找到了新的上限，并在 10 分钟内匹配了 15 个其他实例上之前最知名的上限。最后，我们研究了每个关键算法成分的有用性。它可以在一分钟内稳定地找到所有 22 个具有已知最优值的真实世界实例的已知最优解，并在其余 22 个大型真实世界实例上找到新的上界。对于 54 个合成实例，它在 36 个实例上找到了新的上限，并在 10 分钟内匹配了 15 个其他实例上之前最知名的上限。最后，我们研究了每个关键算法成分的有用性。它可以在一分钟内稳定地找到所有 22 个具有已知最优值的真实世界实例的已知最优解，并在其余 22 个大型真实世界实例上找到新的上界。对于 54 个合成实例，它在 36 个实例上找到了新的上限，并在 10 分钟内匹配了 15 个其他实例上之前最知名的上限。最后，我们研究了每个关键算法成分的有用性。