arXiv 2201.068772022-01-18cs.NEcs.AI

频繁项集驱动的复杂网络最小节点分离器搜索

Frequent Itemset-driven Search for Finding Minimum Node Separators in Complex Networks

Sino-US Global Logistics Institute, Shanghai Jiao Tong University（上海交通大学中美物流研究院）；Macau Institute of System Engineering, Macau University of Science and Technology（澳门科技大学澳门系统工程研究所）；East China University of Science and Technology（华东理工大学）；Antai College of Economics and Management, Shanghai Jiao Tong University（上海交通大学安泰经济与管理学院）；New Jersey Institute of Technology（新泽西理工学院）

Yangming Zhou, Xiaze Zhang, Na Geng, Zhibin Jiang, Mengchu Zhou

备注：: 13 pages, 4 figures

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摘要：

在复杂网络中寻找最优的关键节点集一直是人工智能和运筹学领域的一个长期问题。潜在的应用包括流行病控制、网络安全、碳排放监测、应急响应、药物设计和脆弱性评估。在这项工作中，我们考虑的问题，找到一个最小的节点分离器，其删除分离成多个不同的连接组件，每个组件中的顶点数少于有限的图。为了解决这个问题，我们提出了一个频繁项集驱动的搜索方法，它集成了数据采掘中的频繁项集挖掘的概念到著名的模因搜索框架。该算法从解的构造和种群的修复过程中得到一个高质量的种群开始，迭代地使用频繁项集重组算子（根据高质量解中频繁出现的项集生成有希望的后代解），基于禁忌搜索的模拟退火（寻找高质量的局部最优解），种群修复程序（以修改人口）和基于等级的人口管理策略（以保证健康的人口）。对50个广泛使用的基准测试实例的广泛评估表明，它显着优于国家的最先进的算法。特别是，它发现了29个新的上限，并匹配18个以前最知名的边界。最后通过实验分析验证了该方法关键算法模块的有效性。

英文摘要：

Finding an optimal set of critical nodes in a complex network has been a long-standing problem in the fields of both artificial intelligence and operations research. Potential applications include epidemic control, network security, carbon emission monitoring, emergence response, drug design, and vulnerability assessment. In this work, we consider the problem of finding a minimal node separator whose removal separates a graph into multiple different connected components with fewer than a limited number of vertices in each component. To solve it, we propose a frequent itemset-driven search approach, which integrates the concept of frequent itemset mining in data mining into the well-known memetic search framework. Starting from a high-quality population built by the solution construction and population repair procedures, it iteratively employs the frequent itemset recombination operator (to generate promising offspring solution based on itemsets that frequently occur in high-quality solutions), tabu search-based simulated annealing (to find high-quality local optima), population repair procedure (to modify the population), and rank-based population management strategy (to guarantee a healthy population). Extensive evaluations on 50 widely used benchmark instances show that it significantly outperforms state-of-the-art algorithms. In particular, it discovers 29 new upper bounds and matches 18 previous best-known bounds. Finally, experimental analyses are performed to confirm the effectiveness of key algorithmic modules of the proposed method.

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