Improving Critical Node Detection Using Neural Network-based Initialization in a Genetic Algorithm
Chanjuan Liu, Shike Ge, Zhihan Chen, Wenbin Pei, Enqiang Zhu, Yi Mei, Hisao Ishibuchi
TL;DR
The paper tackles the NP-hard CNP-1a by introducing K2GA, a knowledge-guided genetic algorithm that uses a pretrained Graph Attention Network to predict promising critical nodes for initialization and a cut-node–oriented local search to refine solutions. This hybrid framework combines inductive graph learning with memetic search, achieving superior results on 26 real-world networks, including eight new upper bounds for the best objective value. The approach is validated against state-of-the-art baselines, with extensive ablation showing the neural initialization and cut-node strategy as key drivers of performance. The work demonstrates the practical impact of integrating graph-based priors into evolutionary search for combinatorial network problems and suggests avenues for extending knowledge-guided optimization to other NP-hard tasks.
Abstract
The Critical Node Problem (CNP) is concerned with identifying the critical nodes in a complex network. These nodes play a significant role in maintaining the connectivity of the network, and removing them can negatively impact network performance. CNP has been studied extensively due to its numerous real-world applications. Among the different versions of CNP, CNP-1a has gained the most popularity. The primary objective of CNP-1a is to minimize the pair-wise connectivity in the remaining network after deleting a limited number of nodes from a network. Due to the NP-hard nature of CNP-1a, many heuristic/metaheuristic algorithms have been proposed to solve this problem. However, most existing algorithms start with a random initialization, leading to a high cost of obtaining an optimal solution. To improve the efficiency of solving CNP-1a, a knowledge-guided genetic algorithm named K2GA has been proposed. Unlike the standard genetic algorithm framework, K2GA has two main components: a pretrained neural network to obtain prior knowledge on possible critical nodes, and a hybrid genetic algorithm with local search for finding an optimal set of critical nodes based on the knowledge given by the trained neural network. The local search process utilizes a cut node-based greedy strategy. The effectiveness of the proposed knowledgeguided genetic algorithm is verified by experiments on 26 realworld instances of complex networks. Experimental results show that K2GA outperforms the state-of-the-art algorithms regarding the best, median, and average objective values, and improves the best upper bounds on the best objective values for eight realworld instances.