Identifying the cardinality-constrained critical nodes with a hybrid evolutionary algorithm

Abstract

Identifying the critical nodes in a network is crucial for understanding its characteristics, controlling its structure, and determining its functionality. Cardinality-constrained CNP (CC-CNP) is a nondeterministic polynomial-time (NP)-hard combinatorial optimization problem that refers to minimizing a set of nodes such that after deletion, the size of the largest connected component in the residual subgraph is smaller than a prescribed value. CC-CNP is applicable to a variety of fields, such as epidemic and infectious disease control, electric power network construction and maintenance, and traffic network control.In this work, we present a multistage local search (MSLS) algorithm for generating high-quality initial solutions for CC-CNP, where two strategies, circular node deletion and node change and the tabu search-based first in, first out (FIFO) principle, are utilized to prevent search detours. Then, a population-based strategy is incorporated, resulting in a genetic algorithm-based multistage local search algorithm (GAMSLS) that adopts a genetic algorithm framework, refines the initial solutions in the crossover process, and utilizes a new population update strategy to ensure the diversity and individual quality of the population. The proposed algorithm is evaluated on 75 network instances and is shown to outperform state-of-the-art algorithms for CC-CNP.