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Critical node problems involve identifying a subset of critical nodes from anundirected graph whose removal results in optimizing a pre-defined measure overthe residual graph. As useful models for a variety of practical applications,these problems are computational challenging. In this paper, we study theclassic critical node problem (CNP) and introduce an effective memeticalgorithm for solving CNP. The proposed algorithm combines a doublebackbone-based crossover operator (to generate promising offspring solutions),a component-based neighborhood search procedure (to find high-quality localoptima) and a rank-based pool updating strategy (to guarantee a healthypopulation). Specially, the component-based neighborhood search integrates twokey techniques, i.e., two-phase node exchange strategy and node weightingscheme. The double backbone-based crossover extends the idea of generalbackbone-based crossovers. Extensive evaluations on 42 synthetic and real-worldbenchmark instances show that the proposed algorithm discovers 21 new upperbounds and matches 18 previous best-known upper bounds. We also demonstrate therelevance of our algorithm for effectively solving a variant of the classicCNP, called the cardinality-constrained critical node problem. Finally, weinvestigate the usefulness of each key algorithmic component.

Memetic search for identifying critical nodes in sparse graphs