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Population-based memetic algorithms have been successfully applied to solvemany difficult combinatorial problems. Often, a population of fixed size wasused in such algorithms to record some best solutions sampled during thesearch. However, given the particular features of the problem instance underconsideration, a population of variable size would be more suitable to ensurethe best search performance possible. In this work, we propose variablepopulation memetic search (VPMS), where a strategic population sizing mechanismis used to dynamically adjust the population size during the memetic searchprocess. Our VPMS approach starts its search from a small population of onlytwo solutions to focus on exploitation, and then adapts the population sizeaccording to the search status to continuously influence the balancing betweenexploitation and exploration. We illustrate an application of the VPMS approachto solve the challenging critical node problem (CNP). We show that the VPMSalgorithm integrating a variable population, an effective local optimizationprocedure (called diversified late acceptance search) and a backbone-basedcrossover operator performs very well compared to state-of-the-art CNPalgorithms. The algorithm is able to discover new upper bounds for 13 instancesout of the 42 popular benchmark instances, while matching 23 previousbest-known upper bounds.

Variable Population Memetic Search: A Case Study on the Critical Node Problem