A Memetic Algorithm for Minimum-Cost Vertex-Biconnectivity Augmentation of Graphs

This paper considers the problem of augmenting a given graph by a cheapest possible set of additional edges in order to make the graph vertex-biconnected. A real-world instance of this problem is the enhancement of an already established computer network to become robust against single node failures. The presented memetic algorithm includes effective preprocessing of problem data and a fast local improvement strategy which is applied before a solution is included into the population. In this way, the memetic algorithm's population consists always of only feasible, locally optimal solution candidates. Empirical results on two sets of test instances indicate the superiority of the new approach over two previous heuristics and an earlier genetic algorithm.