A Memetic Algorithm with Population Management for the Generalized Minimum Vertex-Biconnected Network Problem

We consider the generalized minimum vertex-biconnected network problem (GMVBCNP). Given a graph where nodes are partitioned into clusters, the goal is to find a minimal cost sub graph containing exactly one node from each cluster and satisfying the vertex-biconnectivity constraint. The problem is NP-hard. The GMVBCNP has applications in the design of survivable backbone networks when single component outages are considered. We propose a Memetic Algorithm with two crossover operators, three mutation operators, and a local search component based on two neighborhood structures. Furthermore, two different population management approaches are investigated. Experimental results document the efficiency of the new approach. In particular, the local search component and the population management strategies have a substantial impact on solution quality as well as running time.