Heuristic methods for solving two Generalized Network Problems

This thesis examines two combinatorial optimization problems: the Generalized Degree Constrained Minimum Spanning Tree Problem (d-GMSTP) and the Generalized Minimum Vertex Bi-connected Network Problem (GMVBCNP). Both problems are NPhard. Given a clustered graph where nodes are partitioned into clusters, the goal is to find a minimal cost subgraph containing exactly one node from each cluster and satisfying other constraints. For the d-GMSTP the subgraph has to fulfill degree constraint. It plays an important role in telecommunication areas where network nodes are divided into clusters and they need to be connected via tree architecture using exactly one node per cluster and satisfying degree constraint for transfer quality. The GMVBCNP can be applied to the design of survivable backbone networks that should be fault tolerant to the single component outage. In order to ensure that the failure of a single service vertex would not lead to disconnection of other services, redundant connections need to be created. For solving the d-GMSTP two approaches are proposed: Variable Neighborhood Search (VNS) which uses different types of neighborhoods, which work in complementary ways to maximize the collaboration efficiency and a Memetic Algorithm (MA) involving local improvement. For solving the GMVBCNP a Memetic Algorithm (MA) is proposed. Two different population management approaches are considered, as well as local improvement involving graph reduction technique that reduces the search space significantly. Both problems are tested on Euclidean instances with up to 442 nodes.