MAGISTERARBEIT An Ant Colony Optimisation Algorithm for the Bounded Diameter Minimum Spanning Tree Problem

This master thesis presents an ant colony optimisation algorithm for the bounded diameter minimum spanning tree problem, a NP-hard combinatorial optimisation problem with various application fields, e.g. when considering certain aspects of quality in communication network design. The algorithm is extended with local optimisation in terms of a variable neighbourhood descent algorithm based on four different neighbourhood structures. These neighbourhood structures have been designed in a way to enable a fast identification of the best neighbouring solution. The proposed algorithm is empirically compared to various evolutionary algorithms and a variable neighbourhood search implementation on Euclidean instances based on complete graphs with up to 1000 nodes considering either solution quality as well as computation time. It turns out that the ant colony optimisation algorithm performs best among these heuristics with respect to quality of solution, but cannot reach the results of the variable neighbourhood search implementation concerning computation time.