Ant Colony Optimization For The Edge-weighted k-cardinality Tree Problem

In this paper we deal with an NP -hard combinatorial optimization problem, the kcardinality tree problem in edge-weighted graphs. This problem has several applications in practice, which justify the need for eÆcient methods to obtain good solutions. Metaheuristic applications have already been shown to be successful in tackling the kcardinality tree problem in the past. In this paper we propose an ACO algorithm for the edge-weighted k-cardinality tree problem based on the Hyper-Cube Framework for Ant Colony Optimization. We investigate the usefulness of a higher order pheromone representation in contrast to the standard rst order pheromone representation and compare our algorithms to a multi{start local search and a heuristic developed to tackle the problem.