A new hybrid evolutionary algorithm for the k-cardinality tree problem

Abstract

In recent years it has been shown that an intelligent combination of metaheuristics with other optimization techniques can significantly improve over the application of a pure metaheuristic. In this paper, we combine the evolutionary computation paradigm with dynamic programming for the application to the NP-hard k-cardinality tree problem. Given an undirected graph G with node and edge weights, this problem consists of finding a tree in G with exactly k edges such that the sum of the weights is minimal. The genetic operators of our algorithm are based on an existing dynamic programming algorithm from the literature for finding optimal subtrees in a given tree. The simulation results show that our algorithm is able to improve the best known results for benchmark problems from the literature in 60 cases.