An Evolutionary Algorithm with Solution Archive for the Generalized Minimum Spanning Tree Problem

Abstract

We propose a concept of enhancing an evolutionary algorithm (EA) with a complete solution archive that stores evaluated solutions during the optimization in a trie in order to detect duplicates and to efficiently convert them into yet unconsidered solutions. As an application we consider the generalized minimum spanning tree problem where we are given a graph with nodes partitioned into clusters and exactly one node from each cluster must be connected. For this problem there exist two compact solution representations that can be efficiently decoded, and we use them jointly in our EA. The solution archive contains two tries – each is based on one representation, respectively. We show that these two tries complement each other well. Test results on TSPlib instances document the strength of this concept and that it can match up with the leading state-of-the-art metaheuristic approaches from the literature.