A genetic algorithm for solving the Euclidean non-uniform Steiner tree problem

Abstract

In this paper, we present a genetic algorithm developed to solve a variation of the Euclidean Steiner tree problem. In the problem we consider, the non-uniform Steiner tree problem, the goal is to connect a set of nodes located on an uneven landscape, in a tree in the cheapest possible way. Using a combination of novel operators, our genetic algorithm is able to find optimal or near-optimal solutions in a small fraction of the time taken by an exact algorithm. In tutorial fashion, we describe the problem and some of its applications, our algorithm along with other possible approaches, and present images of several solved problem instances. © 2007 by Springer Science+Business Media, LLC.