A Permutation-Coded Evolutionary Algorithm for the Bounded-Diameter Minimum Spanning Tree Problem

The diameter of a tree is the largest number of edges on any path between two vertices in it. Given a weighted, connected, undirected graph G and a bound D ≥ 2, the bounded-diameter minimum spanning tree problem seeks a spanning tree on G of minimum weight whose diameter does not exceed D. An evolutionary algorithm for this NP-hard problem encodes candidate trees as permutations of their vertices. The first vertex (if D is even) or the first two vertices (if D is odd) form the center of the tree a permutation represents. A greedy heuristic appends the remaining vertices to the tree in their listed order, as economically as possible, while maintaining the diameter bound. In tests on 25 Euclidean problem instances, this EA identifies shorter trees on average than does an EA that encodes trees as sets of their edges, though it takes longer.