An effective genetic algorithm for the minimum-label spanning tree problem

Given a connected, undirected graph G with labeled edges, the minimum-label spanning tree problem seeks a spanning tree on G to whose edges are attached the smallest possible number of labels. A greedy heuristic for this NP-hard problem greedily chooses labels so as to reduce the number of components in the subgraphs they induce as quickly as possible. A genetic algorithm for the problem encodes candidate solutions as permutations of the labels; an initial segment of such a chromosome lists the labels that appear on the edges in the chromosome's tree. Three versions of the CA apply generic or heuristic crossover and mutation operators and a local search step. In tests on 27 randomly-generated instances of the minimum-label spanning tree problem, versions of the CA that apply generic operators, with and without the local search step, perform less well than the greedy heuristic, but a version that applies the local search step and operators tailored to the problem returns solutions that require on average 10% fewer labels than the heuristic's.