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 per mutations 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 GA 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 GA 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.
genetic algorithms labeled spanning trees greedy heuristics local search spanning subgraphs