A local search heuristic for bounded-degree minimum spanning trees

The bounded-degree minimum spanning tree (BDMST) problem has many practical applications. Unlike the unbounded case, the BDMST problem is NP-hard, and many attempts have been made to devise good approximation methods, including evolutionary algorithms. Inspired by recent applications to wireless communications, the present article focuses on the geometric version of the problem, i.e. the weights assigned to links (u, v) are equal to the Euclidean distance between u and v, but no grid geometry is used as an underlying structure. The proposed genetic local search procedure for BDMST-approximations utilizes a specific edge crossover operation, and the local search in-between applications of crossover performs alternating sequences of descending and ascending steps for each individual of the population. The length of a sequence with uniform direction is controlled by the estimated value of the maximum depth of local minima of the associated fitness landscape. The computational experiments were executed on ten synthetic networks, and a comparison to two recently published BDMST algorithms is presented.