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.