New genetic algorithm approach for the min-degree constrained minimum spanning tree

A novel approach is proposed for the NP-hard min-degree constrained minimum spanning tree (md-MST). The NP-hardness of the md-MST demands that heuristic approximations are used to tackle its intractability and thus an original genetic algorithm strategy is described using an improvement of the Martins-Souza heuristic to obtain a md-MST feasible solution, which is also presented. The genetic approach combines the latter improvement with three new approximations based on different chromosome representations for trees that employ diverse crossover operators. The genetic versions compare very favourably with the best known results in terms of both the run time and obtaining better quality solutions. In particular, new lower bounds are established for instances with higher dimensions.