Two approaches for the min-degree constrained minimum spanning tree problem

Abstract

Given an undirected, connected and weighted graph, the min-degree constrained minimum spanning tree (md_MST) problem aims to find a spanning tree (T) with minimum cost subject to each non-leaf vertex in T must have at least d degree, where d is a constant positive integer. Being a NP-hard problem, it finds several practical applications in the design of networks. In this paper, we present two approaches for this problem in which the first approach is a hybrid metaheuristic technique (hABC) combining an artificial bee colony algorithm with local search, and the second approach is iterated local search (ILS). The proposed hABC distinguishes itself from the existing hybrid artificial bee colony algorithm particularly by its size of employed bee population, initial solution generation, neighborhood operators, the way scout bee phase is handled and the local search. The proposed hABC works with a population of only 3 solutions that effectively coordinates with other key components of hABC and helps in finding new high quality solutions particularly for larger size of available benchmark instances. Extensive experiments on four data-sets of 105 benchmark instances demonstrate that ILS and hABC dominate state-of-the-art approaches. Specifically, hABC finds new best values for 41 instances, whereas ILS finds new best values for 28 instances in comparison to state-of-the-art approaches. Experimental results also show that hABC without local search (hABC-LS) is overall superior to state-of-the-art approaches except one where hABC-LS is comparable, but computationally faster on available benchmark instances.