A hybrid genetic algorithm for the degree-constrained minimum spanning tree problem

Abstract

Given an undirected, connected, edge-weighted graph G and a positive integer d, the degree-constrained minimum spanning tree (dc-MST) problem aims to find a minimum spanning tree T on G subject to the constraint that each vertex is either a leaf vertex or else has degree at most d in T, where d is a given positive integer. The dc-MST is $\mathcal {NP}$-hard problem for d$\ge$ 2 and finds several real-world applications. This paper proposes a hybrid approach ($\mathcal {H}$SSGA) combining a steady-state genetic algorithm and local search strategies for the this problem. An additional step (based on perturbation strategy at a regular interval of time) in the replacement strategy is applied in order to maintain diversity in the population throughout the search process. On a set of available 107 benchmark instances, computational results show the superiority of our proposed $\mathcal {H}$SSGA in comparison with the state-of-the-art metaheuristic techniques.