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

Abstract

Given an undirected, connected and edge-weighted graph, the min-degree constrained minimum spanning tree (md-MST) problem aims to find a minimum spanning tree (T) in such a way that each non-leaf vertex in T has degree at least d, where d is given a positive integer constant. This paper proposes a hybrid steady-state genetic algorithm (HSSGA) for the md-MST problem. The proposed HSSGA combines various components – such as problem-specific genetic operators (crossover operator and mutation operator) that are designed in such a way that the min-degree constraint is always maintained, hence resulting into a feasible child solution; and a population updating strategy that helps in maintaining diversity in the population – of the steady-state genetic algorithm with a fast local search. On a set of standard benchmark instances, the proposed HSSGA shows its effectiveness in comparison to state-of-the-art approaches such as four versions of variable neighborhood search, branch and cut algorithm and three versions of generational genetic algorithm. Moreover, HSSGA finds new best values on 32 out of 105 benchmark instances.