A Steady-State Genetic Algorithm for the Dominating Tree Problem

Abstract

Dominating tree problem DTP is a recent variant of dominating set problems in graph theory and finds its root in providing virtual backbone routing in wireless sensor networks. This problem consists in finding a tree, say DT, with minimum total edge weight on an undirected, weighted and connected graph such that each vertex of the graph is either in DT or adjacent to a vertex in DT. In this paper, a steady-state genetic algorithm SSGA is proposed for the solution of DTP. In particular, crossover operator of SSGA is designed in such a way that it generates a DT of the child solution which not only avoids the generation of a forest of trees, but also contributes in finding a high quality of child solution. Crossover and mutation of SSGA as well as other elements such as pruning procedure for the DTP are effectively coordinated in such a way that they help in evolving high quality solutions in a less time. SSGA has been compared with the best approaches in the literature. Computational results show the superiority of SSGA over these state-of-the-art approaches in terms of both solution quality and computational time.