Trejo-Sánchez, Joel Antonio ; Fajardo-Delgado, Daniel ; Gutierrez-Garcia, J. Octavio
Contributor:Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.
Title:A genetic algorithm for the maximum 2-packing set problem
Group publication title: Subject and Keywords:maximum 2-packing set ; genetic algorithms ; graph algorithms
Abstract:Given an undirected connected graph G = (V, E), a subset of vertices S is a maximum 2-packing set if the number of edges in the shortest path between any pair of vertices in S is at least 3 and S has the maximum cardinality. In this paper, we present a genetic algorithm for the maximum 2-packing set problem on arbitrary graphs, which is an NP-hard problem. To the best of our knowledge, this work is a pioneering effort to tackle this problem for arbitrary graphs. For comparison, we extended and outperformed a well-known genetic algorithm originally designed for the maximum independent set problem. ; We also compared our genetic algorithm with a polynomial-time one for the maximum 2-packing set problem on cactus graphs. Empirical results show that our genetic algorithm is capable of finding 2-packing sets with a cardinality relatively close (or equal) to that of the maximum 2-packing sets. Moreover, the cardinality of the 2-packing sets found by our genetic algorithm increases linearly with the number of vertices and with a larger population and a larger number of generations. Furthermore, we provide a theoretical proof demonstrating that our genetic algorithm increases the fitness for each candidate solution when certain conditions are met.
Publisher:Zielona Góra: Uniwersytet Zielonogórski
Date: Resource Type: DOI: Pages: Source:AMCS, volume 30, number 1 (2020) ; click here to follow the link
Language: License CC BY 4.0: Rights: