Effectiveness of Genetic Algorithms in Finding Steinhaus Graphs with Maximal Clique Size

Abstract

The goal of this research was to study the effectiveness of genetic algorithms (GA) in finding Steinhaus graphs of a given size whose maximal cliques were as large as possible. This investigation was based on the results obtained by Dr. Wayne Dymacek (Professor of Mathematics, Washington and Lee University) and Dr. Thomas Whaley (Professor of Computer Science, Washington and Lee University) during their research at Washington and Lee University in 1992. In addition, a report by mathematicians Daekeun Lim and Jin Hwan Kim on cliques in Steinhaus graphs also provided results related to this research. In the first chapter of this thesis, the concept of genetic algorithms will be discussed. The various characteristics of GAs, their applications, and certain theoretical aspects will be described. The second chapter will focus on Steinhaus graphs and the occurrence of maximal clique size in Steinhaus graphs. These graphs are a special type of undirected graphs that have been studied by Dr. Dymacek and Dr. Whaley for numerous years. Chapter 3 will discuss the reasons for studying GAs using this particular problem. It will also explain how GAs were applied to the problem and will include a description of the algorithm. Finally, in Chapter 4, the experiments performed during this research and their results will be explained. Chapter 5 will conclude this paper by looking at some future research possibilities for GAs applied to this problem. [From Introduction]