Date of Award
Honors Bachelor of Arts
Genetic algorithms are a commonly used metaheuristic search method aimed at solving complex optimization problems in a variety of fields. These types of algorithms lend themselves to problems that can incorporate stochastic elements, which allows for a wider search across a search space. However, the nature of the genetic algorithm can often cause challenges regarding time-consumption. Although the genetic algorithm may be widely applicable to various domains, it is not guaranteed that the algorithm will outperform other traditional search methods in solving problems specific to particular domains. In this paper, we test the feasibility of genetic algorithms in solving a common optimization problem in topological graph theory. In the study of Cayley maps, one problem that arises is how one can optimally embed a Cayley map of a complete graph onto an orientable surface with the least amount of holes on the surface as possible. One useful application of this optimization problem is in the design of circuit boards since such a process involves minimizing the number of layers that are required to build the circuit while still ensuring that none of the wires will cross. In this paper, we study complete graphs of the form K_12m + 7 for positive integers m and we work on mappings with the finite cyclic group Z_n. We develop several baseline search algorithms to first gain an understanding of the search space and its complexity. Then, we employ two different approaches to building the genetic algorithm and compare their performances in finding optimal Cayley map embeddings.
Buckelew, Jacob, "Finding Optimal Cayley Map Embeddings Using Genetic Algorithms" (2022). Honors Program Theses. 176.