Shannon Overbay

Extension of a theorem of Whitney

Abstract It is shown that every planar graph with no separating triangles is a subgraph of a Hamiltonian planar graph; that is, Whitney’s theorem holds without the assumption of a triangulation.

Trusses, NP-Completeness, and Genetic Algorithms

The optimization of large trusses often leads to a nearly optimal solution, rather than a truly optimal design. In fact, the problem space for truss optimization grows exponentially with the size of the truss. Using the method of problem reduction, this paper demonstrates that truss optimization is in the set of NP-complete problems. Hence, the only practical techniques for solving the truss problem are heuristic in nature. Genetic algorithms provide a viable solution for large trusses.

Optimizing Resources in Undergraduate Research

The Gonzaga University Center for Evolutionary Algorithms (GUCEA) is an interdisciplinary and collaborative research group which brings together faculty and undergraduate students from Civil Engineering, Computer Science, and Mathematics. GUCEA students develop genetic algorithm (GA) software which is applied to difficult problems in structural engineering and mathematics. Gonzaga University is primarily an undergraduate institution, so developing a research program involves challenges unique to smaller schools. This paper presents ways to overcome these challenges, discusses the benefits of creating a research program involving undergraduate students, and highlights GUCEA findings in optimal truss design and book embeddings of graphs. GONZAGA UNIVERSITY CENTER FOR EVOLUTIONARY ALGORITHMS (GUCEA) The Gonzaga University Center for Evolutionary Algorithms (GUCEA) aims at advancing the knowledge of genetic algorithms (GA) in optimization problems. Optimization deals with seeking the best possible solution to a design problem. GA reach this goal, mimicking the natural selection process [Haupt and Haupt, 1998]. The center was founded in the fall of 2005 as a result of a collaborative effort between Professor Paul De Palma in the Department of Computer Science, Dr. Sara Ganzerli in the Department of Civil Engineering, and Dr. Shannon Overbay in the Department of Mathematics. The development of GUCEA as a research center followed six years of collaboration between Professor Paul De Palma and Dr. Sara Ganzerli. Dr. Ganzerli came to Gonzaga in 1999 looking to expand her graduate research, which focused on structural optimization considering uncertainty by using GA. Professor De Palma identified an undergraduate student who could develop the software needed to perform the structural optimization. During the next year, Professor De Palma took an active role in this research effort, training new students in the area of GA. The newly-founded research team designed GA software to optimize structures. The resulting research activities generated peer-reviewed publications and invited presentations, and