It was hypothesized that the variations in time to solution are driven by the competing mechanisms of exploration and exploitation.This thesis explores this hypothesis by examining two contrasting problems that embody the hypothesized tradeoff between exploration and exploitation. Plus one recall store (PORS) is an optimization problem based on the idea of a simple calculator with four buttons: plus, one, store, and recall. Integer addition and store are classified as operations, and one and memory recall are classified as terminals. The goal is to arrange a fixed number of keystrokes in a way that maximizes the numerical result. PORS 15 (15 keystrokes) represents the subset of difficult PORS problems and PORS 16 (16 keystrokes) represents the subset of PORS problems that are easiest to optimize. The goal of this work is to examine the tradeoff between exploitation and exploration in graph based evolutionary algorithm (GBEA) optimization. To do this, computational experiments are used to examine how solutions evolve in PORS 15 and 16 problems when solved using GBEAs. The experiment is comprised of three components; the graphs and the population, the evolutionary algorithm rule set, and the example problems. The complete, hypercube, and cycle graphs were used for this experiment. …