This work presents a method for evolving finite state machines for the classification of polymerase chain reaction primers in mice using graph based evolutionary algorithms. Using these machine learning tools we can compensate for many lab, organism, and chemical specific factors that can cause these primers to fail. Using Finite State Classifiers can help to decrease the number of primers that fail to amplify correctly. For training these classifiers, fifteen different graph based evolutionary algorithms were used in two different experiments to explore the effects of diversity preservation on the development of these classifiers. By controlling the rate at which information is shared in the evolving population, classifiers with a high likelihood of not accepting bad primers were found. This proposed tool can act as a post-production add-on to the standard primer picking algorithm for gene expression detection in mice to compensate for local factors that may induce errors.