A population of Self-Driving Automata (SDAs) is evolved using a steady-state evolutionary algorithm tasked with matching six DNA sequences. This is a step towards using SDAs to assist in identifying patterns within groups of DNA sequences for which conventional methods for identifying patterns fail. The fitness function uses both a primary and a secondary fitness metric to determine the overall fitness of an SDA. The primary metric is sequence matching fitness, evaluating how well the evolved sequence matches the target sequence. The secondary metric is sequence diversity fitness: considering pairs of sequences with the same primary fitness, this counts the number of differences that exist between them. It is found that promoting diversity in this manner by using a secondary fitness metric dramatically improves results for the primary fitness metric.