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Hidden Markov models (HHMs) have become an increasingly useful tool for the analysis of biological data. HMM based tools are currently used for generating protein sequence profiles, predicting protein secondary structure, finding motifs in DNA sequence data, and many other bioinformatics applications. Such models are often constructed using gradient-decent based training methods such as a Baum-Welch learning algorithm or a Segmental K-means algorithm. HMM training involves estimating the model parameters based on an existing set of data. Evolutionary algorithms (EAs) have also been applied to this problem, but have typically been observed to perform best when combined with BW learning forming a hybrid approach In this work we describe a sequential parameter optimization approach for investigating the effectiveness of using EAs for training HMMs. We discuss preliminary results of this approach as obtained using synthetic DNA data sets. This approach not only offers the possibility for improving the effectiveness of the EA but will also provide much needed insight into directions for future improvements in the design of EAs for the construction of HMMs in general.