Protein binding microarray (PBM) is a high-throughput platform that can measure the DNA binding preference of a protein in a comprehensive and unbiased manner. In this paper, we describe the PBM motif model building problem. We apply several evolutionary computation methods and compare their performance with the interior point method, demonstrating their performance advantages. In addition, given the PBM domain knowledge, we propose and describe a novel method called kmerGA which makes domain-specific assumptions to exploit PBM data properties to build more accurate models than the other models built. The effectiveness and robustness of kmerGA is supported by comprehensive performance benchmarking on more than 200 datasets, time complexity analysis, convergence analysis, parameter analysis, and case studies. To demonstrate its utility further, kmerGA is applied to two real world applications: 1) PBM rotation testing and 2) ChIP-Seq peak sequence prediction. The results support the biological relevance of the models learned by kmerGA, and thus its real world applicability.