An epistatic genetic architecture can have a significant impact on prediction accuracies of genomic prediction (GP) methods. Machine learning methods predict traits comprised of epistatic genetic architectures more accurately than statistical methods based on additive mixed linear models. The differences between these types of GP methods suggest a diagnostic for revealing genetic architectures underlying traits of interest. In addition to genetic architecture, the performance of GP methods may be influenced by the sample size of the training population, the number of QTL, and the proportion of phenotypic variability due to genotypic variability (heritability). Possible values for these factors and the number of combinations of the factor levels that influence the performance of GP methods can be large. Thus, efficient methods for identifying combinations of factor levels that produce most accurate GPs is needed. Herein, we employ response surface methods (RSMs) to find the experimental conditions that produce the most accurate GPs. We illustrate RSM with an example of simulated doubled haploid populations and identify the combination of factors that maximize the difference between prediction accuracies of best linear unbiased prediction (BLUP) and support vector machine (SVM) GP methods. The greatest impact on the response is due to the genetic architecture of the population, heritability of the trait, and the sample size. When epistasis is responsible for all of the genotypic variance and heritability is equal to one and the sample size of the training population is large, the advantage of using the SVM method vs. the BLUP method is greatest. However, except for values close to the maximum, most of the response surface shows little difference between the methods. We also determined that the conditions resulting in the greatest prediction accuracy for BLUP occurred when genetic architecture consists solely of additive effects, and heritability is equal to one.