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Microarray Classification compares thousands of genes of an unknown patient with the genes of known patients in order to predict and diagnose diseases. Since first introduced, many algorithms and techniques have been applied in search of the best solution. In response, the Seventh International Conference on Machine Learning and Applications (ICMLA) is holding a competition in search of the best classification technique. As an entry, the authors use a General Regression Neural Network, in conjunction with a Particle Swarm Optimizer to predict microarray classifications. The GRNN is trained and tested on two datasets: colon cancer and leukemia. The algorithm is evaluated using two measures: Area Under the Receiver Operating Characteristics Curve (AUROC) and Accuracy. The algorithmpsilas best averages for the colon cancer dataset are an AUROC value of 0.90044 and an accuracy of 78.4% and for the leukemia dataset, 0.978214 and 89.5%, proving it to be a useful tool.