Diagnosis of students with learning disabilities has long been a difficult issue as it requires extensive man power and takes a long time. Through genetic algorithm based feature selection method and genetic based parameters optimization, artificial neural network (ANN) classifier has proven to be a good predictor to the diagnosis of students with learning disabilities. In this study, we keep focusing on the ANN model and compare three strategies of parallelizing the ANN parameter optimization procedure with OpenMP and MPI APIs. Not surprisingly, the outcomes show that all three parameter optimization procedures indeed converged or executed more quickly with the aid of parallel processing. In particular, the genetic-based method tends to derive the best accuracy and require less execution time. Most important of all, potentially due to a more diverse search space provided by the distributed parallel processing environment, the accuracy of the genetic-based ANN classifier may also be improved in general. In addition, with appropriate combinations of features and parameters setting, the accuracy in LD identification model has exceeded the 90% mark (using 5-fold cross validation), which is the best we have achieved so far. The result suggests that genetic-based (or perhaps similar) optimization methods may be benefited, both in reducing execution time and achieving better outcome, from current grid-based computing technologies.