Automatic Algorithm Selection in Computational Software Using Machine Learning

Computational software programs, such as Maple and Mathematica, heavily rely on superfunctions and meta-algorithms to select the optimal algorithm for a given task. These meta-algorithms may require intensive mathematical proof to formulate, incur large computational overhead, or fail to consistently select the best algorithm. Machine learning demonstrates a promising alternative for automatic algorithm selection by easing the design process and overhead while also attaining high accuracy in selection. In a case study on the resultant superfunction, a trained neural network is able to select the best algorithm out of the four available 86% of the time in Maple and 78% of the time in Mathematica. When used as a replacement for pre-existing meta-algorithms, the neural network brings about a 68% runtime improvement in Maple and 49% improvement in Mathematica. Random forests, k-nearest neighbors, and both linear and RBF kernel SVMs are also compared to the neural network model, the latter of which offers the best performance out of the tested machine learning methods.