With modern management of primary liver cancer shifting towards non-invasive diagnostics, accurate tumor classification on medical imaging is increasingly critical for disease surveillance and appropriate targeting of therapy. Recent advancements in machine learning raise the possibility of automated tools that can accelerate workflow, enhance performance, and increase the accessibility of artificial intelligence to clinical researchers. We explore the use of an automated Tree-Based Optimization Tool that leverages a genetic programming algorithm for differentiation of the two common primary liver cancers on multiphasic MRI. Manual and automated analyses were performed to select an optimal machine learning model, with an accuracy of 73-75% (95% CI 0.59-0.85), sensitivity of 70-75% (95% CI 0.48-0.89), and specificity of 71-79% (95% CI 0.52-0.90) on manual optimization, and an accuracy of 73-75% (95% CI 0.59-0.85), sensitivity of 65-75% (95% CI 0.43-0.89) and specificity of 75-79% (95% CI 0.56-0.90) for automated machine learning. We found that automated machine learning performance was similar to that of manual optimization, and it could classify hepatocellular carcinoma and intrahepatic cholangiocarcinoma with an sensitivity and specificity comparable to that of radiologists. However, automated machine learning performance was poor on a subset of scans that met LI-RADS criteria for LR-M. Exploration of additional feature selection and classifier methods with automated machine learning to improve performance on LR-M cases as well as prospective validation in the clinical setting are needed prior to implementation.