ICU mortality scoring systems attempt to predict patient mortality using predictive models with various clinical predictors. Examples of such systems are APACHE, SAPS and MPM. However, most such scoring systems do not actively look for and include interaction terms, despite physicians intuitively taking such interactions into account when making a diagnosis. One barrier to including such terms in predictive models is the difficulty of using most variable selection methods in high-dimensional datasets. A genetic algorithm framework for variable selection with logistic regression models is used to search for two-way interaction terms in a clinical dataset of adult ICU patients, with separate models being built for each category of diagnosis upon admittance to the ICU. The models had good discrimination across all categories, with a weighted average AUC of 0.84 (>0.90 for several categories) and the genetic algorithm was able to find several significant interaction terms, which may be able to provide greater insight into mortality prediction for health practitioners. The GA selected models had improved performance against stepwise selection and random forest models, and provides greater flexibility in terms of variable selection by being able to optimize over any modeler-defined model performance metric instead of a specific variable importance metric.