Star discrepancy is a measure for the uniformity of point distribution. Low star discrepancy point sets have applications in multidimensional integration and multiobjective optimization problems. However, computing the star discrepancy is an NP-hard problem. In this work we employ a novel approach of computing star discrepancies via evolutionary algorithms (EAs). Our goal is to obtain lower bounds for the star discrepancy of a given point set. With this approach we want to prove the possibility of obtaining good approximations for the discrepancy of point sets without much computational burden.