Disclosed herein are systems and methods for multiplex primer design and selection. In one example, a system includes non-transitory memory configured to store executable instructions; and a hardware processor programmed by the executable instructions to receive a plurality of target gene sequences and determine a set of primers for each target gene sequence based on a penalty score associated with the set of primers, wherein the penalty score is based on a non-linear combination of a primer-level penalty score and a set-level penalty score.