  When developing empirical equations, domain experts require these to be
accurate and adhere to physical laws. Often, constants with unknown units need
to be discovered alongside the equations. Traditional unit-aware genetic
programming (GP) approaches cannot be used when unknown constants with
undetermined units are included. This paper presents a method for dimensional
analysis that propagates unknown units as ''jokers'' and returns the magnitude
of unit violations. We propose three methods, namely evolutive culling, a
repair mechanism, and a multi-objective approach, to integrate the dimensional
analysis in the GP algorithm. Experiments on datasets with ground truth
demonstrate comparable performance of evolutive culling and the multi-objective
approach to a baseline without dimensional analysis. Extensive analysis of the
results on datasets without ground truth reveals that the unit-aware algorithms
make only low sacrifices in accuracy, while producing unit-adherent solutions.
Overall, we presented a promising novel approach for developing unit-adherent
empirical equations.
