A genetic algorithm has been used to solve a complex multidimensional parameter-fitting problem. We will focus on the parameters of an empirical tight-binding Hamiltonian. The method is used to approximate the electronic energy band structure if energy values are known for a few wave vectors of high symmetry. Compared to the usual manual procedure this method is more accurate and automatic. This approach, based on the extended H{umlt u}ckel theory (EHT), has provided a list of EHT parameters for IV-IV and III-V semiconductors with zinc-blende structure and helped us to find a symmetry in the EHT. {copyright} {ital 1996 The American Physical Society.}