Quantum control of coherent interband transitions is analyzed using a simple, valence band as a model. A genetic algorithm is applied to optimize the shape of the pulsed driving radiation fold. The fitness function used in this study maximizes the interband transition probability and simultaneously minimizes the energy of the driving field. It is shown that such optimized ultrashort pulses exist for holes that have a well-defined initial wave vector and band index, The effect of coherent excitation on inversion of a hole distribution was calculated, too. The inverted hole distribution is shown to exhibit a characteristic pattern which depends on the driving pulse shape and band structure.