Computational optimization algorithms coupled with acoustic models of wind instruments provide instrument makers an opportunity to explore new designs. Specifically, they give the possibility to automatically find geometries exhibiting desired resonance characteristics. In this paper, the design optimization of woodwind instruments with complex geometrical features (e.g., non-cylindrical bore profile and side holes with various radii and chimney heights) is investigated. Optimal geometric characteristics are searched to obtain specific target frequencies or amplitude characteristics. However, woodwind instruments exhibit complex input impedance whose features might change drastically for a small variation of the geometry, thus hampering gradient-based optimization. For this reason, this paper introduces new formulations of the impedance characteristics (resonance frequencies and amplitudes). The approach is applied to an illustrative instrument subjected to geometric constraints similar to the ones encountered by manufacturers (a key-less pentatonic clarinet with two-registers). Three optimization problems are considered, demonstrating a strategy to simultaneously adjust several impedance characteristics on all the fingerings.