LES and wind tunnel studies have shown significant benefit when allowing turbines (T) in a wind farm to adopt different heights. This work presents two new genetic algorithms (GA) that perform wind farm layout optimization (WFLO) involving continuous and top-unconstrained Z-coordinate (XYZ-WFLO), applied to different power densities (PD) and using Horns Rev 1 as case study. One provides each turbine the possibility to adopt any height (XY ZInd). The other is a self-adaptive GA allowing turbines to automatically cluster into a fixed number of maximum heights (XY ZClus). When considering 80T, compared to the baseline the levelized cost of energy (LCOE) is reduced up to 2.3% (XY ZInd), vs. a 0.88% improvement obtained through XY- WFLO. XY ZClus shows performances close to XY ZInd even with just 2 Z-clusters (2%), which can entail a more feasible solution for the industry. The allowance for different heights exerts the main role in the performance improvement, in contrast to merely allowing turbines to increase their height. Results considering different PD yield the optimum XYZ-WFLO performance through 70T (2.5% LCOE decrease), while XY-WFLO provides best results considering 60T (1.5%). This indicates that the most efficient XYZ-WFLO solution also allows for bigger power productions. The benefit of XYZ-WFLO against XY-WFLO increases with PD. The optimized solutions arrange turbines into very few different heights, whose amount is positively related to PD. Finally, it is verified that the solutions attained reproduce the vertically staggered patterns proposed in conceptual studies (LES, wind tunnel).