This work studies the power density (PD) optimization in wind farms, and its sensitivity to the available area size. A novel genetic algorithm (PDGA) is introduced, which optimizes PD and the turbine layout, by self-adapting to the PD and to the solutions diversity. PDGA uses the levelized cost of energy (LCOE) as cost function, which in turn employs the EPFL analytical wake model to derive the power output. For the baseline area size, PDGA reduces 2.25% the original LCOE, 2.6 times more than optimizing with constant PD. PDGA-driven solutions provide 11% and 6% LCOE reductions against the default layout for the smallest (6.4 km2) and largest (386 km2) scaled wind farm areas, respectively. Specially relevant for the industry, PDGA solutions depict convex fronts for area vs. LCOE or vs. PD, which allows determining the required area or turbine number given a target LCOE. Unlike default layouts, optimized ones reveal a linear relationship between LCOE and PD. The mean turbine spacing tends to 8-9D for very large areas. The economics-optimized PDs are below the estimated PD available in the atmosphere. This work is limited to a simplified, offshore wind climatology, a specific wind turbine model, and the LCOE specifications used herein.