This paper applies genetic optimization with an adaptive penalty function to the shape-constrained unequal-area facility layout problem. We implement a genetic search for unequal-area facility layout, and show how optimal solutions are affected by constraints on permitted department shapes, as specified by a maximum allowable aspect ratio for each department. We show how an adaptive penalty function can be used to find good feasible solutions to even the most highly constrained problems. We describe our genetic encoding, reproduction and mutation operators, and penalty evolution strategy. We provide results from several test problems that demonstrate the robustness of this approach across different problems and parameter settings.