Labyrinth seals are extensively used in gas turbines to control leakage between components. In this research, the effects of geometry on the sealing performance are investigated. To obtain the best sealing performance, an investigation is undertaken into the possibility of optimising labyrinthseal planforms using a genetic algorithm (GA). Large Eddy Simulation (LES) is used for its ability to accurately capture the complex unsteady behaviour of this type of flow. Three hundred LES calculations are carried out. By making use of a large number of processors, an optimum geometry can be achieved within design cycle timescales. The optimised design shows a leakage reduction of about27.6% compared to the baseline geometry. An immersed boundary method (IBM) is used with LES to generate complex geometries on a background Cartesian grid. The GA is inherently parallel, and this enables the exploitation of the reliability and accuracy benefit of LES as demonstrated.