In micro-electro-mechanical-system (MEMS) containing moving components, there is a need to achieve low friction and high load carrying capacity by lubrication. The aim of this paper is to study the hydrodynamic performance of a two-dimensional lubricated sliding contact in which one of the solid surfaces is designed such that partly slip boundary takes place, i.e. the complex slip surface (CSS). The approach is to use the genetic algorithm for determining the optimized complex slip surface (CSS) pattern as well as an optimized slope incline ratio simultaneously. A surface with an optimized complex slip surface (CSS) pattern in a lubricated contact generates many advantages compared to a surface without slip. The sliding surfaces considered show that the maximum load carrying capacity can be increased by approximately three times when compared to what the traditional hydrodynamics (no-slip) predict for a lubricated slider with an optimal slope incline ratio. The friction force can also be decreased significantly. The effect of an optimized complex slip surface on the hydrodynamic performance is much larger at a low initial critical shear stress than at a high initial critical shear stress. Numerical analyses indicate that varying the location and size area of the CSS pattern by taking into account the transverse direction (perpendicular to the sliding direction) in the optimization process, significantly affects the hydrodynamic performance.