This paper presents the constrained optimization of the tilting pad bearing design on a gas turbine rotor system. A real coded genetic algorithm with a robust constraint handling technique is used as the optimization method. The objective is to develop a formulation of the optimization problem for the late bearing design of a complex rotor-bearing system. Furthermore, the usefulness of the search method is evaluated on a difficult problem. The effects considered are power loss and limiting temperatures in the bearings as well as the dynamics at the system level, i.e., stability and unbalance responses. The design variables are the bearing widths and radial clearances. A nominal design is the basis for comparison of the optimal solution found. An initial numerical experiment shows that finding a solution that fulfills all the constraints for the system design is likely impossible. Still, the optimization shows the possibility of finding a solution resulting in a reduced power loss while not violating any of the constraints more than the nominal design. Furthermore, the result also shows that the used search method and constraint handling technique works on this difficult problem.