An optimum design of thrust magnetic bearings has been carried out using multi-objective genetic algorithms (MOGAs). The power-loss and the weight have been selected as the minimization type objective functions for the optimum design. The maximum space available, the maximum current density that can be supplied in the coil, the maximum magnetic flux density that is allowed in the stator-iron (i.e., the magnetic flux density at the saturation), and the load required to be supported have been chosen as constraints. The inner and outer radii of the coil, and the height of the coil have been proposed as design variables. Apart from the comparison of performance parameters in the form of figures and tables, designs are also compared through line diagrams. Post-processing has been done on the final optimized population by studying the variation of different parameters with respect to objective functions. The saturation of magnetic flux density and the saturation of coil current density are observed to be the salient points, where the major changes occur in the behavior of different design parameters. A criterion for the choice of one of the best design based on the minimum normalized distance near the utopia point is used. A sensitivity analysis has been done on a chosen design by giving small perturbations on the design variables. It is observed that the effect of the outer radius of the coil on the objective functions is nearly double as compared to other two design variables.