In the present work, an optimum design and analyses of active magnetic thrust bearings (AMTB) and hybrid magnetic thrust bearings (HMTB) have been carried out. The active magnetic bearing contains only electromagnets, whereas, the hybrid contains both the electro-magnets and permanent magnets. Initially, the optimization has been carried out using single-objective genetic algorithms (SOGA). Two objectives, namely the power-loss and overall weight of the bearing, are considered one at a time. Different constraints considered are the maximum current density flow in the coil, the maximum flux density flow in the stator iron, the maximum power-loss allowed, and the maximum space occupied by the bearing. Two objectives considered are found to be conflicting. This led to the attempt of optimization by using multi-objective genetic algorithms (MOGA) by considering two objectives simultaneously namely, the power-loss and overall weight of the bearing. The effect of load on the Pareto frontier has been studied, and the load is found out to be an objective in addition to the weight and the power-loss. A complex system of double-acting hybrid magnetic thrust bearings (DAHMTB) with a centralized controller as an integrated system has been optimized by using MOGA. Five objectives are considered with three for the actuator and two for the controller. Additional constraints considered are stability conditions of the controller. Though power amplifiers can be designed with respect to designed controller requirements, sometimes it is not possible to have the required power amplifiers as a standard one, and one has to design the controller by taking the constraints of the power amplifier available at hand. Though centralization of controller requires less number of power amplifiers, but needs some complex winding scheme and control strategies. To go for a simpler winding and control strategies one may have to go for a decentralized actuator, controller and power amplifier in double acting magnetic bearing systems. Hence, the design optimization methodology is extended to the DAHMTB with decentralized controller systems by taking consideration of constraints of the power amplifier, namely the maximum power rating, and the voltage of the power amplifier. The overall exercise of the optimization gives rise to a novel methodology of analysis of Pareto optimal systems called Pareto optimal design analysis by which one can predict the behavior of different designs in the Pareto front with respect to each other. It has also lead to a general integrated design optimization methodology by which one can optimize magnetic bearing systems with the actuator, controller, and amplifier as an integrated system by using the SOGA or the MOGA. The behavior of different parameters with respect to tradeoffs has been explored in detail.