The design of a superconducting magnetic energy storage (SMES) device requires the determination of a current system that produces a magnetic field of a given magnetic energy and a low stray field outside the device. To optimize the design, the amount of conductor and the device volume is minimized. High-temperature superconductor technology is utilized. Quench conditions must be fulfilled, In order to solve the multiobjective optimization problem, two different methods have been used: the objective weighting method, which combines the two objective functions (conductor volume and device volume) into a new cost function by means of penalty coefficients, and one based on fuzzy logic. In both methods the (1 + 1) evolution strategy minimization algorithm has been utilized. Moreover, in order to improve the solution of the objective weighting method, the results given by the evolution strategy algorithm are used as the starting point of a deterministic method (standard SQP method), The results are compared and discussed.