There is growing interest for small antennas that concurrently have higher functionality and operability. Multiobjective optimization is an important tool in the design of such antennas since conflicting goals such as higher gain, increased bandwidth, and size reduction must be addressed simultaneously. In this paper, we present a novel optimization algorithm which permits full volumetric antenna design by combining genetic algorithms with a fast hybrid finite element-boundary integral method. To our knowledge, this is the first time that a full three dimensional antenna design is pursued using concurrent shape, size, metallization as well as dielectric and magnetic material volume optimization. In comparison to previous optimization pursuits, our approach employs a wide-frequency sweep using a single geometry model, thus, enhancing speed, along with several discrete material choices for realizable optimized designs. The developed algorithm can be interpreted as a three dimensional Pareto optimization scheme and provides the designer with several choices among the best antennas, according to design goals and constraints. The final designs are associated with very thin (~0.01lambda) material substrates and yield as much as 15% bandwidth using a 0.1lambda--0.4lambda aperture subject to various gain and bandwidth requirements