This work examines the reduced-cost design optimization of dual- and multi-band antennas. The primary challenge is independent yet simultaneous control of the antenna responses at two or more frequency bands. In order to handle this task, a feature-based optimization approach is adopted where the design objectives are formulated on the basis of the coordinates of so-called characteristic points (or response features) of the antenna response. Due to only slightly nonlinear dependence of the feature points on antenna geometry parameters, optimization can be attained at a low computational cost. Our approach is demonstrated using two antenna structures with the optimum designs obtained in just a few dozen of EM simulations of the respective structure.