Optimization of Yagi-Uda antennas is a challenging design problem, since the antenna characteristics such as gain, input impedance, maximum sidelobe level etc., are known to be extremely sensitive to the design variables viz., element lengths and their spacings. This corresponds to a highly nonlinear and multimodal function space with functional and slope discontinuities that limit the use of conventional gradient based optimization approaches. Although, stochastic, zeroth-order methods like genetic algorithm and evolutionary algorithm are attractive choices for such classes of problems, their successful application requires scaling and aggregating parameters to handle constraints and objectives that may not be easy to provide. In this paper, we introduce a stochastic, zeroth-order optimization algorithm that handles constraints and objectives separately via Pareto ranking that eliminates the problem of scaling and aggregation. The algorithm is based on principles of learning and is embedded with three key learning strategies that control whom to learn from (i.e., leader identification and leader selection) and what to learn (i.e., information acquisition) in order to better guide the search. The leader identification mechanism partitions the individuals into a set of leaders and a set of followers. The followers interact with the leader and move toward the better performing leaders in search for better solutions. As the algorithm does not require parameters for scaling or aggregation, it provides the designer the true flexibility that is necessary to handle various forms of the design problem effectively and at a computational cost that is comparable to existing stochastic optimization methods. Results of three single objective antenna design examples (a four-element, a 15-element and a fixed boom length 22-element design) are presented and compared with published results to illustrate the behavior of the proposed algorithm and highlight its benefits in solving a wide variety of antenna design problems. A new set of results are presented for a multiobjective formulation of the design problem.