In this paper, we present a hybrid of Evolutionary Programming (EP) and Particle Swarm Optimization (PSO) algorithms for numerically efficient global optimization of antenna arrays and metasurfaces. The hybrid EP-PSO algorithm uses an evolutionary optimization approach that incorporates swarm directions in the standard self-adaptive EP algorithm. As examples, we have applied this hybrid technique to two antenna problems: the side-lobe-level reduction of a non-uniform spaced (aperiodic) linear array and the beam shaping of a printed antenna loaded with a partially reflective metasurface. Detailed comparisons between the proposed hybrid EP-PSO technique and EP-only and PSO-only techniques are given, demonstrating the efficiency of this hybrid technique in the complex antenna design problems.