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The design of dual-band base station antennas under constraints for mobile communications is addressed in this paper. Given the antenna geometry, the method of moments (MoM) is used to compute the antenna characteristics. Two distinct multi-objective evolutionary algorithms are applied in order to find the Pareto front of the feasible solutions that satisfy the design constraints. In the present work, the Multi-Objective Particle Swarm Optimization with fitness sharing (MOPSO-fs) is compared with the Nondominated Sorting Genetic Algorithm-II (NSGA-II) in order to optimize the antenna geometry. Two design cases are presented. The first case is a five-element array operating in GSM1800/UMTS frequency bands. The second base station antenna array consists of six elements operating in UMTS/WLAN (2.4 GHz) frequency bands.