In the paper, the authors apply tuning-space mapping to multi-objective synthesis of a filtering antenna. The antenna is going to be implemented as a planar dipole array with serial feeding. Thanks to the multi-objective approach, the authors can deal with conflicting requirements on gain, impedance matching, side-lobe level and main-lobe direction. MOSOMA (Multi-Objective Self-Organizing Migration Algorithm) algorithm is applied to compute Pareto front of optimal solutions by changing lengths of dipoles and parameters of transmission lines connecting them into a serial array.