Vibration control is essential to reduce excessive oscillation amplitudes, suppress undesirable resonances, and avoid early fatigue failure of structures and structural elements. The use of piezoelectric materials, which convert mechanical energy into electrical energy and vice-versa, along with shunted circuits where energy is dissipated, is a technique that can be used to improve vibration attenuation and has long been researched. A numerical model of a plate with piezoelectric patches with resistive-inductive (RL) shunts is implemented in a commercial finite element software, and a multi-objective optimization problem is formulated to improve the circuit configuration for multiple resonant frequencies. The frequency response functions for the displacement around the first few resonant frequencies are used to evaluate the performance of the method for a benchmark example [1] – a simply supported plate with four pairs of piezoelectric patches. The multi-objective optimization solutions provide the shunted circuits configurations that minimize the displacement amplitudes for the first few resonant frequencies. The used solver is Direct MultiSearch (DMS) [2] and the solutions obtained by the tuning method [1] are compared with the optimization results for the multi-mode approach.