In this study, single-objective and multi-objective optimization of curved sandwich panel with composite face sheets and magneto-rheological core have been done to maximize the first modal loss factor and minimize the mass by using genetic algorithm. The studied sandwich panel was curved with simply support boundary condition. In order to derive the governing equations of motion, an improved high order sandwich panel theory and Hamilton's principle were used for the first time. The face sheet thickness, core thickness, fiber angles and intensity of the magnetic field have been considered as optimization variables. In single-objective optimization, the optimized values of variables were calculated. The results showed that the structures tend to have thick core and thin face sheets which seems physically true. As the magneto-rheological fluid placed in the core, it has a significant effect on the increasing of the modal loss factor. For the multi-objective optimization the Pareto front of optimal technique was presented. Then for the first time at this field, the set of optimal points are selected based on TOPSIS method and it was showed that in the case of similar size and mass, modal loss factor of double-curved panel is more than sigle-curved.