Electroactive polymers (EAPs) are a class of non-linear electro-mechanically coupled polymer materials, where dielectric elastomers are considered in this work. A typical configuration consists of a thin layer of EAP material sandwiched between two compliant electrodes. A potential difference between the electrodes causes the EAP to deform. Possible applications include actuators and artificial muscles in soft robotics. Existing research on topology optimization of EAP structures has predominantly relied on prescribed fixed potentials and focused on the topology optimization. However, independently controlling the electrical potential at each load step enables tailoring of the output deformation, which may be exploited in applications such as robotics. The goal of this work is to introduce a novel methodology for achieving tailored deformations through large-scale, simultaneous optimization of both topology and electrical potential. The layout and placement of the electrode and EAP materials is optimized using a density-based multi-material formulation previously developed by the authors [1]. In addition to the traditional density design variables, the prescribed electrical potentials at each source and load step are introduced as additional design variables. Performing simultaneous optimization results in designs in which the prescribed potentials control the deformation to produce the tailored response. In contrast, if only the potentials are optimized, different tailored responses can be obtained for a given, fixed design. In conclusion, the proposed methodology is shown to be a promising approach for optimizing tailored responses of EAP structures. Furthermore, it is shown that EAP structures consisting of multi-million degrees of freedom and multiple load steps can be designed within a reasonable time frame.