This paper considers protograph-based LDPC codes, and proposes an optimization method to select protographs that minimize the energy consumption of quantized Min-Sum decoders. This method first estimates the average number of iterations required by the decoder, and includes this estimate into two high level models that evaluate the decoder energy consumption. The optimization problem is then formulated as minimizing the energy consumption of the decoder while satisfying a performance criterion on the Frame Error Rate. Finally, an optimization algorithm based on differential evolution is introduced. Protograph optimized for energy consumption shows a gain in energy of approximately 15% compared to a baseline protograph optimized for performance only.