Solid oxide fuel cell has a high energy conversion efficiency and emits a low level of pollutants. Two of the crucial elements are electrodes that are typically a composite of ion and electron-conducting materials with a complex microstructure to promote the electrochemical reactions. The microstructure morphology of an electrode plays an important role in determining the electrochemical performances of a single cell and, consequently, a stack of cells. Therefore, the microstructure optimization design should be a part of developing a system at a very early stage. The electrode material microstructure can be locally-resolved to fulfill the role it has at a particular location in the stack. This study focuses on the optimization of the morphological features of solid oxide fuel cell electrodes for the given working conditions. For the optimization method, an evolutionary algorithm is adopted. The chosen optimization method allows screening of hundreds of candidate solutions represented by the vector of microstructural parameters. The functional dependencies among the microstructural parameters are obtained using representative volume element generation techniques to ensure a feasible solution. Each set of microstructure parameters is evaluated by an extremely fast reduced model of SOFC. The properties of the best electrodes are combined to create a new generation of solutions. The algorithm is iteratively repeated until converging criteria are met, and an optimal microstructure is found. The feasibility of the obtained optimal solution was validated by reconstructing the three-dimensional digital model of the optimal microstructure with parameters proposed by the algorithm. It was shown that the presented approach supports the design of electrodes and thereby can lead to the improvement of the solid oxide fuel cell stack's performance. Optimal structures promote gas and ion transport phenomena by increasing the volume fraction of pores and ionic conductors. Because of the high mobility of electrons, the electron-conducting phase fraction is at the minimum necessary to maintain connectivity and high reaction domain. The obtained values of microstructural parameters and relations between them are in good agreement with the literature. The obtained results unveil the direction to optimize complex 3D structures, which would further improve the microstructure design in the future.