We propose multilayers of perovskite and related ternary oxides with a general formula of ABO(3) as high reflectivity mirrors, especially for use in water window region (2.3-4.4 nm). The high reflectivity combinations of oxide multilayers were deduced using evolutionary search algorithms such as genetic algorithms, and the calculation speed was accelerated via parallel computing methods We also propose a figure of merit for X-ray reflectivity in periodic multilayers systems, which can simplify the future efforts on identifying material combinations, and the search through this multi-dimensional parameter space. The highest reflectivity value was found to be over 33% at 3.1 nm in the water window region. The effect of interface roughness was simulated and the decrease in reflectivity was found to be modest for practically achievable roughness values. This work establishes the foundation for future experimental and theoretical studies towards achieving high reflectivity x-ray mirrors of complex oxide multilayers.