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Light can exert forces on objects, promising to propel a meter-scale lightsail to near the speed of light. The key to address many challenges in such an ambition hinges on the nanostructuring of lightsails to tailor their optical scattering properties. In this letter, we present a first exhaustive study of photonic design of lightsails by applying large-scale optimization techniques to a generic geometry based on stacked photonic crystal layers. The optimization is performed by rigorous coupled-wave analysis amended with automatic differentiation methods for adjoint-variable gradient evaluations. Employing these methods the propulsion efficiency of a lightsail that involves a tradeoff between high broadband reflectivity and mass reduction is optimized. Surprisingly, regardless of the material choice, the optimal structures turn out to be simply one-dimensional subwavelength gratings, exhibiting nearly 50% improvement in acceleration distance performance compared to prior studies. Our framework can be extended to address other lightsail challenges such as thermal management and propulsion stability, and applications in integrated photonics such as compact mirrors.