An optimization technique is coupled with crystal plasticity based finite element (CPFE) computations to aid the microstructural design of a wrought magnesium alloy for improved strength and ductility. The initial microstructure consists of a collection of sub-micron sized grains containing deformation twins. The variables used in the simulations are crystallographic texture, and twin spacing within the grains. It is assumed that plastic deformation occurs mainly by dislocation slip on two sets of slip systems classified as hard and soft modes. The hard modes are those slip systems that are inclined to the twin planes and the soft mode consists of dislocation glide along the twin plane. The CPFE code calculates the stress-strain response of the microstructure as a function of the microstructural parameters and the length-scale of the features. A failure criterion based on a critical shear strain and a critical hydrostatic stress is used to define ductility. The optimization is based on the sequential generation of an initial population defined by the texture and twin spacing variables. The CPFE code and the optimizer are coupled in parallel so that new generations are created and analyzed dynamically. In each successive generation, microstructures that satisfy at least 90% of the mean strength and mean ductility in the current generation are retained. Multiple generation runs based on the above procedure are carried out in order to obtain maximum strength-ductility combinations. The implications of the computations for the design of a wrought magnesium alloy are discussed. Research sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U. S. Department of Energy.