The technology of fabricating microneedle arrays to deliver high molecular weight drugs across skin in a minimally invasive manner is receiving increasing attention. Microneedle arrays with different geometries have been manufactured using materials such as glass, polymer, metal, etc. However, a framework that can identify the optimum designs of these arrays seems to be lacking. This is important since by optimizing the microneedles dimensions (e.g., surface area of the patch, microneedle radius, etc.) the permeability of drugs in skin can be increased. To address this issue, this study presents an optimization framework for transdermal delivery of high molecular weight drug from microneedle. The optimization process is based on determining an optimization function (g) for various microneedles patterns (e.g., square, diamond, triangular, etc.). We argue that higher the value of g is the higher the drug permeability in skin is. The outputs of the developed framework have allowed us to identify the optimum design of both solid and hollow microneedles. In particular, the results have been used to predict skin permeability of high molecular weight using microneedle system. Also, optimum designs based on different classifications of skin thickness (e.g., race, age, etc.) for transdermal delivery of drugs are suggested.