Solving the multi-layer thin films problem with optimization techniques

Suppose that we have a metallic substrate and our aim is to increase its reflectance by coating it with dielectric materials. Our aim is to coat this substrate with layers (N in number) of thin films from a list of alternative materials (K in number) with varying thickness so as to maximize the reflectance. This problem can be formulated as an optimization problem involving matrix multiplication. A straightforward solution approach would be to explicitly enumerate all the permutations with repetitions, which is computationally expensive. In this project, we propose to use mixed-integer nonlinear programming techniques to model and solve this challenging problem.
IE students with a strong background in operations research (IE 312 level) and computing will be preferred.