MTL Annual Research Report 2012

Advances Towards the Globally Optimal Design of Some Important Engineering Systems

Given recent advances in the field of global optimization, we aim to make advances towards deterministic global optimization of some important engineering systems (namely, multilayer filters, lens systems, and semiconductors),. The design of these systems is an activity popularly regarded as an art, and it may potentially be turned into a science using the deterministic global optimization technique of branch-and-bound. The technique of branch-bound is briefly illustrated in Figure 1 below.

Figure 1: An illustration of the technique of branch-and-bound.

As Figure 1 shows, this methodology requires the cheap construction of tight bounds on the merit function defining each optimization problem. With the recent availability of extensively verified and parallelizable software for suppressing the dependency problem (using the technique of Taylor arithmetic) arising in attempts to bound explicit merit functions (of sufficient differentiability), we aim to identify the subset of the important classes of multilayer filters and lens systems accessible by rigorous global optimization. Given recent advances in mathematical theory for constructing parametric bounds on ODE solutions (in particular, suppressing the wrapping effect using the technique of generalized McCormick Relaxations), we have developed a mathematical methodology for constructing parametric bounds on semilinear parabolic PDE solutions. The specific long-term goal of the PDE work is rigorous global optimization of semiconductors. The project is presently in the supercomputing software development phase. Preliminary serial work in the domain of multilayer filters yielded an important broadband omnidirectional antireflection coating design for silicon solar cells. Work is in progress to experimentally demonstrate this design.