A parallel deterministic global optimization algorithm for thin-film multilayer optical coatings is developed. This algorithm enables locating a global solution to an optimization problem in this class to within a user-specified tolerance. More specifically, the algorithm is a parallel branch-and-bound method with applicable bounds on the merit function computed using Taylor models. This study is the first one, to the best of our knowledge, to attempt guaranteed global optimization of this important class of problems, thereby providing an overview and an assessment of the current state of such techniques in this domain. As a proof of concept on a small scale, the method is illustrated numerically and experimentally in the context of antireflection coatings for silicon solar cells-we design and fabricate a three-layer dielectric stack on silicon that exhibits an average reflectance of (2.53±0.10)%, weighted over a broad range of incident angles and the solar spectrum. The practicality of our approach is assessed by comparing its computational cost relative to traditional stochastic global optimization techniques which provide no guarantees on their solutions. While our method is observed to be significantly more computationally expensive, we demonstrate via our proof of concept that it is already feasible to optimize sufficiently simple practical problems at a reasonable cost, given the current accessibility of cloud computing resources. Ongoing advances in distributed computing are likely to bring more design problems within the reach of deterministic global optimization methods, yielding rigorous guaranteed solutions in the presence of practical manufacturing constraints.
A.1. Parallel algorithm implementation issuesThe parallel branch-and-bound algorithm was implemented on Amazon's EC2 platform using the COSY INFINITY system [33]. In particular, single work queue dynamic scheduling components of the algorithm on any given server were implemented using the scheduling construct PLOOP made recently available by COSY INFINITY's authors, this construct providing an interface to the Message Passing Interface but restricted to allto-all communication between processes. It is emphasized that because this construct only allows all-to-all communication between running processes, the communication and synchronization costs prohibit dynamic scheduling of tasks across multiple servers. Further details on this in [28].All models were tested against analytic examples in the literature while also being validated against real data. Merit lower bounding code was tested for consistency, i.e. we verified that the bounds become tighter as the parameter interval on which the lower bound is computed is made smaller, and that the merit value is attained on a thin/degenerate interval. This allows us to conjecture that our algorithm is provably convergent [9]. Moreover, the model was tested against real data in the context of the numerical example below, and found to be accurate, which validates our modeling assumptions, choice of in...