Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction

Numerical optimization is an important tool in the field of computational physics in general and in nano-optics in specific. It has attracted attention with the increase in complexity of structures that can be realized with current nanofabrication technologies for which a rational design is no longer feasible. Also, numerical resources are available to enable the computational photonic material design and to identify structures that meet predefined optical properties for specific applications. However, the optimization objective function is in general nonconvex and its computation remains resource demanding such that the right choice for the optimization method is crucial to obtain excellent results. Here, we benchmark five global optimization methods for three typical nano-optical optimization problems: particle swarm optimization, differential evolution, and Bayesian optimization as well as multistart versions of downhill simplex optimization and the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm. In the shown examples from the field of shape optimization and parameter reconstruction, Bayesian optimization, mainly known from machine learning applications, obtains significantly better results in a fraction of the run times of the other optimization methods.