  Local-gradient-based optimization approaches lack nonlocal exploration
ability required for escaping from local minima in non-convex landscapes. A
directional Gaussian smoothing (DGS) approach was recently proposed by the
authors (Zhang et al., 2020) and used to define a truly nonlocal gradient,
referred to as the DGS gradient, in order to enable nonlocal exploration in
high-dimensional black-box optimization. Promising results show that replacing
the traditional local gradient with the nonlocal DGS gradient can significantly
improve the performance of gradient-based methods in optimizing highly
multi-modal loss functions. However, the current DGS method is designed for
unbounded and unconstrained optimization problems, making it inapplicable to
real-world engineering design optimization problems where the tuning parameters
are often bounded and the loss function is usually constrained by physical
processes. In this work, we propose to extend the DGS approach to the
constrained inverse design framework in order to find a better design. The
proposed framework has its advantages in portability and flexibility to
naturally incorporate the parameterization, physics simulation, and objective
formulation together to build up an effective inverse design workflow. A series
of adaptive strategies for smoothing radius and learning rate updating are
developed to improve the computational efficiency and robustness. To enable a
clear binarized design, a dynamic growth mechanism is imposed on the projection
strength in parameterization. Our methodology is demonstrated by an example of
designing a nanoscale wavelength demultiplexer and shows superior performance
compared to the state-of-the-art approaches. By incorporating volume
constraints, the optimized design achieves an equivalently high performance but
significantly reduces the amount of material usage.
