ATNAS: Automatic Termination for Neural Architecture Search.

Neural architecture search (NAS) is a framework for automating the design process of a neural network structure. While the recent one-shot approaches have reduced the search cost, there still exists an inherent trade-off between cost and performance. It is important to appropriately stop the search and further reduce the high cost of NAS. Meanwhile, the differentiable architecture search (DARTS), a typical one-shot approach, is known to suffer from overfitting. Heuristic early-stopping strategies have been proposed to overcome such performance degradation. In this paper, we propose a more versatile and principled early-stopping criterion on the basis of the evaluation of a gap between expectation values of generalisation errors of the previous and current search steps with respect to the architecture parameters. The stopping threshold is automatically determined at each search epoch without cost. In numerical experiments, we demonstrate the effectiveness of the proposed method. We stop the one-shot NAS algorithms and evaluate the acquired architectures on the benchmark datasets: NAS-Bench-201 and NATS-Bench. Our algorithm is shown to reduce the cost of the search process while maintaining a high performance.

Adaptive Ranking-Based Constraint Handling for Explicitly Constrained Black-Box Optimization.

We propose a novel constraint-handling technique for the covariance matrix adaptation evolution strategy (CMA-ES). The proposed technique is aimed at solving explicitly constrained black-box continuous optimization problems, in which the explicit constraint is a constraint whereby the computational time for the constraint violation and its (numerical) gradient are negligible compared to that for the objective function. This method is designed to realize two invariance properties: invariance to the affine transformation of the search space, and invariance to the increasing transformation of the objective and constraint functions. The CMA-ES is designed to possess these properties for handling difficulties that appear in black-box optimization problems, such as non-separability, ill-conditioning, ruggedness, and the different orders of magnitude in the objective. The proposed constraint-handling technique (CHT), known as ARCH, modifies the underlying CMA-ES only in terms of the ranking of the candidate solutions. It employs a repair operator and an adaptive ranking aggregation strategy to compute the ranking. We developed test problems to evaluate the effects of the invariance properties, and performed experiments to empirically verify the invariance of the algorithm. We compared the proposed method with other CHTs on the CEC 2006 constrained optimization benchmark suite to demonstrate its efficacy. Empirical studies reveal that ARCH is able to exploit the explicitness of the constraint functions effectively, sometimes even more efficiently than an existing box-constraint handling technique on box-constrained problems, while exhibiting the invariance properties. Moreover, ARCH overwhelmingly outperforms CHTs by not exploiting the explicit constraints in terms of the number of objective function calls.

Electromagnetic-acoustic biphysical cloak designed through topology optimization.

Various strategies have been proposed to achieve invisibility cloaking, but usually only one phenomenon is controlled by each device. Cloaking an object from two different waves, such as electromagnetic and acoustic waves, is a challenging problem, if not impossible, to be achieved using transformation theory and metamaterials, which are the major approaches in physics. Here, by developing topology optimization for controlling both electromagnetic and acoustic waves, we present a multidisciplinary attempt for designing biphysical cloaks with triple-wave cloaking capabilities, specifically for Ez- and Hz-polarized waves and acoustic wave. The topology-optimized biphysical cloak cancels the scattering of the three waves and reproduces the original propagating waves as if nothing is present, thus instilling the desired cloaking capability. In addition, we describe cloaking structures for multiple incident directions of the three waves and structures that work for both electromagnetic waves and sound waves of different wavelengths.

dc electric cloak concentrator via topology optimization.

We succeeded in simultaneously cloaking and concentrating direct current in a conducting material through topology optimization based on a level-set method. To design structures that perform these functions simultaneously, optimal topology is explored for improving two objective functions that govern separately the cloaking and concentration of current. Our design scheme, i.e., the topology optimization of a direct-current electric cloak concentrator, provides this bifunctionality well despite simple, common bulk materials being used to make up the structures. The materials also rigorously obey the electric conduction equation in contrast to the approximated artificial materials, so-called metamaterials, of other design schemes. The structural features needed for this simultaneous bifunctionality are found by adopting level-set method to generate material domains and clear structural interfaces. Furthermore, robust performances of the bifunctional structures against fluctuations in electrical conductivity was achieved by improving the fitness incorporating multiple objective functions. Additionally, the influence of the size of the current-concentrating domain on the performances of the optimal configuration is investigated.

DC carpet cloak designed by topology optimization based on covariance matrix adaptation evolution strategy.

Optimal designs of direct current (DC) carpet cloaks are obtained using topology optimization based on the covariance matrix adaptation evolution strategy. The cloaking structures are expressed using an immersed boundary-level set method visualized as gray-scale-free configurations and composed simply of homogeneous materials. These cloaks successfully hide bumps made electrically invisible through topology optimization by minimizing the difference in voltage distributions around the cloaked bump and over the flat surface in the absence of the bump. Moreover, reproducing the electric potential field without a bump for DC flowing over a wide angle is achieved by the optimal cloak despite the presence of the bump on the flat surface.