Covariance Matrix Adaptation Evolutionary Strategy with Worst-Case Ranking Approximation for Min--Max Optimization and its Application to Berthing Control Tasks

In this study, we consider a continuous min--max optimization problem $\min_{x \in \mathbb{X} \max_{y \in \mathbb{Y}}}f(x,y)$ whose objective function is a black-box. We propose a novel approach to minimize the worst-case objective function $F(x) = \max_{y} f(x,y)$ directly using a covariance matrix adaptation evolution strategy (CMA-ES) in which the rankings of solution candidates are approximated by our proposed worst-case ranking approximation (WRA) mechanism. We develop two variants of WRA combined with CMA-ES and approximate gradient ascent as numerical solvers for the inner maximization problem. Numerical experiments show that our proposed approach outperforms several existing approaches when the objective function is a smooth strongly convex--concave function and the interaction between $x$ and $y$ is strong. We investigate the advantages of the proposed approach for problems where the objective function is not limited to smooth strongly convex--concave functions. The effectiveness of the proposed approach is demonstrated in the robust berthing control problem with uncertainty.ngly convex--concave functions. The effectiveness of the proposed approach is demonstrated in the robust berthing control problem with uncertainty

Evaluation of first-order optimization algorithms in robust topology optimization of nanophotonic devices

La fotónica en silicio es un área en desarrollo emergente y constante en las últimas décadas. Los dispositivos fotónicos muestran potencial de aplicación para mejorar los sistemas de cómputo, telecomunicaciones y otras áreas. Sin embargo, aún es un reto integrar una gran cantidad de dispositivos fotónicos fundamentales en un chip con área reducida y baja pérdida. En el presente trabajo se diseñaron dos dispositivos fundamentales: (i) bend y (ii) 2-channel wavelength-demultiplexer (WDM). Los diseños se realizaron en un área de 2µm × 2µm siguiendo una estrategia basada en optimización topológica robusta. Realizamos la evaluación y comparativa de cinco algoritmos de optimización de primer orden: (i) Limited-memory Broyden–Fletcher–Goldfarb–Shanno with boundaries (L-BFGS-B), (ii) Method of Moving asymptotes (MMA), (iii) Covariance Matrix Adapatation Evolution Strategy (G-CMA-ES), (iv) Gradient Particle Swarm Optimization (GPSO) y (v) Gradient Genetic Algorithm (G-GA). Los últimos tres algoritmos son variaciones propuestas a sus versiones más populares (CMA-ES, PSO y GA) donde se incluye el cálculo de la gradiente para guiar su proceso de optimización. En nuestros resultados los diseños mejor optimizados presentan: (i) transmitancias mayores al 90 % y robustez ante errores de fabricación de dilatación y erosión, (ii) porcentaje de gris menor al 2 % y (iii) desempeño consistente y con cambios suaves en un rango de longitudes de onda (1500-1600 nm bend y 1250-1600 nm WDM) incluso si se eliminan sus regiones no conexas. Estos resultados son prometedores para (i) la integración de dispositivos WDM en un área menor al reportado en el estado del arte (<2.8µm × 2.8µm) y (ii) el diseño de bends con menores pérdidas que el diseño intuitivo-tradicional de 1µm de radio.Silicon photonics is an emerging area with constant growth in the last decades. Photonic devices show potential applications to improve computing systems, telecommunications and other areas. Nevertheless, it is still a challenge to integrate a great number of fundamental photonic devices in a chip with small area and low loss. In this work we designed two fundamental photonic devices: (i) bend and (ii) 2-channel wavelengthdemultiplexer (WDM). The designs were done on a 2µm × 2µm area following a robust topology optimization based strategy. We evaluated and comparated five first-order optimization algorithms: (i) Limitedmemory Broyden–Fletcher–Goldfarb–Shanno with boundaries (L-BFGS-B), (ii) Method of Moving asymptotes (MMA), (iii) Covariance Matrix Adapatation Evolution Strategy (G-CMA-ES), (iv) Gradient Particle Swarm Optimization (G-PSO) and (v) Gradient Genetic Algorithm (G-GA). The last three algorithms are variations of their more standard versions (CMA-ES, PSO and GA) where the computation of the gradient is included to guide the optimization process. The best optimized designs show: (i) transmission greater than 90 % and robustness to over/under-etching, (ii) a gray percentage of less than 2 % and (iii) their performance is broadband consistent with smooth changes (1500-1600 nm bend and 1250-1600 nm WDM) even after deleting non-convex regions. These results are promising for (i) the integration of WDM devices in an lower area than state of the art (<2.8µm × 2.8µm) and (ii) the design of bends with lower los than intuitive-traditional designs of 1µm radius

CMA-ES and advanced adaptation mechanisms

Doctora

CMA-ES and advanced adaptation mechanisms

International audienceDoctora

CMA-ES and Advanced Adaptation Mechanisms

International audienc