Analysis of Noisy Evolutionary Optimization When Sampling Fails

In noisy evolutionary optimization, sampling is a common strategy to deal with noise. By the sampling strategy, the fitness of a solution is evaluated multiple times (called \emph{sample size}) independently, and its true fitness is then approximated by the average of these evaluations. Previous studies on sampling are mainly empirical. In this paper, we first investigate the effect of sample size from a theoretical perspective. By analyzing the (1+1)-EA on the noisy LeadingOnes problem, we show that as the sample size increases, the running time can reduce from exponential to polynomial, but then return to exponential. This suggests that a proper sample size is crucial in practice. Then, we investigate what strategies can work when sampling with any fixed sample size fails. By two illustrative examples, we prove that using parent or offspring populations can be better. Finally, we construct an artificial noisy example to show that when using neither sampling nor populations is effective, adaptive sampling (i.e., sampling with an adaptive sample size) can work. This, for the first time, provides a theoretical support for the use of adaptive sampling

Bounded perturbation resilience of extragradient-type methods and their applications

In this paper we study the bounded perturbation resilience of the extragradient and the subgradient extragradient methods for solving variational inequality (VI) problem in real Hilbert spaces. This is an important property of algorithms which guarantees the convergence of the scheme under summable errors, meaning that an inexact version of the methods can also be considered. Moreover, once an algorithm is proved to be bounded perturbation resilience, superiorizion can be used, and this allows flexibility in choosing the bounded perturbations in order to obtain a superior solution, as well explained in the paper. We also discuss some inertial extragradient methods. Under mild and standard assumptions of monotonicity and Lipschitz continuity of the VI's associated mapping, convergence of the perturbed extragradient and subgradient extragradient methods is proved. In addition we show that the perturbed algorithms converges at the rate of $O(1/t)$. Numerical illustrations are given to demonstrate the performances of the algorithms.Comment: Accepted for publication in The Journal of Inequalities and Applications. arXiv admin note: text overlap with arXiv:1711.01936 and text overlap with arXiv:1507.07302 by other author

Forget metamaterial: It does not improve sound absorption performance as it claims

The term `sub-wavelength' is commonly used to describe innovative sound-absorbing structures usually labeled as `metamaterials'. Such structures, however, inherently do not bring groundbreaking advancements. This study addresses the limitations imposed by the thickness criterion of Yang et al. by introducing the concept of equivalent mass-spring-damping parameters within the resonator framework. This innovative approach introduces an index of `half-absorption bandwidth' to effectively overcome the thickness restriction. Four practical cases are then presented to correct prevalent misleading conceptions about low-frequency, broadband absorption as claimed. The phenomenon of mass disappearing in the expression of sound absorption coefficient supports the conclusion that volume is the only determinant factor in sound absorption performance. Any attempts to improve sound absorption solely through geometry and structural designs would inevitably sacrifice the half-absorption bandwidth. Additionally, the concept of negative stiffness or bulk modulus is merely a mathematical convention without any real improvement in absorption performance. Overall, this research focuses on the physical mechanism of sound-absorbing structures by correcting traditional misunderstandings, and offers a comprehensive framework for assessing and enhancing sound absorption.Comment: 12 pages, 5 figures, part of the first author's Ph.D. thesi