On the Effectiveness of Sampling for Evolutionary Optimization in Noisy Environments

Abstract

Sampling has been often employed by evolutionary algorithms to cope with noise when solving noisy real-world optimization problems. It can improve the estimation accuracy by averaging over a number of samples, while also increasing the computation cost. Many studies focused on designing efficient sampling methods, and conflicting empirical results have been reported. In this paper, we investigate the effectiveness of sampling in terms of rigorous running time, and find that sampling can be ineffective. We provide a general sufficient condition under which sampling is useless (i.e., sampling increases the running time for finding an optimal solution), and apply it to analyzing the running time performance of (1+1)-EA for optimizing OneMax and Trap problems in the presence of additive Gaussian noise. Our theoretical analysis indicates that sampling in the above examples is not helpful, which is further confirmed by empirical simulation results.

An Application of Transfer Learning and Ensemble Learning Techniques for Cervical Histopathology Image Classification

“…Ensemble learning (EL) is the strategic generation and combination of multiple models, such as classifiers or experts, to solve particular computational intelligence problems [43]. EL is primarily used to improve the performance (e.g., classification, prediction, and function approximation) of a model, or reduce the likelihood of an unfortunate selection of a poor one.…”

Analysis of runtime of optimization algorithms for noisy functions over discrete codomains

“…We remark that Qian et al [21] has investigated the impact of the resampling in the 1+1-EA on the expected first hitting time. They have concluded in Theorem 2 of [21] that the resampling is useless for 1 + 1-EA optimizing the OneMax with Gaussian noise, i.e., the expected first hitting time will increase as k increases.…”

“…There are several variants for choosing k, such as: taking a fixed k, or incrementing k as the iteration does, or adapting k during the optimization. The impact of resampling on the convergence rate has been empirically or theoretically investigated in the references [23,1,12,22,21]. We here focus on the adaptation of resampling works from continuous codomains [2] to discrete ones and we cover a broad class of optimizers stated in the next subsection.…”

“…They have concluded in Theorem 2 of [21] that the resampling is useless for 1 + 1-EA optimizing the OneMax with Gaussian noise, i.e., the expected first hitting time will increase as k increases. Our result does not say anything about the runtime of Opt on a noisy problem, but states how many function evaluations we will use when k-Opt is employed to optimize a class of noisy problems compared to when Opt is used to solve the class of noiseless counterpart.…”

On the robustness of evolutionary algorithms to noise

“…Qian, Yu, and Zhou [27] showed that noise can be handled eiciently by combining reevaluation and threshold selection. Akimoto, Astete-Morales, and Teytaud [1] as well as Qian, Yu, Tang, Jin, Yao, and Zhou [26] showed that resampling can essentially eliminate the efect of noise.…”