Noisy Optimization With Evolution Strategies

Abstract

Evolution strategies are general, nature-inspired heuristics for search and optimization. Supported both by empirical evidence and by recent theoretical findings, there is a common belief that evolution strategies are robust and reliable, and frequently they are the method of choice if neither derivatives of the objective function are at hand nor differentiability and numerical accuracy can be assumed. However, despite their widespread use, there is little exchange between members of the "classical" optimization community and people working in the field of evolutionary computation. It is our belief that both sides would benefit from such an exchange. In this paper, we present a brief outline of evolution strategies and discuss some of their properties in the presence of noise. We then empirically demonstrate that for a simple but nonetheless nontrivial noisy objective function, an evolution strategy outperforms other optimization algorithms designed to be able to cope with noise. The environment in which the algorithms are tested is deliberately chosen to afford a transparency of the results that reveals the strengths and shortcomings of the strategies, making it possible to draw conclusions with regard to the design of better optimization algorithms for noisy environments.

Evolutionary optimisation of noisy multi-objective problems using confidence-based dynamic resampling

“…Noisy objective values like these are likely to cause a reduced convergence rate of the optimisation and a deterioration of the quality of the final sub-optimum (Beyer, 2000;Arnold and Beyer, 2002;Branke and Schmidt, 2003;Jin and Branke, 2005), since the evolutionary process, more or less, degenerates into a random search (Tan and Goh, 2008). In the next section, techniques that have been suggested to handle this problem in multi-objective optimisation are presented.…”

Selection in the Presence of Noise

“…Miller [Mil97,MG96] has developed some simplified theoretical models which allow to simultaneously optimize the population size and the sample size. A good overview of theoretical work on EAs applied to noisy optimization problems can be found in [Bey00] or [Arn02].…”

On the Effectiveness of Sampling for Evolutionary Optimization in Noisy Environments

“…Handling noise in fitness evaluations is important in that a poor solution can appear to be good due to the noise, which can mislead the search direction, resulting in an inefficient optimization. Many studies thus have focused on dealing with noise in evolutionary optimization [2,6,18].…”