133 research outputs found
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
Towards a Theory-Guided Benchmarking Suite for Discrete Black-Box Optimization Heuristics: Profiling EA Variants on OneMax and LeadingOnes
Theoretical and empirical research on evolutionary computation methods
complement each other by providing two fundamentally different approaches
towards a better understanding of black-box optimization heuristics. In
discrete optimization, both streams developed rather independently of each
other, but we observe today an increasing interest in reconciling these two
sub-branches. In continuous optimization, the COCO (COmparing Continuous
Optimisers) benchmarking suite has established itself as an important platform
that theoreticians and practitioners use to exchange research ideas and
questions. No widely accepted equivalent exists in the research domain of
discrete black-box optimization.
Marking an important step towards filling this gap, we adjust the COCO
software to pseudo-Boolean optimization problems, and obtain from this a
benchmarking environment that allows a fine-grained empirical analysis of
discrete black-box heuristics. In this documentation we demonstrate how this
test bed can be used to profile the performance of evolutionary algorithms.
More concretely, we study the optimization behavior of several EA
variants on the two benchmark problems OneMax and LeadingOnes. This comparison
motivates a refined analysis for the optimization time of the EA
on LeadingOnes
On the Robustness of Median Sampling in Noisy Evolutionary Optimization
In real-world optimization tasks, the objective (i.e., fitness) function
evaluation is often disturbed by noise due to a wide range of uncertainties.
Evolutionary algorithms (EAs) have been widely applied to tackle noisy
optimization, where reducing the negative effect of noise is a crucial issue.
One popular strategy to cope with noise is sampling, which evaluates the
fitness multiple times and uses the sample average to approximate the true
fitness. In this paper, we introduce median sampling as a noise handling
strategy into EAs, which uses the median of the multiple evaluations to
approximate the true fitness instead of the mean. We theoretically show that
median sampling can reduce the expected running time of EAs from exponential to
polynomial by considering the (1+1)-EA on OneMax under the commonly used
one-bit noise. We also compare mean sampling with median sampling by
considering two specific noise models, suggesting that when the 2-quantile of
the noisy fitness increases with the true fitness, median sampling can be a
better choice. The results provide us with some guidance to employ median
sampling efficiently in practice.Comment: 19 pages. arXiv admin note: text overlap with arXiv:1810.05045,
arXiv:1711.0095
Analysis of Evolutionary Algorithms in Dynamic and Stochastic Environments
Many real-world optimization problems occur in environments that change
dynamically or involve stochastic components. Evolutionary algorithms and other
bio-inspired algorithms have been widely applied to dynamic and stochastic
problems. This survey gives an overview of major theoretical developments in
the area of runtime analysis for these problems. We review recent theoretical
studies of evolutionary algorithms and ant colony optimization for problems
where the objective functions or the constraints change over time. Furthermore,
we consider stochastic problems under various noise models and point out some
directions for future research.Comment: This book chapter is to appear in the book "Theory of Randomized
Search Heuristics in Discrete Search Spaces", which is edited by Benjamin
Doerr and Frank Neumann and is scheduled to be published by Springer in 201
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