Robustness of Populations in Stochastic Environments

Gießen, Christian; Kötzing, Timo

doi:10.1007/s00453-015-0072-0

Cited by 65 publications

(87 citation statements)

References 18 publications

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“…In [8,9,11], the inefficiency of (1 + 1) EA has been rigorously demonstrated for noisy and dynamic optimisation of OneMax and LeadingOnes. The reason behind this inefficiency is that in such environments, it is difficult for the algorithm to compare the quality of solutions, e. g., often it will choose the wrong candidate.…”

Section: Optimisation Under Incomplete Informationmentioning

confidence: 99%

“…The reason behind this inefficiency is that in such environments, it is difficult for the algorithm to compare the quality of solutions, e. g., often it will choose the wrong candidate. On the other hand, such effects could be reduced by having a population, for example the model of infinite population in [27] or finite elitist populations in [11].…”

Section: Optimisation Under Incomplete Informationmentioning

confidence: 99%

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Runtime Analysis of Non-elitist Populations: From Classical Optimisation to Partial Information

Dang

Lehre

2016

Algorithmica

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Although widely applied in optimisation, relatively little has been proven rigorously about the role and behaviour of populations in randomised search processes. This paper presents a new method to prove upper bounds on the expected optimisation time of population-based randomised search heuristics that use non-elitist selection mechanisms and unary variation operators. Our results follow from a detailed drift analysis of the population dynamics in these heuristics. This analysis shows that the optimisation time depends on the relationship between the strength of the selective pressure and the degree of variation introduced by the variation operator. Given limited variation, a surprisingly weak selective pressure suffices to optimise many functions in expected polynomial time. We derive upper bounds on the expected optimisation time of nonelitist Evolutionary Algorithms (EA) using various selection mechanisms, including fitness proportionate selection. We show that EAs using fitness proportionate selection can optimise standard benchmark functions in expected polynomial time given a sufficiently low mutation rate.As a second contribution, we consider an optimisation scenario with partial information, where fitness values of solutions are only partially available. We prove that non-elitist EAs under a set of specific conditions can optimise benchmark functions in expected polynomial time, even when vanishingly little information about the fitness values of individual solutions or populations is available. To our knowledge, this is the first runtime analysis of randomised search heuristics under partial information.

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Section: Optimisation Under Incomplete Informationmentioning

confidence: 99%

Section: Optimisation Under Incomplete Informationmentioning

confidence: 99%

Runtime Analysis of Non-elitist Populations: From Classical Optimisation to Partial Information

Dang

Lehre

2016

Algorithmica

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“…1. We have further shown that using the same algorithm we can also solve onemax in the presence of noise of variance n. Gießen and Kötzing had previously shown in [5] that a (µ + 1)-EA was able to solve onemax in the presence of noise of variance O(1). However, for an mutation-based search algorithm the variation in fitness of a child population will be dwarfed by our noise.…”

Section: Resultsmentioning

confidence: 61%

Run-Time Analysis of Population-Based Evolutionary Algorithm in Noisy Environments

Prügel-Bennett

Rowe

Shapiro

2015

Proceedings of the 2015 ACM Conference on Foundations of Genetic Algorithms XIII

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“…is bit-wise noise with parameter q. For LeadingOnes they improve results from [15], showing that the (1+1) EA runs in polynomial expected time if p = O((log n)/n 2 ) and that it runs in superpolynomial time if p = ω((log n)/n). This holds for one-bit noise with probability p, the (p, 1/n) model and bit-wise noise with probability p/n (see Table 1).…”

Section: Settingmentioning

confidence: 83%

“…Gießen and Kötzing [15] studied a more general class of algorithms, including the (1+1) EA, (1+λ) EA, and (µ+1) EA on prior noise and posterior noise, where posterior noise means that noise is added to the itness value. They presented an elegant approach that gives results in both noise models.…”

Section: Introductionmentioning

confidence: 99%

On the robustness of evolutionary algorithms to noise

Sudholt

2018

Proceedings of the Genetic and Evolutionary Computation Conference

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We present reined results for the expected optimisation time of the (1+1) EA and the (1+λ) EA on LeadingOnes in the prior noise model, where in each itness evaluation the search point is altered before evaluation with probability p. Previous work showed that the (1+1) EA runs in polynomial time if p = O((log n)/n 2 ) and needs superpolynomial time if p = Ω((log n)/n), leaving a huge gap for which no results were known. We close this gap by showing that the expected optimisation time is Θ(n 2 ) · exp(Θ(pn 2 )), allowing for the irst time to locate the threshold between polynomial and superpolynomial expected times at p = Θ((log n)/n 2 ). Hence the (1+1) EA on LeadingOnes is much more sensitive to noise than previously thought. We also show that ofspring populations of size λ ≥ 3.42 log n can efectively deal with much higher noise than known before.Finally, we present an example of a rugged landscape where prior noise can help to escape from local optima by blurring the landscape and allowing a hill climber to see the underlying gradient.

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Robustness of Populations in Stochastic Environments

Cited by 65 publications

References 18 publications

Runtime Analysis of Non-elitist Populations: From Classical Optimisation to Partial Information

Runtime Analysis of Non-elitist Populations: From Classical Optimisation to Partial Information

Run-Time Analysis of Population-Based Evolutionary Algorithm in Noisy Environments

On the robustness of evolutionary algorithms to noise

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