The linear hidden subset problem for the (1 + 1) EA with scheduled and adaptive mutation rates

Einarsson, Hafsteinn; Lengler, Johannes; Gauy, Marcelo Matheus; Meier, Florian; Mujika, Asier; Steger, Angelika; Weissenberger, Felix

doi:10.1145/3205455.3205519

Cited by 6 publications

(4 citation statements)

References 12 publications

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“…The setting where k corresponds to an unknown initial number of bits which impact fitness has become known as the initial segment uncertainty model. The closely related hidden subset problem, which is analogous to the initial segment model except the k meaningful bits can be anywhere in the bitstring, has also been studied for LeadingOnes k and OneMax k [15,16,26]. Since our algorithm always flips all bits with equal probability during mutation, our results immediately extend to this class of problems.…”

Section: Optimisation Against An Adversarymentioning

confidence: 85%

“…They also show the log 1+ε k term can be further reduced by more carefully choosing the positional bitflip probabilities or the distribution Q; however, in a follow-up work, it is shown that the upper bound for both of these algorithms is nearly tight, that is, the expected runtime is ω(k 2 log k) [15]. In [26], a different sort of self-adjusting (1 + 1) EA is introduced for the hidden subset problem on the class of linear functions. Rather than adjusting the mutation rate in each generation during the actual search process, the algorithm instead spends O(k) generations approximating the hidden value k, and then O(k log k) generations actually optimising f k now that k is approximately known.…”

Section: Optimisation Against An Adversarymentioning

confidence: 99%

“…However, progress in the empirical and theoretical study of EAs has shown many exceptions to these statements. It is now known that even small changes to the basic parameters of an EA can drastically increase the runtime on some problems [20,31], and more recently [34], and that hiding some aspects of the problem structure from an EA can decrease performance [5,15,16,26].…”

Section: Introductionmentioning

confidence: 99%

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Self-Adaptation in Nonelitist Evolutionary Algorithms on Discrete Problems With Unknown Structure

Case

Lehre

2020

IEEE Trans. Evol. Computat.

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A key challenge to make effective use of evolutionary algorithms is to choose appropriate settings for their parameters. However, the appropriate parameter setting generally depends on the structure of the optimisation problem, which is often unknown to the user. Non-deterministic parameter control mechanisms adjust parameters using information obtained from the evolutionary process. Self-adaptation -where parameter settings are encoded in the chromosomes of individuals and evolve through mutation and crossover -is a popular parameter control mechanism in evolutionary strategies. However, there is little theoretical evidence that self-adaptation is effective, and self-adaptation has largely been ignored by the discrete evolutionary computation community.Here we show through a theoretical runtime analysis that a non-elitist, discrete evolutionary algorithm which self-adapts its mutation rate not only outperforms EAs which use static mutation rates on LeadingOnes k , but also improves asymptotically on an EA using a state-of-the-art control mechanism. The structure of this problem depends on a parameter k, which is a priori unknown to the algorithm, and which is needed to appropriately set a fixed mutation rate. The self-adaptive EA achieves the same asymptotic runtime as if this parameter was known to the algorithm beforehand, which is an asymptotic speedup for this problem compared to all other EAs previously studied. An experimental study of

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Section: Optimisation Against An Adversarymentioning

confidence: 85%

Section: Optimisation Against An Adversarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Self-Adaptation in Nonelitist Evolutionary Algorithms on Discrete Problems With Unknown Structure

Case

Lehre

2020

IEEE Trans. Evol. Computat.

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“…We note that such scenarios have been analyzed theoretically, and different ways to deal with this unknown solution length have been proposed. Efficient EAs can obtain almost the same performance (in asymptotic terms) than EAs "knowing" the problem dimension [Einarsson et al(2018)Einarsson, Lengler, Gauy, Meier, Mujika, Steger, andWeissenberger, Doerr et al(2017)Doerr, Doerr, and. Dummy variables are also among the characteristics of the benchmark functions contained in Facebook's nevergrad platform [Rapin and Teytaud(2018)], which might be seen as evidence for practical relevance.…”

Section: The Basic Transformationsmentioning

confidence: 99%

Benchmarking discrete optimization heuristics with IOHprofiler

Doerr

Ye²,

Horesh³

et al. 2019

Proceedings of the Genetic and Evolutionary Computation Conference Companion

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Automated benchmarking environments aim to support researchers in understanding how different algorithms perform on different types of optimization problems. Such comparisons provide insights into the strengths and weaknesses of different approaches, which can be leveraged into designing new algorithms and into the automation of algorithm selection and configuration. With the ultimate goal to create a meaningful benchmark set for iterative optimization heuristics, we have recently released IOHprofiler, a software built to create detailed performance comparisons between iterative optimization heuristics. With this present work we demonstrate that IOHprofiler provides a suitable environment for automated benchmarking. We compile and assess a selection of 23 discrete optimization problems that subscribe to different types of fitness landscapes. For each selected problem we compare performances of twelve different heuristics, which are as of now available as baseline algorithms in IOHprofiler. We also provide a new module for IOHprofiler which extents the fixed-target and fixed-budget results for the individual problems by ECDF results, which allows one to derive aggregated performance statistics for groups of problems.

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Theory for non-theoreticians

Doerr

2019

Proceedings of the Genetic and Evolutionary Computation Conference Companion

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The linear hidden subset problem for the (1 + 1) EA with scheduled and adaptive mutation rates

Cited by 6 publications

References 12 publications

Self-Adaptation in Nonelitist Evolutionary Algorithms on Discrete Problems With Unknown Structure

Self-Adaptation in Nonelitist Evolutionary Algorithms on Discrete Problems With Unknown Structure

Benchmarking discrete optimization heuristics with IOHprofiler

Theory for non-theoreticians

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