Optimal Mutation Rates for the $$(1+\lambda )$$ EA on OneMax

Buzdalov, Maxim; Doerr, Benjamin

doi:10.1007/978-3-030-58115-2_40

Cited by 15 publications

(18 citation statements)

References 16 publications

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“…Our work has recently been extended to (1 + λ)-type RLS and EAs (Buzdalov and Doerr, 2020). In that work, not only the optimal mutation rates are computed, but also the expected remaining running times for sub-optimal mutation rates -information that can be used to identify weak spots of parameter control mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Maximizing Drift Is Not Optimal for Solving OneMax

Buskulic¹,

Doerr²

2021

Evolutionary Computation

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It seems very intuitive that for the maximization of the OneMax problem OM( x) := Σi=1nxi the best that an elitist unary unbiased search algorithm can do is to store a best so far solution, and to modify it with the operator that yields the best possible expected progress in function value. This assumption has been implicitly used in several empirical works. In [Doerr, Doerr, Yang: Optimal parameter choices via precise black-box analysis, TCS, 2020] it was formally proven that this approach is indeed almost optimal. In this work we prove that drift maximization is not optimal. More precisely, we show that for most fitness levels between n/2 and 2 n/3 the optimal mutation strengths are larger than the drift-maximizing ones. This implies that the optimal RLS is more riskaffine than the variant maximizing the step-wise expected progress. We show similar results for the mutation rates of the classic (1+1) Evolutionary Algorithm (EA) and its resampling variant, the (1+1) EA>0. As a result of independent interest we show that the optimal mutation strengths, unlike the drift-maximizing ones, can be even.

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Section: Introductionmentioning

confidence: 99%

Maximizing Drift Is Not Optimal for Solving OneMax

Buskulic¹,

Doerr²

2021

Evolutionary Computation

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“…We have extended in this work the dynamic programming approach for computing optimal state-dependent, dynamic mutation rates suggested in [27], [28] to settings in which the transition probabilities cannot necessarily be computed by closed-form expressions, but where they need to be approximated by Monte Carlo simulations. We have applied this approach to derive optimal parameter choices for the (1 + λ) EA on RUGGEDNESS.…”

Section: Discussionmentioning

confidence: 99%

“…While doing it, we assume, similarly to [27], [28], that for all higher fitness values the best possible expected running times are already computed. However, since we aim at dealing with various fitness functions, we use the Monte Carlo approach to approximate transition probabilities instead.…”

Section: A High-level Descriptionmentioning

confidence: 99%

“…In this section we outline several kinds of insights that can be derived from the results computed by the proposed algorithm. Some of them, namely lower bounds for parameter control methods, plots of optimal parameter values, and parameter efficiency heatmaps, have been previously proposed in [27], [28], and the regret plots are new to this paper.…”

Section: Example Application Of Our Approachmentioning

confidence: 99%

“…Our experiments consistently use problem size n = 100. This choice is motivated by three main factors: it is large enough to see absolute differences in algorithms' behavior, yet small enough to finish the Monte Carlo simulations, and it allows a straightforward comparison with the previous works [28], [31].…”

Section: A the Ruggedness Functionmentioning

confidence: 99%

See 2 more Smart Citations

Blending Dynamic Programming with Monte Carlo Simulation for Bounding the Running Time of Evolutionary Algorithms

Antonov

Buzdalov

Buzdalova

et al. 2021

2021 IEEE Congress on Evolutionary Computation (CEC)

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With the goal to provide absolute lower bounds for the best possible running times that can be achieved by (1 + λ)-type search heuristics on common benchmark problems, we recently suggested a dynamic programming approach that computes optimal expected running times and the regret values inferred when deviating from the optimal parameter choice.Our previous work is restricted to problems for which transition probabilities between different states can be expressed by relatively simple mathematical expressions. With the goal to cover broader sets of problems, we suggest in this work an extension of the dynamic programming approach to settings in which the transition probabilities cannot necessarily be computed exactly, but in which they can be approximated numerically, up to arbitrary precision, by Monte Carlo sampling.We apply our hybrid Monte Carlo dynamic programming approach to a concatenated jump function and demonstrate how the obtained bounds can be used to gain a deeper understanding into parameter control schemes.

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