Fast mutation in crossover-based algorithms

Antipov, Denis; Buzdalov, Maxim; Doerr, Benjamin

doi:10.1145/3377930.3390172

Cited by 34 publications

(15 citation statements)

References 23 publications

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“…This operator was shown to give a uniformly good performance of the (1 + 1) EA on all jump functions, whereas each fixed mutation rate was seen to be good only for a small range of jump sizes. The heavy-tailed operator and variations of it have shown a good performance also in other works, for example, Mironovich and Buzdalov (2017); Friedrich et al (2018aFriedrich et al ( , 2018b; Friedrich, Quinzan et al (2018); Wu et al (2018); Antipov et al (2020aAntipov et al ( , 2020b; Antipov and Doerr (2020); and Ye et al (2020). The heavy-tailed mutation operator is nothing else than standard bit mutation with a random mutation rate, chosen from a heavy-tailed distribution.…”

Section: Standard Bit Mutation With Random Mutation Ratementioning

confidence: 96%

Lower Bounds for Non-Elitist Evolutionary Algorithms via Negative Multiplicative Drift

Doerr

2021

Evolutionary Computation

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A decent number of lower bounds for non-elitist population-based evolutionary algorithms has been shown by now. Most of them are technically demanding due to the (hard to avoid) use of negative drift theorems — general results which translate an expected movement away from the target into a high hitting time. We propose a simple negative drift theorem for multiplicative drift scenarios and show that it can simplify existing analyses. We discuss in more detail Lehre's (PPSN 2010) negative drift in populations method, one of the most general tools to prove lower bounds on the runtime of non-elitist mutation-based evolutionary algorithms for discrete search spaces. Together with other arguments, we obtain an alternative and simpler proof of this result, which also strengthens and simplifies this method. In particular, now only three of the five technical conditions of the previous result have to be verified. The lower bounds we obtain are explicit instead of only asymptotic. This allows to compute concrete lower bounds for concrete algorithms, but also enables us to show that super-polynomial runtimes appear already when the reproduction rate is only a [Formula: see text] factor below the threshold. For the special case of algorithms using standard bit mutation with a random mutation rate (called uniform mixing in the language of hyper-heuristics), we prove the result stated by Dang and Lehre (PPSN 2016) and extend it to mutation rates other than [Formula: see text], which includes the heavytailed mutation operator proposed by Doerr, Le, Makhmara, and Nguyen (GECCO 2017). We finally use our method and a novel domination argument to show an exponential lower bound for the runtime of the mutation-only simple genetic algorithm on ONEMAX for arbitrary population size.

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Section: Standard Bit Mutation With Random Mutation Ratementioning

confidence: 96%

Lower Bounds for Non-Elitist Evolutionary Algorithms via Negative Multiplicative Drift

Doerr

2021

Evolutionary Computation

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“…The configurable parameters of CMA-ES were: population size 10, initial step size 1.0, random initial guess, computational budget 100𝑛 2 . The optimizer, however, did not reach the computational budget, as, in all runs, it converged to a single point and terminates at one of the degeneration criteria much earlier than that.…”

Section: Optimization With Separable Cma-esmentioning

confidence: 99%

“…The benefits of generalized mutation operators are very likely not restricted to mutation-only algorithms, but could also improve algorithms that use variation operators of different arities. First examples demonstrating clear advantages of heavy-tailed mutation in the (1 + (𝜆, 𝜆)) GA [12] were recently shown in [2,3].…”

Section: ) Interplay Of Generalized Mutation With Other Variation Ope...mentioning

confidence: 99%

Optimal Static Mutation Strength Distributions for the $(1+λ)$ Evolutionary Algorithm on OneMax

Buzdalov,

Doerr

2021

Preprint

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Most evolutionary algorithms have parameters, which allow a great flexibility in controlling their behavior and adapting them to new problems. To achieve the best performance, it is often needed to control some of the parameters during optimization, which gave rise to various parameter control methods. In recent works, however, similar advantages have been shown, and even proven, for sampling parameter values from certain, often heavy-tailed, fixed distributions. This produced a family of algorithms currently known as "fast evolution strategies" and "fast genetic algorithms".However, only little is known so far about the influence of these distributions on the performance of evolutionary algorithms, and about the relationships between (dynamic) parameter control and (static) parameter sampling. We contribute to the body of knowledge by presenting, for the first time, an algorithm that computes the optimal static distributions, which describe the mutation operator used in the well-known simple (1 + 𝜆) evolutionary algorithm on a classic benchmark problem OneMax. We show that, for large enough population sizes, such optimal distributions may be surprisingly complicated and counter-intuitive. We investigate certain properties of these distributions, and also evaluate the performance regrets of the (1 + 𝜆) evolutionary algorithm using commonly used mutation distributions.

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“…A second parameterless approach for the (1 + (λ, λ)) GA was recently analyzed in [ABD20], namely to choose the parameter λ randomly from a power-law distribution. Such a heavy-tailed parameter choice was shown to give a performance only slightly below the one obtainable from the best instance-specific values for the (1 + 1) EA optimizing jump functions [DLMN17].…”

Section: The (1 + (λ λ)) Ga Starting With Good Solutionsmentioning

confidence: 99%

First Steps Towards a Runtime Analysis When Starting With a Good Solution

Antipov¹,

Buzdalov²,

Doerr³

2020

Preprint

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The mathematical runtime analysis of evolutionary algorithms traditionally regards the time an algorithm needs to find a solution of a certain quality when initialized with a random population. In practical applications it may be possible to guess solutions that are better than random ones. We start a mathematical runtime analysis for such situations. We observe that different algorithms profit to a very different degree from a better initialization. We also show that the optimal parameterization of the algorithm can depend strongly on the quality of the initial solutions. To overcome this difficulty, self-adjusting and randomized heavy-tailed parameter choices can be profitable. Finally, we observe a larger gap between the performance of the best evolutionary algorithm we found and the corresponding black-box complexity. This could suggest that evolutionary algorithms better exploiting good initial solutions are still to be found. These first findings stem from analyzing the performance of the (1 + 1) evolutionary algorithm and the static, self-adjusting, and heavy-tailed (1 + (λ, λ)) GA on the OneMax benchmark, but we are optimistic that the question how to profit from good initial solutions is interesting beyond these first examples.

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Fast mutation in crossover-based algorithms

Cited by 34 publications

References 23 publications

Lower Bounds for Non-Elitist Evolutionary Algorithms via Negative Multiplicative Drift

Lower Bounds for Non-Elitist Evolutionary Algorithms via Negative Multiplicative Drift

Optimal Static Mutation Strength Distributions for the $(1+λ)$ Evolutionary Algorithm on OneMax

First Steps Towards a Runtime Analysis When Starting With a Good Solution

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