Does comma selection help to cope with local optima?

Doerr, Benjamin

doi:10.1145/3377930.3389823

Cited by 36 publications

(16 citation statements)

References 56 publications

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“…We refer to Lengler (2020, Section 2.4.3) for more details. Another approach to negative drift was used in Antipov et al (2019) and Doerr (2019bDoerr ( , 2020a. There the original process was transformed suitably (via an exponential function), but in a way that the drift of the new process still is negative or at most a small constant.…”

Section: Related Workmentioning

confidence: 99%

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: Related Workmentioning

confidence: 99%

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

Doerr

2021

Evolutionary Computation

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“…For the (µ, λ) EA optimizing jump functions, however, the existence of a profitable middle regime was disproven in [Doe20a]. Some more results exist that show situations where only an inefficient regime exists, e.g., when using (1+1)-type hillclimbers with fitness-proportionate selection to optimize linear pseudo-Boolean functions [HJKN08] or when using a mutation-only variant of the simple genetic algorithm to optimize OneMax [NOW09].…”

Section: Non-elitist Evolutionary Algorithmsmentioning

confidence: 99%

Choosing the Right Algorithm With Hints From Complexity Theory

Wang¹,

Zheng²,

Doerr³

2021

Preprint

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Choosing a suitable algorithm from the myriads of different search heuristics is difficult when faced with a novel optimization problem. In this work, we argue that the purely academic question of what could be the best possible algorithm in a certain broad class of black-box optimizers can give fruitful indications in which direction to search for good established optimization heuristics. We demonstrate this approach on the recently proposed DLB benchmark, for which the only known results are O(n 3 ) runtimes for several classic evolutionary algorithms and an O(n 2 log n) runtime for an estimation-of-distribution

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“…In comparison to the prosperous theoretical work on the elitist evolutionary algorithms, the theory for the non-elitist evolutionary algorithms has been few. Recently, in his work about the classic non-elitist (µ, λ) EA on the Jump function, Doerr [Doe20a] conducted a thorough survey on the theory for the classic non-elitist evolutionary algorithms, such as (1, λ) EA and (µ, λ) EA. He divided the non-elitist theoretical work into three categories.…”

Section: Literature Review On Non-elitist Theorymentioning

confidence: 99%

“…• When the selection pressure is low, the classic non-elitist evolutionary algorithms need exponential runtime. See the literatures mentioned in [Doe20a]. This category points the negative evidence of the classic non-elitist evolutionary algorithms.…”

Section: Literature Review On Non-elitist Theorymentioning

confidence: 99%

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When Non-Elitism Meets Time-Linkage Problems

Zheng

Zhang

Chen

et al. 2021

Preprint

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Many real-world applications have the time-linkage property, and the only theoretical analysis is recently given by Zheng, et al. (TEVC 2021) on their proposed time-linkage OneMax problem, OneMax (0,1 n ) . However, only two elitist algorithms (1 + 1) EA and (µ + 1) EA are analyzed, and it is unknown whether the non-elitism mechanism could help to escape the local optima existed in OneMax (0,1 n ) . In general, there are few theoretical results on the benefits of the non-elitism in evolutionary algorithms. In this work, we analyze on the influence of the non-elitism via comparing the performance of the elitist (1 + λ) EA and its non-elitist counterpart (1, λ) EA. We prove that with probability 1 − o(1) (1 + λ) EA will get stuck in the local optima and cannot find the global optimum, but with probability 1, (1, λ) EA can reach the global optimum and its expected runtime is O(n 3+c log n) with λ = c log e e−1 n for the constant c ≥ 1. Noting that a smaller offspring size is helpful for escaping from the local optima, we further resort to the compact genetic algorithm where only two individuals are sampled to update the probabilistic model, and prove its expected runtime of O(n 3 log n). Our computational experiments also verify the efficiency of the two non-elitist algorithms.

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Does comma selection help to cope with local optima?

Cited by 36 publications

References 56 publications

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

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

Choosing the Right Algorithm With Hints From Complexity Theory

When Non-Elitism Meets Time-Linkage Problems

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