A General Dichotomy of Evolutionary Algorithms on Monotone Functions

Lengler, Johannes

doi:10.1007/978-3-319-99259-4_1

Cited by 39 publications

(73 citation statements)

References 23 publications

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“…Lengler provided an example of a class of unimodal functions to highlight the robustness of the crossover based version with respect to the mutation rate compared to the mutation-only version i.e., the (µ+1) GA is e cient for any mutation rate c/n while the (µ+1) EA requires exponential time as soon as approx. c > 2.13 [15]. In all three examples the population size has to be large enough for the results to hold, thus providing evidence of the importance of populations in combination with crossover.…”

Section: Introductionmentioning

confidence: 82%

On the benefits of populations for the exploitation speed of standard steady-state genetic algorithms

Corus

Oliveto

2019

Proceedings of the Genetic and Evolutionary Computation Conference

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It is generally accepted that populations are useful for the global exploration of multi-modal optimisation problems. Indeed, several theoretical results are available showing such advantages over single-trajectory search heuristics. In this paper we provide evidence that evolving populations via crossover and mutation may also bene t the optimisation time for hillclimbing unimodal functions. In particular, we prove bounds on the expected runtime of the standard (µ+1) GA for OneMax that are lower than its unary black box complexity and decrease in the leading constant with the population size up to µ = O( log n). Our analysis suggests that the optimal mutation strategy is to ip two bits most of the time. To achieve the results we provide two interesting contributions to the theory of randomised search heuristics: 1) A novel application of dri analysis which compares absorption times of di erent Markov chains without de ning an explicit potential function. 2) e inversion of fundamental matrices to calculate the absorption times of the Markov chains. e la er strategy was previously proposed in the literature but to the best of our knowledge this is the rst time is has been used to show non-trivial bounds on expected runtimes.

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Section: Introductionmentioning

confidence: 82%

On the benefits of populations for the exploitation speed of standard steady-state genetic algorithms

Corus

Oliveto

2019

Proceedings of the Genetic and Evolutionary Computation Conference

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“…It is furthermore discussed in [DLMN17] that the advantages of the fast-GA do not sacrifice too drastically the performance on uni-modal benchmark functions such as OneMax and LeadingOnes. This work has already received considerable attention in the literature [MB17,FQW18,FGQW18,COY18,Len18]. However, only static distributions are considered so far, and it is very likely that a control mechanism similar to the ones proposed in this work would be beneficial.…”

Section: Related Workmentioning

confidence: 99%

Interpolating Local and Global Search by Controlling the Variance of Standard Bit Mutation

Doerr

Bäck

2019

2019 IEEE Congress on Evolutionary Computation (CEC)

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A key property underlying the success of evolutionary algorithms (EAs) is their global search behavior, which allows the algorithms to "jump" from a current state to other parts of the search space, thereby avoiding to get stuck in local optima. This property is obtained through a random choice of the radius at which offspring are sampled from previously evaluated solutions. It is well known that, thanks to this global search behavior, the probability that an EA using standard bit mutation finds a global optimum of an arbitrary function f : {0, 1} n → R tends to one as the number of function evaluations grows. This advantage over heuristics using a fixed search radius, however, comes at the cost of using non-optimal step sizes also in those regimes in which the optimal rate is stable for a long time. This downside results in significant performance losses for many standard benchmark problems.We introduce in this work a simple way to interpolate between the random global search of EAs and their deterministic counterparts which sample from a fixed radius only. To this end, we introduce normalized standard bit mutation, in which the binomial choice of the search radius is replaced by a normal distribution. Normalized standard bit mutation allows a straightforward way to control its variance, and hence the degree of randomness involved. We experiment with a self-adjusting choice of this variance, and demonstrate its effectiveness for the two classic benchmark problems LeadingOnes and OneMax. Our work thereby also touches a largely ignored question in discrete evolutionary computation: multi-dimensional parameter control.

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“…Since each of the λ individuals in population P t are sampled independently and identically, Eqs. (34) and (35) imply |B∩P t | is stochastically dominated by a binomially distributed random variable Z ∼ Bin(λ, 1−ζ α0 ) which has expectation µ(1 − ζ). By a Chernoff bound,…”

Section: Individuals With Too High Mutation Ratesmentioning

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%

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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A General Dichotomy of Evolutionary Algorithms on Monotone Functions

Cited by 39 publications

References 23 publications

On the benefits of populations for the exploitation speed of standard steady-state genetic algorithms

On the benefits of populations for the exploitation speed of standard steady-state genetic algorithms

Interpolating Local and Global Search by Controlling the Variance of Standard Bit Mutation

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

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