Theory of Estimation-of-Distribution Algorithms

Krejca, Martin S.; Witt, Carsten

doi:10.1007/978-3-030-29414-4_9

Cited by 41 publications

(31 citation statements)

References 55 publications

(143 reference statements)

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“…Costa, Jones, and Kroese [2] proved that a constant smoothing parameter for the Cross Entropy (CE) algorithm (which is equivalent to a constant learning rate ρ for PBIL) results in that the probability mass function converges to a unit mass at some random candidate, but no convergence speed analysis was given. In summary, as Krejca and Witt said in [10], the genetic drift in EDAs is a general problem of martingales, that is, that a random process with zero expected change will eventually stop at the absorbing boundaries of the range. Results of Witt [16] and Lengler, Sudholt, and Witt [13] as well as the two works by Lehre and Nguyen [12] and by Doerr and GECCO '20 Companion, July 8-12, 2020, Cancún, Mexico Benjamin Doerr and Weijie Zheng Krejca [3] showed that genetic drift can result in a considerable performance loss.…”

Section: Summary Of Our Resultsmentioning

confidence: 97%

“…Since almost all theoretical results for EDAs regard univariate models [10], this paper deals exclusively with univariate EDAs, that is, the bit positions of the probabilistic model are mutually independent. Univariate EDAs include Population-Based Incremental Learning (PBIL) with special cases Univariate Marginal Distribution Algorithm (UMDA) and Max-Min Ant System with iteration-best update, and the Compact Genetic Algorithm (cGA).…”

Section: Summary Of Our Resultsmentioning

confidence: 99%

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Sharp bounds for genetic drift in estimation of distribution algorithms (Hot-off-the-press track at GECCO 2020)

Doerr

Zheng

2020

Proceedings of the 2020 Genetic and Evolutionary Computation Conference Companion

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Estimation of distribution algorithms (EDAs) are a successful branch of evolutionary algorithms (EAs) that evolve a probabilistic model instead of a population. Analogous to genetic drift in EAs, EDAs also encounter the phenomenon that the random sampling in the model update can move the sampling frequencies to boundary values not justified by the fitness. This can result in a considerable performance loss. This work gives the first tight quantification of this effect for three EDAs and one ant colony optimizer, namely for the univariate marginal distribution algorithm, the compact genetic algorithm, population-based incremental learning, and the max-min ant system with iteration-best update. Our results allow to choose the parameters of these algorithms in such a way that within a desired runtime, no sampling frequency approaches the boundary values without a clear indication from the objective function. This paper for the Hot-off-the-Press track at GECCO 2020 summarizes the work "Sharp Bounds for Genetic Drift in Estimation of Distribution Algorithms" by B. Doerr and W. Zheng, which has been accepted for publication in the IEEE Transactions on Evolutionary Computation [5].

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Section: Summary Of Our Resultsmentioning

confidence: 97%

Section: Summary Of Our Resultsmentioning

confidence: 99%

Sharp bounds for genetic drift in estimation of distribution algorithms (Hot-off-the-press track at GECCO 2020)

Doerr

Zheng

2020

Proceedings of the 2020 Genetic and Evolutionary Computation Conference Companion

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“…Theoretical analyses of EDAs also often suggest an advantage of EDAs when compared to evolutionary algorithms (EAs); for an in-depth survey of run time results for EDAs, please refer to the article by Krejca and Witt (2020). With respect to simple unimodal functions, EDAs seem to be comparable to EAs.…”

Section: Introductionmentioning

confidence: 99%

The Univariate Marginal Distribution Algorithm Copes Well with Deception and Epistasis

Doerr

Krejca

2020

Evolutionary Computation in Combinatorial Optimization

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In their recent work, Lehre and Nguyen (FOGA 2019) show that the univariate marginal distribution algorithm (UMDA) needs time exponential in the parent populations size to optimize the DeceptiveLeadingBlocks (DLB) problem. They conclude from this result that univariate EDAs have difficulties with deception and epistasis. In this work, we show that this negative finding is caused by an unfortunate choice of the parameters of the UMDA. When the population sizes are chosen large enough to prevent genetic drift, then the UMDA optimizes the DLB problem with high probability with at most λ(n 2 + 2e ln n) fitness evaluations. Since an offspring population size λ of order n log n can prevent genetic drift, the UMDA can solve the DLB problem with O(n 2 log n) fitness evaluations. In contrast, for classic evolutionary algorithms no better run time guarantee than O(n 3) is known (which we prove to be tight for the (1 + 1) EA), so our result rather suggests that the UMDA can cope well with deception and epistatis. From a broader perspective, our result shows that the UMDA can cope better with local optima than evolutionary algorithms; such a result was previously known only for the compact genetic algorithm. Together with the result of Lehre and Nguyen, our result for the first time rigorously proves that running EDAs in the regime with genetic drift can lead to drastic performance losses.

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“…Therefore, design hybrid methods that combine metaheuristics and local search are highly needed to obtain practical efficient solvers [25][26][27]. Estimation of Distribution Algorithms (EDAs) are promising metaheuristics-in which exploration for potential solutions in search space depends on building and sampling explicit probabilistic models of promising candidates' solutions [28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Simulation-Based EDAs for Stochastic Programming Problems

2020

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With the rapid growth of simulation software packages, generating practical tools for simulation-based optimization has attracted a lot of interest over the last decades. In this paper, a modified method of Estimation of Distribution Algorithms (EDAs) is constructed by a combination with variable-sample techniques to deal with simulation-based optimization problems. Moreover, a new variable-sample technique is introduced to support the search process whenever the sample sizes are small, especially in the beginning of the search process. The proposed method shows efficient results by simulating several numerical experiments.

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Theory of Estimation-of-Distribution Algorithms

Cited by 41 publications

References 55 publications

Sharp bounds for genetic drift in estimation of distribution algorithms (Hot-off-the-press track at GECCO 2020)

Sharp bounds for genetic drift in estimation of distribution algorithms (Hot-off-the-press track at GECCO 2020)

The Univariate Marginal Distribution Algorithm Copes Well with Deception and Epistasis

Simulation-Based EDAs for Stochastic Programming Problems

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