Level-Based Analysis of the Population-Based Incremental Learning Algorithm

Lehre, Per Kristian; Nguyen, Phan Trung Hai

doi:10.1007/978-3-319-99259-4_9

Cited by 11 publications

(17 citation statements)

References 14 publications

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“…The only other known EDA run time result for BinVal was recently proven by Lehre and Nguyen [29]. They show that the PBIL optimizes BinVal with O(n 2 ) fitness function evaluations in expectation (considering best parameter choices).…”

Section: Leadingonesmentioning

confidence: 98%

Significance-based estimation-of-distribution algorithms

Doerr

Krejca

2018

Proceedings of the Genetic and Evolutionary Computation Conference

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Estimation-of-distribution algorithms (EDAs) are randomized search heuristics that maintain a probabilistic model of the solution space. This model is updated from iteration to iteration, based on the quality of the solutions sampled according to the model. As previous works show, this short-term perspective can lead to erratic updates of the model, in particular, to bit-frequencies approaching a random boundary value. Such frequencies take long to be moved back to the middle range, leading to significant performance losses.In order to overcome this problem, we propose a new EDA based on the classic compact genetic algorithm (cGA) that takes into account a longer history of samples and updates its model only with respect to information which it classifies as statistically significant. We prove that this significance-based compact genetic algorithm (sig-cGA) optimizes the commonly regarded benchmark functions OneMax, LeadingOnes, and BinVal all in O(n log n) time, a result shown for no other EDA or evolutionary algorithm so far.For the recently proposed scGA -an EDA that tries to prevent erratic model updates by imposing a bias to the uniformly distributed model -we prove that it optimizes OneMax only in a time exponential in the hypothetical population size 1/ρ. Similarly, we show that the convex search algorithm cannot optimize OneMax in polynomial time.

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Section: Leadingonesmentioning

confidence: 98%

Significance-based estimation-of-distribution algorithms

Doerr

Krejca

2018

Proceedings of the Genetic and Evolutionary Computation Conference

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“…While rigorous runtime analyses provide deep insights into the performance of randomised search heuristics, it is highly challenging even for simple algorithms on toy functions. Most current runtime results merely concern univariate EDAs on functions like OneMax [32,51,36,53,40], LeadingOnes [15,22,37,53,38], BinVal [52,37] and Jump [26,11,12], hoping that this provides valuable insights into the development of new techniques for analysing multivariate variants of EDAs and the behaviour of such algorithms on easy parts of more complex problem spaces [13]. There are two main reasons accounted for this.…”

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confidence: 99%

On the limitations of the univariate marginal distribution algorithm to deception and where bivariate EDAs might help

Lehre

Nguyen

2019

Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms

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We introduce a new benchmark problem called Deceptive Leading Blocks (DLB) to rigorously study the runtime of the Univariate Marginal Distribution Algorithm (UMDA) in the presence of epistasis and deception. We show that simple Evolutionary Algorithms (EAs) outperform the UMDA unless the selective pressure µ/λ is extremely high, where µ and λ are the parent and offspring population sizes, respectively. More precisely, we show that the UMDA with a parent population size of µ = Ω(log n) has an expected runtime of e Ω(µ) on the DLB problem assuming any selective pressure µ λ ≥ 14 1000 , as opposed to the expected runtime of O nλ log λ + n 3 for the non-elitist (µ, λ) EA with µ/λ ≤ 1/e. These results illustrate inherent limitations of univariate EDAs against deception and epistasis, which are common characteristics of real-world problems. In contrast, empirical evidence reveals the efficiency of the bi-variate MIMIC algorithm on the DLB problem. Our results suggest that one should consider EDAs with more complex probabilistic models when optimising problems with some degree of epistasis and deception. * Preliminary version of this work will appear in the Proceedings of 15th ACM/SIGEVO Workshop on FoundationsEstimation of distribution algorithms (EDAs) [42,43,33] are a class of randomised search heuristics with many real-world applications (see [27] and references therein). Unlike traditional EAs, which define implicit models of promising solutions via genetic operations such as crossover and mutation, EDAs optimise objective functions by constructing and sampling explicit probabilistic models to generate offspring for the next iteration. The workflow of EDAs is an iterative process, where the initial model is a uniform distribution over the search space. The starting population consists of λ individuals sampled from the uniform distribution. A fitness function then scores each individual, and the algorithm selects the µ fittest individuals to update the model (where µ < λ). The procedure is repeated until some termination condition is fulfilled, which is usually a threshold on the number of iterations or on the quality of the fittest offspring [27, 19]. Many variants of EDAs have been proposed over the last decades. They differ in the way their models are represented, updated as well as sampled over iterations. In general, EDAs are categorised into two main classes: univariate and multivariate. Univariate EDAs take advantage of first-order statistics (i.e. the mean) to build a probability vector-based model and assume independence between decision variables. The probabilistic model is represented as an n-vector, where each component is called a marginal (also frequency) and n is the problem instance size. Typical univariate EDAs are compact Genetic Algorithm (cGA [25]), Univariate Marginal Distribution Algorithm (UMDA [42]) and Population-Based Incremental Learning (PBIL [3]). In contrast, multivariate EDAs apply higher-order statistics to model the correlations between decision variables of the addressed problems.Th...

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“…Often, a runtime analysis of LeadingOnes also gives a runtime bound for BinVal (e. g., for UMDA/PBIL, Lehre and Nguyen, 2018).…”

Section: Recent Results For Leadingonesmentioning

confidence: 99%