When is an estimation of distribution algorithm better than an evolutionary algorithm?

Tang

2009 IEEE Congress on Evolutionary Computation

et al. 2009

Self Cite

Abstract-Univariate Marginal Distribution Algorithms (UMDAs) are a kind of Estimation of Distribution Algorithms (EDAs) which do not consider the dependencies among the variables. In this paper, on the basis of our proposed approach in [1], we present a rigorous proof for the result that the UMDA with margins (in [1] we merely showed the effectiveness of margins) cannot find the global optimum of the TRAPLEADINGONES problem [2] within polynomial number of generations with a probability that is super-polynomially close to 1. Such a theoretical result is significant in sheding light on the fundamental issues of what problem characteristics make an EDA hard/easy and when an EDA is expected to perform well/poorly for a given problem.

Section: Introductionmentioning

confidence: 77%

Rigorous time complexity analysis of Univariate Marginal Distribution Algorithm with margins

Tang

2009 IEEE Congress on Evolutionary Computation

et al. 2009

Self Cite

Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms

“…− O log n n 1/4 ≥ n −η , for some η = η(n) = o (1). Combining this with the probability of not exceeding 5/6, the probability of pj hitting the lower border within T iterations is, in any case, Ω(n −η ).…”

Section: Establishing the Lyapunov Conditionmentioning

confidence: 90%

“…The UMDA is an EDA that samples λ solutions each iteration, selects µ < λ best solutions, and then sets pi to the relative occurrence of 1s among these µ individuals. The algorithm has already been analyzed some years ago for several artificially designed example functions [1,2,3,4]. However, none these papers considers the most important benchmark function in theory, the OneMax function.…”

Section: Introductionmentioning

confidence: 99%

Lower Bounds on the Run Time of the Univariate Marginal Distribution Algorithm on OneMax

Krejca

Witt

2017

The Univariate Marginal Distribution Algorithm (UMDA), a popular estimation of distribution algorithm, is studied from a run time perspective. On the classical OneMax benchmark function, a lower bound of Ω(µ √ n + n log n), where µ is the population size, on its expected run time is proved. This is the first direct lower bound on the run time of the UMDA. It is stronger than the bounds that follow from general black-box complexity theory and is matched by the run time of many evolutionary algorithms. The results are obtained through advanced analyses of the stochastic change of the frequencies of bit values maintained by the algorithm, including carefully designed potential functions. These techniques may prove useful in advancing the field of run time analysis for estimation of distribution algorithms in general.

Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

“…Another simple EDA is the Univariate Marginal Distribution Algorithm (UMDA) which was analysed in a series of papers [1,2,3,4]. UMDA was proposed in [17], assuming as the cGA independence between decision variables.…”

Section: Introductionmentioning

confidence: 99%

Simplified Runtime Analysis of Estimation of Distribution Algorithms

Dang

Lehre

2015

Self Cite

Estimation of distribution algorithms (EDA) are stochastic search methods that look for optimal solutions by learning and sampling from probabilistic models. Despite their popularity, there are only few rigorous theoretical analyses of their performance. Even for the simplest EDAs, such as the Univariate Marginal Distribution Algorithm (UMDA) which assumes independence between decision variables, there are only a handful of results about its runtime, and results for simple functions such as OneMax are still missing.In this paper, we show that the recently developed levelbased theorem for non-elitist populations is directly applicable to runtime analysis of EDAs. To demonstrate this approach, we derive easily upper bounds on the expected runtime of the UMDA.