The choice of the offspring population size in the (1,λ) EA

Rowe, Jonathan E.; Sudholt, Dirk

doi:10.1145/2330163.2330350

Cited by 43 publications

(37 citation statements)

References 18 publications

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“…Unlike the analysis in Oliveto and Witt (2012), the drift is not monotone in X t . Therefore, the standard assumption of the variable drift theorem (see Rowe and Sudholt, 2012 for the most recent version) does not hold. We use the following variant (correcting a minor mistake in a formulation by Feldmann and Kötzing, 2013) instead.…”

Section: Lemma 4 For T ≥ 0 It Holdsmentioning

confidence: 99%

Improved time complexity analysis of the Simple Genetic Algorithm

Oliveto

Witt

2015

Theoretical Computer Science

121

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A runtime analysis of the Simple Genetic Algorithm (SGA) for the OneMax problem has recently been presented proving that the algorithm with population size µ ≤ n 1/8−ε requires exponential time with overwhelming probability. This paper presents an improved analysis which overcomes some limitations of the previous one. Firstly, the new result holds for population sizes up to µ ≤ n 1/4−ε which is an improvement up to a power of 2 larger. Secondly, we present a technique to bound the diversity of the population that does not require a bound on its bandwidth. Apart from allowing a stronger result, we believe this is a major improvement towards the reusability of the techniques in future systematic analyses of GAs. Finally, we consider the more natural SGA using selection with replacement rather than without replacement although the results hold for both algorithmic versions. Experiments are presented to explore the limits of the new and previous mathematical techniques.

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Section: Lemma 4 For T ≥ 0 It Holdsmentioning

confidence: 99%

Improved time complexity analysis of the Simple Genetic Algorithm

Oliveto

Witt

2015

Theoretical Computer Science

121

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“…This process is performed by measuring the progress of a function, a so-called distance function, which assigns each state of the search heuristic to a non-negative number reflecting the distance between that state and the optimal solution. A range of drift theorems have been presented in the literature (see for example [8] [9]). Very recently, a general drift theorem that can be considered to be a generalisation of most of the existing drift theorems is introduced in [10].…”

Section: Preliminariesmentioning

confidence: 99%

Runtime analysis of selection hyper-heuristics with classical learning mechanisms

Alanazi

Lehre

2014

2014 IEEE Congress on Evolutionary Computation (CEC)

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The term selection hyper-heuristics refers to a randomised search technique used to solve computational problems by choosing and executing heuristics from a set of pre-defined low-level heuristic components. Selection hyper-heuristics have been successfully employed in many problem domains. Nevertheless, a theoretical foundation of these heuristics is largely missing. Gaining insight into the behaviour of selection hyperheuristics is challenging due to the complexity and random design of these heuristics. This paper is one of the initial studies to analyse rigorously the runtime of selection hyperheuristics with a number of the most commonly used learning mechanisms; namely, simple random, random gradient, greedy, and permutation. We derive the runtime of selection hyperheuristic with these learning mechanisms not only on a classical example problem, but also on a general model of fitness landscapes. This in turn helps in understanding the behaviour of hyper-heuristics. Our results show that all the considered selections hyper-heuristics have roughly the same performance. This suggests that the learning mechanisms do not necessarily improve the performance of hyper-heuristics. A new learning mechanism that improves the performance of hyper-heuristic on our example problem is presented.

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“…Afterwards we combine the progress made in [4] and [21] on variable drift theorems to new such drift theorem, before we show in a second step that here the restriction to finite state sets is (with a minor restriction) not necessary either.…”

Section: Drift Theorem Adaptationsmentioning

confidence: 99%

“…For the mathematical analysis we use the multiplicative and the variable drift theorem (see [5] and [15,18], respectively), as well as well as recent improvements [4,21]. But as these drift theorems require discrete search spaces, we adapt both formally to continuous domains.…”

Section: Introductionmentioning

confidence: 99%

Optimizing expected path lengths with ant colony optimization using fitness proportional update

Feldmann

Kötzing

2013

Proceedings of the Twelfth Workshop on Foundations of Genetic Algorithms XII

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We study the behavior of a Max-Min Ant System (MMAS) on the stochastic single-destination shortest path (SDSP) problem. Two previous papers already analyzed this setting for two slightly different MMAS algorithms, where the pheromone update fitness-independently rewards edges of the best-so-far solution.The first paper showed that, when the best-so-far solution is not reevaluated and the stochastic nature of the edge weights is due to noise, the MMAS will find a tree of edges successfully and efficiently identify a shortest path tree with minimal noise-free weights. The second paper used reevaluation of the best-so-far solution and showed that the MMAS finds paths which beat any other path in direct comparisons, if existent. For both results, for some random variables, this corresponds to a tree with minimal expected weights.In this work we analyze a variant of MMAS that works with fitness-proportional update on stochastic-weight graphs with arbitrary random edge weights from [0, 1]. For δ such that any suboptimal path is worse by at least δ than an optimal path, then, with suitable parameters, the graph will be optimized after O n 3 ln (n/δ) δ 3 iterations (in expectation). In order to prove the above result, the multiplicative and the variable drift theorem are adapted to continuous search spaces.

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The choice of the offspring population size in the (1,λ) EA

Cited by 43 publications

References 18 publications

Improved time complexity analysis of the Simple Genetic Algorithm

Improved time complexity analysis of the Simple Genetic Algorithm

Runtime analysis of selection hyper-heuristics with classical learning mechanisms

Optimizing expected path lengths with ant colony optimization using fitness proportional update

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