Elitist Black-Box Models: Analyzing the Impact of Elitist Selection on the Performance of Evolutionary Algorithms

Abstract : Black-box complexity theory provides lower bounds for the runtime %classes of black-box optimizers like evolutionary algorithms and serves as an inspiration for the design of new genetic algorithms. Several black-box models covering different classes of algorithms exist, each highlighting a different aspect of the algorithms under considerations. In this work we add to the existing black-box notions a new \emph{elitist black-box model}, in which algorithms are required to base all decisions solely on (a fixed number of) the best search points sampled so far. Our model combines features of the ranking-based and the memory-restricted black-box models with elitist selection. We provide several examples for which the elitist black-box complexity is exponentially larger than that the respective complexities in all previous black-box models, thus showing that the elitist black-box complexity can be much closer to the runtime of typical evolutionary algorithms. We also introduce the concept of $p$-Monte Carlo black-box complexity, which measures the time it takes to optimize a problem with failure probability at most p. Even for small $p$, the $p$-Monte Carlo black-box complexity of a function class F can be smaller by an exponential factor than its typically regarded Las Vegas complexity (which measures the expected time it takes to optimize F).
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Contributor : Carola Doerr <>
Submitted on : Thursday, February 11, 2016 - 2:47:10 PM
Last modification on : Thursday, March 21, 2019 - 2:44:57 PM

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Carola Doerr, Johannes Lengler. Elitist Black-Box Models: Analyzing the Impact of Elitist Selection on the Performance of Evolutionary Algorithms. GECCO '15 - 2015 Annual Conference on Genetic and Evolutionary Computation, Jul 2015, Madrid, Spain. ACM, pp.839-846, 〈10.1145/2739480.2754654〉. 〈hal-01272867〉

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