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OneMax Is Not the Easiest Function for Fitness Improvements

Authors: Marc Kaufmann; Maxime Larcher; Johannes Lengler; Xun Zou;

OneMax Is Not the Easiest Function for Fitness Improvements

Abstract

Abstract We study the (1:s+1) success rule for controlling the population size of the (1,λ)-EA. It was shown by Hevia Fajardo and Sudholt that this parameter control mechanism can run into problems for large s if the fitness landscape is too easy. They conjectured that this problem is worst for the OneMax benchmark, since in some well-established sense OneMax is known to be the easiest fitness landscape. In this paper, we disprove this conjecture. We show that there exist s and ɛ such that the self-adjusting (1,λ)-EA with the (1:s+1)-rule optimizes OneMax efficiently when started with ɛn zero-bits, but does not find the optimum in polynomial time on Dynamic BinVal. Hence, we show that there are landscapes where the problem of the (1:s+1)-rule for controlling the population size of the (1,λ)-EA is more severe than for OneMax. The key insight is that, while OneMax is the easiest function for decreasing the distance to the optimum, it is not the easiest fitness landscape with respect to finding fitness-improving steps.

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Keywords

Population Density, FOS: Computer and information sciences, 68W50, Computer Science - Neural and Evolutionary Computing, Computer Simulation, Genetic Fitness, Neural and Evolutionary Computing (cs.NE), Biological Evolution, Algorithms

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
7
Top 10%
Average
Top 10%
Green