12,581 research outputs found
Improved Runtime Bounds for the Univariate Marginal Distribution Algorithm via Anti-Concentration
Unlike traditional evolutionary algorithms which produce offspring via
genetic operators, Estimation of Distribution Algorithms (EDAs) sample
solutions from probabilistic models which are learned from selected
individuals. It is hoped that EDAs may improve optimisation performance on
epistatic fitness landscapes by learning variable interactions. However, hardly
any rigorous results are available to support claims about the performance of
EDAs, even for fitness functions without epistasis. The expected runtime of the
Univariate Marginal Distribution Algorithm (UMDA) on OneMax was recently shown
to be in by Dang and Lehre
(GECCO 2015). Later, Krejca and Witt (FOGA 2017) proved the lower bound
via an involved drift analysis.
We prove a bound, given some restrictions
on the population size. This implies the tight bound when , matching the runtime
of classical EAs. Our analysis uses the level-based theorem and
anti-concentration properties of the Poisson-Binomial distribution. We expect
that these generic methods will facilitate further analysis of EDAs.Comment: 19 pages, 1 figur
copulaedas: An R Package for Estimation of Distribution Algorithms Based on Copulas
The use of copula-based models in EDAs (estimation of distribution
algorithms) is currently an active area of research. In this context, the
copulaedas package for R provides a platform where EDAs based on copulas can be
implemented and studied. The package offers complete implementations of various
EDAs based on copulas and vines, a group of well-known optimization problems,
and utility functions to study the performance of the algorithms. Newly
developed EDAs can be easily integrated into the package by extending an S4
class with generic functions for their main components. This paper presents
copulaedas by providing an overview of EDAs based on copulas, a description of
the implementation of the package, and an illustration of its use through
examples. The examples include running the EDAs defined in the package,
implementing new algorithms, and performing an empirical study to compare the
behavior of different algorithms on benchmark functions and a real-world
problem
An Exponential Lower Bound for the Runtime of the cGA on Jump Functions
In the first runtime analysis of an estimation-of-distribution algorithm
(EDA) on the multi-modal jump function class, Hasen\"ohrl and Sutton (GECCO
2018) proved that the runtime of the compact genetic algorithm with suitable
parameter choice on jump functions with high probability is at most polynomial
(in the dimension) if the jump size is at most logarithmic (in the dimension),
and is at most exponential in the jump size if the jump size is
super-logarithmic. The exponential runtime guarantee was achieved with a
hypothetical population size that is also exponential in the jump size.
Consequently, this setting cannot lead to a better runtime.
In this work, we show that any choice of the hypothetical population size
leads to a runtime that, with high probability, is at least exponential in the
jump size. This result might be the first non-trivial exponential lower bound
for EDAs that holds for arbitrary parameter settings.Comment: To appear in the Proceedings of FOGA 2019. arXiv admin note: text
overlap with arXiv:1903.1098
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