167 research outputs found
Convergence Properties of Two ({\mu} + {\lambda}) Evolutionary Algorithms On OneMax and Royal Roads Test Functions
We present a number of bounds on convergence time for two elitist
population-based Evolutionary Algorithms using a recombination operator
k-Bit-Swap and a mainstream Randomized Local Search algorithm. We study the
effect of distribution of elite species and population size.Comment: accepted for ECTA 201
Elitism Levels Traverse Mechanism For The Derivation of Upper Bounds on Unimodal Functions
In this article we present an Elitism Levels Traverse Mechanism that we
designed to find bounds on population-based Evolutionary algorithms solving
unimodal functions. We prove its efficiency theoretically and test it on OneMax
function deriving bounds c{\mu}n log n - O({\mu} n). This analysis can be
generalized to any similar algorithm using variants of tournament selection and
genetic operators that flip or swap only 1 bit in each string.Comment: accepted to Congress on Evolutionary Computation (WCCI/CEC) 201
Analysis of Noisy Evolutionary Optimization When Sampling Fails
In noisy evolutionary optimization, sampling is a common strategy to deal
with noise. By the sampling strategy, the fitness of a solution is evaluated
multiple times (called \emph{sample size}) independently, and its true fitness
is then approximated by the average of these evaluations. Previous studies on
sampling are mainly empirical. In this paper, we first investigate the effect
of sample size from a theoretical perspective. By analyzing the (1+1)-EA on the
noisy LeadingOnes problem, we show that as the sample size increases, the
running time can reduce from exponential to polynomial, but then return to
exponential. This suggests that a proper sample size is crucial in practice.
Then, we investigate what strategies can work when sampling with any fixed
sample size fails. By two illustrative examples, we prove that using parent or
offspring populations can be better. Finally, we construct an artificial noisy
example to show that when using neither sampling nor populations is effective,
adaptive sampling (i.e., sampling with an adaptive sample size) can work. This,
for the first time, provides a theoretical support for the use of adaptive
sampling
Upper Bounds on the Runtime of the Univariate Marginal Distribution Algorithm on OneMax
A runtime analysis of the Univariate Marginal Distribution Algorithm (UMDA)
is presented on the OneMax function for wide ranges of its parameters and
. If for some constant and
, a general bound on the expected runtime
is obtained. This bound crucially assumes that all marginal probabilities of
the algorithm are confined to the interval . If for a constant and , the
behavior of the algorithm changes and the bound on the expected runtime becomes
, which typically even holds if the borders on the marginal
probabilities are omitted.
The results supplement the recently derived lower bound
by Krejca and Witt (FOGA 2017) and turn out as
tight for the two very different values and . They also improve the previously best known upper bound by Dang and Lehre (GECCO 2015).Comment: Version 4: added illustrations and experiments; improved presentation
in Section 2.2; to appear in Algorithmica; the final publication is available
at Springer via http://dx.doi.org/10.1007/s00453-018-0463-
- …