2 research outputs found
On the limitations of the univariate marginal distribution algorithm to deception and where bivariate EDAs might help
We introduce a new benchmark problem called Deceptive Leading Blocks (DLB) to
rigorously study the runtime of the Univariate Marginal Distribution Algorithm
(UMDA) in the presence of epistasis and deception. We show that simple
Evolutionary Algorithms (EAs) outperform the UMDA unless the selective pressure
is extremely high, where and are the parent and
offspring population sizes, respectively. More precisely, we show that the UMDA
with a parent population size of has an expected runtime
of on the DLB problem assuming any selective pressure
, as opposed to the expected runtime
of for the non-elitist
with . These results illustrate
inherent limitations of univariate EDAs against deception and epistasis, which
are common characteristics of real-world problems. In contrast, empirical
evidence reveals the efficiency of the bi-variate MIMIC algorithm on the DLB
problem. Our results suggest that one should consider EDAs with more complex
probabilistic models when optimising problems with some degree of epistasis and
deception.Comment: To appear in the 15th ACM/SIGEVO Workshop on Foundations of Genetic
Algorithms (FOGA XV), Potsdam, German
From Understanding Genetic Drift to a Smart-Restart Parameter-less Compact Genetic Algorithm
One of the key difficulties in using estimation-of-distribution algorithms is
choosing the population size(s) appropriately: Too small values lead to genetic
drift, which can cause enormous difficulties. In the regime with no genetic
drift, however, often the runtime is roughly proportional to the population
size, which renders large population sizes inefficient.
Based on a recent quantitative analysis which population sizes lead to
genetic drift, we propose a parameter-less version of the compact genetic
algorithm that automatically finds a suitable population size without spending
too much time in situations unfavorable due to genetic drift.
We prove a mathematical runtime guarantee for this algorithm and conduct an
extensive experimental analysis on four classic benchmark problems both without
and with additive centered Gaussian posterior noise. The former shows that
under a natural assumption, our algorithm has a performance very similar to the
one obtainable from the best problem-specific population size. The latter
confirms that missing the right population size in the original cGA can be
detrimental and that previous theory-based suggestions for the population size
can be far away from the right values; it also shows that our algorithm as well
as a previously proposed parameter-less variant of the cGA based on parallel
runs avoid such pitfalls. Comparing the two parameter-less approaches, ours
profits from its ability to abort runs which are likely to be stuck in a
genetic drift situation.Comment: 4 figures. Extended version of a paper appearing at GECCO 202