7,267 research outputs found
Runtime Analysis for Self-adaptive Mutation Rates
We propose and analyze a self-adaptive version of the
evolutionary algorithm in which the current mutation rate is part of the
individual and thus also subject to mutation. A rigorous runtime analysis on
the OneMax benchmark function reveals that a simple local mutation scheme for
the rate leads to an expected optimization time (number of fitness evaluations)
of when is at least for
some constant . For all values of , this
performance is asymptotically best possible among all -parallel
mutation-based unbiased black-box algorithms.
Our result shows that self-adaptation in evolutionary computation can find
complex optimal parameter settings on the fly. At the same time, it proves that
a relatively complicated self-adjusting scheme for the mutation rate proposed
by Doerr, Gie{\ss}en, Witt, and Yang~(GECCO~2017) can be replaced by our simple
endogenous scheme.
On the technical side, the paper contributes new tools for the analysis of
two-dimensional drift processes arising in the analysis of dynamic parameter
choices in EAs, including bounds on occupation probabilities in processes with
non-constant drift
The contribution of statistical physics to evolutionary biology
Evolutionary biology shares many concepts with statistical physics: both deal
with populations, whether of molecules or organisms, and both seek to simplify
evolution in very many dimensions. Often, methodologies have undergone parallel
and independent development, as with stochastic methods in population genetics.
We discuss aspects of population genetics that have embraced methods from
physics: amongst others, non-equilibrium statistical mechanics, travelling
waves, and Monte-Carlo methods have been used to study polygenic evolution,
rates of adaptation, and range expansions. These applications indicate that
evolutionary biology can further benefit from interactions with other areas of
statistical physics, for example, by following the distribution of paths taken
by a population through time.Comment: 18 pages, 3 figures, glossary. Accepted in Trend in Ecology and
Evolution (to appear in print in August 2011
Better Runtime Guarantees Via Stochastic Domination
Apart from few exceptions, the mathematical runtime analysis of evolutionary
algorithms is mostly concerned with expected runtimes. In this work, we argue
that stochastic domination is a notion that should be used more frequently in
this area. Stochastic domination allows to formulate much more informative
performance guarantees, it allows to decouple the algorithm analysis into the
true algorithmic part of detecting a domination statement and the
probability-theoretical part of deriving the desired probabilistic guarantees
from this statement, and it helps finding simpler and more natural proofs. As
particular results, we prove a fitness level theorem which shows that the
runtime is dominated by a sum of independent geometric random variables, we
prove the first tail bounds for several classic runtime problems, and we give a
short and natural proof for Witt's result that the runtime of any
mutation-based algorithm on any function with unique optimum is subdominated by
the runtime of a variant of the \oea on the \onemax function. As side-products,
we determine the fastest unbiased (1+1) algorithm for the \leadingones
benchmark problem, both in the general case and when restricted to static
mutation operators, and we prove a Chernoff-type tail bound for sums of
independent coupon collector distributions.Comment: Significantly extended version of a paper that appeared in the
proceedings of EvoCOP 201
Unbiased Black-Box Complexities of Jump Functions
We analyze the unbiased black-box complexity of jump functions with small,
medium, and large sizes of the fitness plateau surrounding the optimal
solution.
Among other results, we show that when the jump size is , that is, only a small constant fraction of the fitness values
is visible, then the unbiased black-box complexities for arities and higher
are of the same order as those for the simple \textsc{OneMax} function. Even
for the extreme jump function, in which all but the two fitness values
and are blanked out, polynomial-time mutation-based (i.e., unary unbiased)
black-box optimization algorithms exist. This is quite surprising given that
for the extreme jump function almost the whole search space (all but a
fraction) is a plateau of constant fitness.
To prove these results, we introduce new tools for the analysis of unbiased
black-box complexities, for example, selecting the new parent individual not by
comparing the fitnesses of the competing search points, but also by taking into
account the (empirical) expected fitnesses of their offspring.Comment: This paper is based on results presented in the conference versions
[GECCO 2011] and [GECCO 2014
Efficient Detectors for MIMO-OFDM Systems under Spatial Correlation Antenna Arrays
This work analyzes the performance of the implementable detectors for
multiple-input-multiple-output (MIMO) orthogonal frequency division
multiplexing (OFDM) technique under specific and realistic operation system
condi- tions, including antenna correlation and array configuration.
Time-domain channel model has been used to evaluate the system performance
under realistic communication channel and system scenarios, including different
channel correlation, modulation order and antenna arrays configurations. A
bunch of MIMO-OFDM detectors were analyzed for the purpose of achieve high
performance combined with high capacity systems and manageable computational
complexity. Numerical Monte-Carlo simulations (MCS) demonstrate the channel
selectivity effect, while the impact of the number of antennas, adoption of
linear against heuristic-based detection schemes, and the spatial correlation
effect under linear and planar antenna arrays are analyzed in the MIMO-OFDM
context.Comment: 26 pgs, 16 figures and 5 table
Offspring Population Size Matters when Comparing Evolutionary Algorithms with Self-Adjusting Mutation Rates
We analyze the performance of the 2-rate Evolutionary Algorithm
(EA) with self-adjusting mutation rate control, its 3-rate counterpart, and a
~EA variant using multiplicative update rules on the OneMax
problem. We compare their efficiency for offspring population sizes ranging up
to and problem sizes up to .
Our empirical results show that the ranking of the algorithms is very
consistent across all tested dimensions, but strongly depends on the population
size. While for small values of the 2-rate EA performs best, the
multiplicative updates become superior for starting for some threshold value of
between 50 and 100. Interestingly, for population sizes around 50,
the ~EA with static mutation rates performs on par with the best
of the self-adjusting algorithms.
We also consider how the lower bound for the mutation rate
influences the efficiency of the algorithms. We observe that for the 2-rate EA
and the EA with multiplicative update rules the more generous bound
gives better results than when is
small. For both algorithms the situation reverses for large~.Comment: To appear at Genetic and Evolutionary Computation Conference
(GECCO'19). v2: minor language revisio
The CMA Evolution Strategy: A Tutorial
This tutorial introduces the CMA Evolution Strategy (ES), where CMA stands
for Covariance Matrix Adaptation. The CMA-ES is a stochastic, or randomized,
method for real-parameter (continuous domain) optimization of non-linear,
non-convex functions. We try to motivate and derive the algorithm from
intuitive concepts and from requirements of non-linear, non-convex search in
continuous domain.Comment: ArXiv e-prints, arXiv:1604.xxxx
- …