26 research outputs found
Genetic Algorithms in Time-Dependent Environments
The influence of time-dependent fitnesses on the infinite population dynamics
of simple genetic algorithms (without crossover) is analyzed. Based on general
arguments, a schematic phase diagram is constructed that allows one to
characterize the asymptotic states in dependence on the mutation rate and the
time scale of changes. Furthermore, the notion of regular changes is raised for
which the population can be shown to converge towards a generalized
quasispecies. Based on this, error thresholds and an optimal mutation rate are
approximately calculated for a generational genetic algorithm with a moving
needle-in-the-haystack landscape. The so found phase diagram is fully
consistent with our general considerations.Comment: 24 pages, 14 figures, submitted to the 2nd EvoNet Summerschoo
Dynamic fitness landscapes: Expansions for small mutation rates
We study the evolution of asexual microorganisms with small mutation rate in
fluctuating environments, and develop techniques that allow us to expand the
formal solution of the evolution equations to first order in the mutation rate.
Our method can be applied to both discrete time and continuous time systems.
While the behavior of continuous time systems is dominated by the average
fitness landscape for small mutation rates, in discrete time systems it is
instead the geometric mean fitness that determines the system's properties. In
both cases, we find that in situations in which the arithmetic (resp.
geometric) mean of the fitness landscape is degenerate, regions in which the
fitness fluctuates around the mean value present a selective advantage over
regions in which the fitness stays at the mean. This effect is caused by the
vanishing genetic diffusion at low mutation rates. In the absence of strong
diffusion, a population can stay close to a fluctuating peak when the peak's
height is below average, and take advantage of the peak when its height is
above average.Comment: 19 pages Latex, elsart style, 4 eps figure
An analysis of the XOR dynamic problem generator based on the dynamical system
This is the post-print version of the article - Copyright @ 2010 Springer-VerlagIn this paper, we use the exact model (or dynamical system approach) to describe the standard evolutionary algorithm (EA) as a discrete dynamical system for dynamic optimization problems (DOPs). Based on this dynamical system model, we analyse the properties of the XOR DOP Generator, which has been widely used by researchers to create DOPs from any binary encoded problem. DOPs generated by this generator are described as DOPs with permutation, where the fitness vector is changed according to a permutation matrix. Some properties of DOPs with permutation are analyzed, which allows explaining some behaviors observed in experimental results. The analysis of the properties of problems created by the XOR DOP Generator is important to understand the results obtained in experiments with this generator and to analyze the similarity of such problems to real world DOPs.This work was supported by Brazil FAPESP under Grant 04/04289-6 and by UK EPSRC under Grant EP/E060722/2
On the Incommensurate Phase of Pure and Doped Spin-Peierls System CuGeO_3
Phases and phase transitions in pure and doped spin-Peierls system CuGeO_3
are considered on the basis of a Landau-theory. In particular we discuss the
critical behaviour, the soliton width and the low temperature specific heat of
the incommensurate phase. We show, that dilution leads always to the
destruction of long range order in this phase, which is replaced by an
algebraic decay of correlations if the disorder is weak.Comment: 4 pages revtex, no figure
Genetic Algorithms in Time-Dependent Environments
The inuence of time-dependent tnesses on the in nite population dynamics of simple genetic algorithms (without crossover) is analyzed. Based on general arguments, a schematic phase diagram is constructed that allows one to characterize the asymptotic states in dependence on the mutation rate and the time scale of changes. Furthermore, the notion of regular changes is raised for which the population can be shown to converge towards a generalized quasispecies