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1

Time to the convergence of evolution in the space of population states

100%

Karcz-Dulęba I.

International Journal of Applied Mathematics and Computer Science

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2004

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tom 14

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nr 3

279-287

EN

Phenotypic evolution of two-element populations with proportional selection and normally distributed mutation is considered. Trajectories of the expected location of the population in the space of population states are investigated. The expected location of the population generates a discrete dynamical system. The study of its fixed points, their stability and time to convergence is presented. Fixed points are located in the vicinity of optima and saddles. For large values of the standard deviation of mutation, fixed points become unstable and periodical orbits arise. In this case, fixed points are also moved away from optima. The time to convergence to fixed points depends not only on the mutation rate, but also on the distance of the points from unstability. Results show that a population spends most time wandering slowly towards the optimum with mutation as the main evolution factor.

2

Asymptotic behaviour of a discrete dynamical system generated by a simple evolutionary process

88%

Karcz-Dulęba I.

International Journal of Applied Mathematics and Computer Science

|

2004

|

tom 14

|

nr 1

79-90

EN

A simple model of phenotypic evolution is introduced and analysed in a space of population states. The expected values of the population states generate a discrete dynamical system. The asymptotic behaviour of the system is studied with the use of classical tools of dynamical systems. The number, location and stability of fixed points of the system depend on parameters of a fitness function and the parameters of the evolutionary process itself. The influence of evolutionary process parameters on the stability of the fixed points is discussed. For large values of the standard deviation of mutation, fixed points become unstable and periodical orbits arise. An analysis of the periodical orbits is presented.

3

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The impatience mechanism as a diversity maintaining and saddle crossing strategy

88%

Karcz-Duleba I.

International Journal of Applied Mathematics and Computer Science

|

2016

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tom 26

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nr 4

905-918

EN

The impatience mechanism diversifies the population and facilitates escaping from a local optima trap by modifying fitness values of poorly adapted individuals. In this paper, two versions of the impatience mechanism coupled with a phenotypic model of evolution are studied. A population subordinated to a basic version of the impatience mechanism polarizes itself and evolves as a dipole centered around an averaged individual. In the modified version, the impatience mechanism is supplied with extra knowledge about a currently found optimum. In this case, the behavior of a population is quite different than previously-considerable diversification is also observed, but the population is not polarized and evolves as a single cluster. The impatience mechanism allows crossing saddles relatively fast in different configurations of bimodal and multimodal fitness functions. Actions of impatience mechanisms are shown and compared with evolution without the impatience and with a fitness sharing. The efficiency of crossing saddles is experimentally examined for different fitness functions. Results presented in the paper confirm good properties of the impatience mechanism in diversity maintaining and saddle crossing.

Ograniczanie wyników

3 International Journal of Applied Mathematics and Computer Science

2 Karcz-Dulęba I.

1 Karcz-Duleba I.

1 2016

2 2004

Time to the convergence of evolution in the space of population states

Asymptotic behaviour of a discrete dynamical system generated by a simple evolutionary process

The impatience mechanism as a diversity maintaining and saddle crossing strategy