A. Rogers and A. Prugel-Bennett. Genetic drift in genetic algorithm selection schemes. IEEEEC, 3(4):298, November 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....estimates of the cumulants as modelling variables. The average genetic correlation, Q, is defined as Q = hQ i P ; 5) where Q is the pair correlation Q = L X i=1 S i S i : 6) Cumulants and correlations have been used to model the dynamics of a GA (see, for example, [9 13, 19, 22]) To describe the linkage produced by two point crossover we have to introduce functions measuring the auto correlation in a single string and cross correlation between pairs of strings. The auto correlation is defined as U(k) hU (k)i P ; U (k) L X i=1 S i S i k ; 7) where we ....

A. Rogers and A. Prugel-Bennett, "Genetic drift in genetic algorithm selection schemes," IEEE Transactions on Evolutionary Computation, vol. 3, no. 4, pp. 298-- 303, 1999.

.... chain transition matrices in order to analytically approximate the time to absorption [62, 58] An alternative approach to genetic drift consider the rate of decrease in population fitness variance under uniform selection [68, 67, 72] and lead to an exact analytical approach in many cases (see [74] for a quick overview) The ratio between population variances after one generation is given below (the first is exact and the others are approximations accurate up to terms of order 1=N ) Iteration loop ratio of fitness variance of successive populations Generational (choose N members ....

A. Rogers and A. Prugel-Bennet. Genetic drift in genetic algorithm selection schemes. IEEE Transactions on Evolutionary Computation., 1998.

....size of the sampling corrections giving improved performance. The effect of stochastic universal sampling has been studied in [6] and will be reported in this workshop [7] Other types of GAs, such as steady state GAs, give different sampling corrections. A comparison of these schemes is given in [12]. Fluctuations So far we have ignored fluctuations. However, to deal with fluctuations we must consider an ensemble of populations. Each population in the ensemble will have its own set of statistics , oe 2 , 3 , etc. The ensemble can be thought of as a probability distribution, P ( oe 2 ....

A. Rogers and A. Prugel-Bennett. Genetic drift in genetic algorithm selection schemes. IEEE Transactions on Evolutionary Computation, 1999. accepted for publication.

....and ranking selection (using roulette wheel selection) give the same results on average. Their e ect on an in nite population, starting from a Gaussian, was calculated by Blickle and Theile [4] More recently an approximation valid for nite populations was given by Rogers and Pr ugel Bennett [5, 6]. This Complex Systems, 11 (1997) 1 1 ; c 1997 Complex Systems Publications, Inc. 2 Adam Pr ugel Bennett allowed comparison of di erent selection strategies, such as, steadystate, generation gap [7] CHC models [8] evolutionary strategies and stochastic universal sampling [9] However, the ....

....selection for nite populations exactly. The derivation depends on whether the tnesses are continuous valued or discrete. We calculate the corrections in both cases and show that there is a term by term correspondence between the two cases. We brie y re derive the approximation given in [5,6] and extend it to include the third cumulant. For the rst cumulant (i.e. the average tness) the approximation agrees with the exact result. The e ect of selection on the second cumulant (i.e. the variance) and the third cumulant starting from a Gaussian are shown in gure 1. The approximation is ....

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A. Rogers and A. Prugel-Bennett. Genetic drift in genetic algorithm selection schemes. IEEE Transactions on Evolutionary Computation, 3(4):298-303, 1999. accepted for publication.

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A. Rogers and A. Prugel-Bennett. Genetic drift in genetic algorithm selection schemes. IEEE Transactions on Evolutionary Computation, 3(4):298-303, 1999.

....population member is selected and is a function of the population size, selection strength and the selection scheme used roulette wheel or stochastic universal sampling. It has been calculated in another paper [8] and has been used by the authors in a comparison of various selection schemes [9]. Figure 5 shows the results of these against population size. Clearly the curve approaches unity the infinite population limit very quickly. For small population sizes however, the deviation from unity is large. This feature explains the relative lack of dependence of population 11 0 20 ....

A. Rogers and A. Prugel-Bennett. Genetic Drift in Genetic Algorithm Selection Schemes. IEEE Transactions on Evolutionary Computation, 3(4), 1999.

....of magnetization and is simply dependent on hn 2 i a measure of the variance in the number of times any population member is selected. This is a general result and has been used by the authors in another paper as a basis for the comparison of genetic drift in a range of selection schemes [13]. We can combine this result with the infinite population result to give the variance after selection of a finite population hK 2 i s = P Gamma hn 2 i P Gamma 1 1 Gamma 2 (MAX Gamma 1) exp Gamma (M l Gamma K 1 ) 2 K 2 Gamma (MAX Gamma 1) 2 erf 2 M l Gamma K ....

A. Rogers and A. Prugel-Bennett. Genetic Drift in Genetic Algorithm Selection Schemes. IEEE Transactions on Evolutionary Computation, 3(4), 1999.

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A. Rogers and A. Prugel-Bennett. Genetic drift in genetic algorithm selection schemes. IEEEEC, 3(4):298, November 1999.

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