By Sorensen D.C., Wets R.J.-B. (eds.)

ISBN-10: 364200847X

ISBN-13: 9783642008474

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**Extra resources for Algorithms and Theory in Filtering and Control, part 1**

**Example text**

Tournament selection works by taking a random uniform sample of a certain size q > 1 from the population, selecting the best of these q individuals to survive for the next generation, and repeating the process until the new population is filled. Different selection mechanisms which are mostly used in modern GAs, and their relative merits and demerit" can be found in Blickle [19] in detail. In ESs, the selection method and population concept are described by two variables Jl and A. Jl gives the number of parent" (corresponding to the population size) whilst A describes the number of offspring produced in each generation.

Xk(j,max) and that of 1j;j are denoted by Xl(j,mean), X2(j,mean), ... , Xk(j,mean)' The operation of the SBMAC is then carried out to produce two offspring as follows: (I = (~l"" '~k) = (alX1(j,max) + (1- adXl(j,mean), + (1- ak)Xk(j,mean)) = ((1- al)X1(j,max) + alXl(j,mean), ... , (1 - ak)Xk(j,max) + akXk(j,mean)) ... 6) where aI, ... ,ak are generated from the URN[O, 1] for offspring variables 6, ... , respectively. In this way, m number of offspring are generated for the subpopulation j. ~k, Example: Program Trace The whole process of the proposed NES algorithm is illustrated by an example.

4 Evaluation After mutation operation, each offspring (t is evaluated in its cost function (fitness) q>t for a possible solution in each generation. l)-ES is used. l individuals will be selected for the next generation. 4 Proposed NES: How Does It Work? This section presents the step-wise actions of the proposed NES algorithm for a simple optimization problem. Let it be noted first that, without loss of generality, only the maximization problem can be considered. Because, if the optimization problem is to minimize a function f, then this is equivalent to maximization a function g, where g = - f [97, 19].

### Algorithms and Theory in Filtering and Control, part 1 by Sorensen D.C., Wets R.J.-B. (eds.)

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