Evolution Strategy Operators in .NET framework Printing QR Code JIS X 0510 in .NET framework Evolution Strategy Operators 124 Evolution Strategy OperatorsDenso QR Bar Code Decoder In .NET FrameworkUsing Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in .NET applications.x2 2 c2 QR Code JIS X 0510 Creation In Visual Studio .NETUsing Barcode printer for .NET framework Control to generate, create QR Code image in .NET applications.xi c1 QR Code JIS X 0510 Reader In Visual Studio .NETUsing Barcode decoder for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.Figure 122 Directed Mutation Operator for ES results in an asymmetrical mutation probability distribution Here the step size is larger for the x2 axis than for the x1 axis, and positive directions are preferred As each component of the genotype is mutated independently, it is su cient to de ne a 1-dimensional asymmetrical probability density function Hildebrand et al proposed the function, x2 2 if x < 0 (1+ 1+c) e (1234) fD (x) = x2 2 if x 0 (1+ 1+c) e (1+c) where c > 0 is the positive directional value The directional mutation method uses only deviations as strategy parameters, but associates a directional value, cj , with each deviation, j Both and c are self-adapted, giving a total of 2nx strategy parameters This is computationally more e cient than using a nx (nx 1)/2-sized rotational vector, and provides more information about preferred search directions and step sizes than deviations alone If D(c, ) denotes the asymmetric distribution, then xij (t) = Dj (cij (t), ij (t)) Ostermeier and Hansen [645] developed a coordinate system invariant mutation operator, with self-adaptation as discussed in Section 1233 Genotypes are mutated using both deviations and correlations, as follows: xl (t) = 1 xi (t) + l N (0, Cl (t)) Bar Code Printer In Visual Studio .NETUsing Barcode printer for Visual Studio .NET Control to generate, create bar code image in VS .NET applications.i l (t)Recognizing Barcode In .NET FrameworkUsing Barcode decoder for .NET Control to read, scan read, scan image in .NET applications.(1235)Print Denso QR Bar Code In C#Using Barcode maker for .NET framework Control to generate, create Denso QR Bar Code image in .NET framework applications.226 where Cl (t) =Creating QR Code In Visual Studio .NETUsing Barcode drawer for ASP.NET Control to generate, create QR Code image in ASP.NET applications.12 Evolution Strategies Generate QR-Code In VB.NETUsing Barcode maker for VS .NET Control to generate, create QR-Code image in VS .NET applications.nm T lk (t) lk (t)Encoding EAN-13 Supplement 5 In .NETUsing Barcode generator for Visual Studio .NET Control to generate, create European Article Number 13 image in Visual Studio .NET applications.(1236)Universal Product Code Version A Maker In VS .NETUsing Barcode maker for .NET framework Control to generate, create UPC-A image in Visual Studio .NET applications.1 with lk (t) N (0, i l (t) Ci (t)) and nm is the mutation strength For large values of nm , the mutation strength is small, because a large sample, 1 , 2 , , nm , provides a closer approximation to the original distribution than a smaller sample Ostermeier and Hansen suggested that nm = nx Data Matrix 2d Barcode Encoder In .NET FrameworkUsing Barcode generation for .NET Control to generate, create Data Matrix ECC200 image in .NET framework applications.Evolution Strategy Variants ISSN - 13 Creator In VS .NETUsing Barcode creation for .NET Control to generate, create ISSN - 10 image in .NET framework applications.Previous sections have already discussed a number of di erent self-adaptation and mutation strategies for ES This section describes a few ES implementations that di er somewhat from the generic ES algorithm summarized in Algorithm 121Paint Bar Code In Visual Basic .NETUsing Barcode creator for VS .NET Control to generate, create bar code image in .NET framework applications.Polar Evolution Strategies Painting UCC - 12 In JavaUsing Barcode creator for Java Control to generate, create UPC-A Supplement 2 image in Java applications.Bian et al [66], and Sierra and Echeverr [788] independently proposed that the ia components of genotype be transformed to polar coordinates Instead of the original genotype, the polar genotypes are evolved For an nx -dimensional Cartesian coordinate, the corresponding polar coordinate is given as (1237) (r, nx 2 , , 1 , ) where 0 < 2 , 0 q for q = 1, , nx 2, and r > 0 Each individual is therefore represented as (1238) i (t) = (xp (t), i (t)) i where , xp = (r, nx 2, , 1 , ) Polar coordinates are transformed back to Cartei sian coordinates as follows: x1 x2 x3 xi xn = = = = = = = r cos sin 1 sin 2 sin nx 2 r sin sin 1 sin 2 sin nx 2 r cos 1 sin 2 sin nx 2 (1239) r cos i 2 sin i 1 sin nx 2Barcode Decoder In JavaUsing Barcode recognizer for Java Control to read, scan read, scan image in Java applications.r cos nx 2 Decode DataMatrix In .NET FrameworkUsing Barcode recognizer for .NET framework Control to read, scan read, scan image in .NET framework applications.The mutation operator uses deviations to adjust the and q angles: = ( l (t) + ,l (t)N (0, 1)) mod 2 lq (t) + (t)Nq (0, 1)) mod lq (t) = ( lq l (1240) (1241)Paint Barcode In VS .NETUsing Barcode drawer for ASP.NET Control to generate, create bar code image in ASP.NET applications.125 Evolution Strategy Variants Algorithm 122 Polar Evolution Strategy Set the generation counter, t = 0; Initialize the strategy parameters, , ,q , q = 1, , nx 2; Create and initialize the population, C(0), as follows:; for i = 1, , do r = 1; i (0) U (0, 2 ); iq (0) U (0, ), q = 1, , nx 2; xp (0) = (r, i (0), i (0)); i i (0) = (xp (0), i (0)); i end for each individual, l (0) C(0) do Transform polar coordinate xp (0) to Cartesian coordinate nxi (0); i Evaluate the tness, f (xi (0)); end while stopping condition(s) not true do for l = 1, , , generate offspring do Randomly choose two parents; Create o spring, l (t), using local, discrete recombination; Mutate l (t) to produce l (t); Transform xp (t) back to Cartesian xl (t); l Evaluate the tness, f (xi (t)); end Select individuals from the o spring to form C(t + 1); t = t + 1; endCode 128 Code Set A Creation In Visual Studio .NETUsing Barcode generator for ASP.NET Control to generate, create Code 128 image in ASP.NET applications. where l (t) and lq (t), q = 1, , nx 2 refer to the components of the o spring, l (t), l = 1, , produced by the crossover operator, and l (t) = ( ,l (t), ,l1 (t), ,l2 (t), , ,l(nx 2) (t)), is its strategy parameter vector Note that r = 1 is not mutated The polar ES as used in [788] is summarized in Algorithm 122Code128 Drawer In Visual Basic .NETUsing Barcode creator for .NET framework Control to generate, create Code 128B image in .NET applications.Print UPC A In C#Using Barcode maker for .NET framework Control to generate, create Universal Product Code version A image in Visual Studio .NET applications.