we use number systems to encode alleles. Hence, a gene is a"digit location"that can take on different values from a number system (i.e, different types of alleles) Values here=alleles String of genes=chromosome Gene=digit location Figure 4.4 String for representing an individual For instance, in a base-2 number system, alleles come from the set (0, 1), while in a base-10 number system, alleles come from the set 10, 1, 2, 3, 4, 5, 6, 7,, 8, 9). Hence, abinary chromosome has zeros or ones in its gene locations. As an he 1011110001010, which is a binary string of length 13. If we are seeking to optimize parameters of a system that come in a base-10 number system then we will need to encode the numbers into the binary number system(using the standard method for the conversion of base-10 numbers to base-2 numbers ). We will also need to decode the binary strings into base-10 numbers to use them. Here, we will develop the genetic algorithm for base-2 or base-10 number systems but we will favor the use of the base-10 representation since then there is no need for encoding or decoding( which can be computationally expensive for on-line, real-time applications As an example of a base-10 chromosome, consider 8219345127066 that has 13 gene positions. For such chromosomes we add a gene for the sign of the number(either +or"-")and fix a position for the decimal point. For instance,for the above chromosome we could have +821934.5127066, where there is no need to carry along the decimal point; the computer will just have to remember its position. Note that you could also use a floating point repres lon where we could code numbers in a fixed-length string plus the number in the exponent(e.g,as xc x10). The ideas developed here work just as readily for this number representation system as for standard base-2 or base-10 Since we are interested in applying the genetic algorithm to controller or estimator design and tuning, we will have as individuals parameters that represent, for instance, a conventional or fuzzy controller(i.e, a vector of parameters). The vector of parameters that encodes a fuzzy or conventional controller can be loaded into a single chromosome. For example, suppose that you have a Pd controller with Kp=+5. 12, Kd=-2.137, then we would represent this in a chromosome as +051200-021370. which is a concatenation of the digits where we assume that there are six digits for the representation of each parameter plus the sign digit(this is why you see the extra padding of zeros). The computer will have to keep track of where the decimal point is. We see that each chromosome will have a certain structure(its genotype"in biological terms), but here rather than a set of chromosomes for the structure we just concatenate the parameters and use one one chromosome for convenience. Each chromosome represents a point in the search space of the genetic algorithm(.e,, a"phenotype"in biological terms) Next, we develop a flotation for representing a whole set of individuals(i. e, a population). Let be a single parameter at time k(a fixed-length string with sign digit), and suppose that chromosome is composed of N of these parameters which are sometimes called"traits " Let PDF文件使用" pdffactory Pro"试用版本创建ww. fineprint,com,cnwe use number systems to encode alleles. Hence, a gene is a "digit location" that can take on different values from a number system (i.e., different types of alleles). Figure 4.4 String for representing an individual For instance, in a base-2 number system, alleles come from the set {0,1}, while in a base-l0 number system, alleles come from the set {0,1,2,3,4,5,6,7,,8,9}. Hence, abinary chromosome has zeros or ones in its gene locations. As an example, consider the binary chromosome 1011110001010, which is a binary string of length 13. If we are seeking to optimize parameters of a system that come in a base-10 number system then we will need to encode the numbers into the binary number system (using the standard method for the conversion of base-10 numbers to base-2 numbers). We will also need to decode the binary strings into base-10 numbers to use them. Here, we will develop the genetic algorithm for base-2 or base-10 number systems but we will favor the use of the base-10 representation since then there is no need for encoding or decoding (which can be computationally expensive for on-line, real-time applications). As an example of a base-10 chromosome, consider 8219345127066 that has 13 gene positions. For such chromosomes we add a gene for the sign of the number (either "+" or "-") and fix a position for the decimal point. For instance, for the above chromosome we could have +821934.5127066 ,where there is no need to carry along the decimal point; the computer will just have to remember its position. Note that you could also use a floating point representation where we could code numbers in a fixed-length string plus the number in the exponent (e.g., as ). The ideas developed here work just as readily for this number representation system as for standard base-2 or base-10. Since we are interested in applying the genetic algorithm to controller or estimator design and tuning, we will have as individuals parameters that represent, for instance, a conventional or fuzzy controller (i.e., a vector of parameters). The vector of parameters that encodes a fuzzy or conventional controller can be loaded into a single chromosome. For example, suppose that you have a PD controller with Kp = +5.12, Kd = -2.137 , then we would represent this in a chromosome as +051200-021370 , which is a concatenation of the digits, where we assume that there are six digits for the representation of each parameter plus the sign digit (this is why you see the extra padding of zeros). The computer will have to keep track of where the decimal point is. We see that each chromosome will have a certain structure (its "genotype" in biological terms), but here rather than a set of chromosomes for the structure we just concatenate the parameters and use one one chromosome for convenience. Each chromosome represents a point in the search space of the genetic algorithm (i.e., a "phenotype" in biological terms). Next, we develop a flotation for representing a whole set of individuals (i.e., a population). Let be a single parameter at time k (a fixed-length string with sign digit), and suppose that chromosome j is composed of N of these parameters, which are sometimes called "traits." Let PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn