Power Magnetic Devices. Scott D. Sudhoff. Читать онлайн. Newlib. NEWLIB.NET

Автор: Scott D. Sudhoff
Издательство: John Wiley & Sons Limited
Серия:
Жанр произведения: Техническая литература
Год издания: 0
isbn: 9781119674634
Скачать книгу
The portions of the genetic code which have been acted on by the crossover operator are shown in bold. Next, chromosome segregation occurs. In this case, by a random choice the first child inherits the first chromosome from θa2 and the second chromosome from θa1. The second child inherits the remaining chromosomes. Next, let us assume that mutation acts to change the status of the first bit of gene 3 in θb2. This yields θc1 and θc2, where the affected bit is again indicated in boldface.

      At this point, the main points of a canonical GA have been described. This canonical form is the type of algorithm first developed by Holland. The canonical GA can also be used to explain the effectiveness of GAs using schema theory. A schema is a pattern of bits; one reason GAs are so effective is that they can be shown to exhibit an implicit parallelism in which all schema that result in higher than average fitness tend to propagate. The interested reader is referred to textbooks on GAs such as those by Goldberg [4,5].

Schematic illustration of chromosome crossover, segregation, and mutation.

      Real‐coded GAs are very similar to canonical GAs except that instead of each gene being represented as a binary string, each gene is represented by a real number. This proves convenient for coding purposes and makes representing each gene to the numerical precision of floating‐point numbers for a given machine (computer) straightforward. Beyond the change of the way in which a gene is represented, the algorithm presented in Figure 1.8 is still applicable, though we will need to modify the encoding, crossover, and mutation operators.

      Encoding

      The mapping between xi and θi is accomplished on a gene‐by‐gene basis. A simple choice is a linear map. Let x and θ denote a gene (element) of the xi and θi. For a linear mapping, we have

      (1.6-1)equation

      where j denotes the gene number and

      where xmn,j and xmx,j denote the minimum and maximum values of the parameter.

      (1.6-3)equation

      This mapping is useful in choosing, for example, between different types of steel in a design. If the third gene represented the type of steel used, and five types of steels were being considered, then xmn,3 = 1, xmx,3 = 5, and θ ∈ {0.00, 0.25, 0.50, 0.75, 1.00}.

      (1.6-4)equation

      Crossover

      In the case of the canonical GA, crossover is accomplished by breaking the subject chromosomes of the parents at the same point and interchanging them to form the corresponding chromosomes of the children. This interchange substantially alters the gene where the chromosome is interchanged, and it results in an interchange of genes falling after the interchange point.

      Single‐point crossover is very similar to biological crossover. However, note that gene values cannot become altered using this operator. This limits the amount of genetic diversity that can be brought about.

      Simple‐blend crossover can be used to increase the genetic diversity. Let us consider the jth gene of parents θp1 and θp2. If the jth gene is being crossed over, the new gene values are determined by first computing a random number υ given by

      where U(·) denotes a random number generator that generates a uniformly distributed random number in the range [0,1]. Next, the gene values of the children are set to

      (1.6-6)equation

      (1.6-7)equation