Читать книгу Power Magnetic Devices - Scott D. Sudhoff - Страница 24

Let us begin our development by considering the form of the genetic code for the ith individual. In the case of the canonical GA, this was given by (1.5-2), where each element of θⁱ was represented by a string. In the real‐coded GA, (1.5-2) still applies. However, instead of each element of θⁱ being represented by a string, in a real‐coded GA each element is represented by a real number. In fact, a real‐coded GA could be written such that θⁱ = xⁱ. However, it will be convenient to provide a mapping of xⁱ to θⁱ so that the gene values of θⁱ fall into the domain [0,1].

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)

where j denotes the gene number and

(1.6-2)

where x_mn,j and x_mx,j denote the minimum and maximum values of the parameter.

Closely related to linear mapping is integer mapping, wherein x, x_mn,j, and x_mx,j are integers. In this case, (1.6-2) still applies, but we require

(1.6-3)

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 x_mn,3 = 1, x_mx,3 = 5, and θ ∈ {0.00, 0.25, 0.50, 0.75, 1.00}.

In some cases, the domain of a parameter may span many decades in magnitude. If the domain of the parameter is always positive, then a logarithmic mapping is appropriate. In this case,

(1.6-4)