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Mutation is necessary in order to create new parameter values, as crossing simply generates new combinations of existing values. The Gaussian variance along each dimension is for the .rst generation set as the span of the initial range. The variances for the following generations are set as a function of ini-tial variance and generation number, so that the standard deviation reaches to zero when max generation count is reached. This way, large parts of the parameter space is explored early in the evolution, before the individuals converges on the optimal solution.

Figure A.1: Evolutionary optimization overview.

A.5 Classi.cation Systems
Classi.cation systems are system for categorizing some input. A classi.cation system accepts an input vector, generating an output vector. The output usually corresponds to class probabilities, so that the value of an output vector element is equivalent to the probability of the input vector belonging to the associated class.
In the most general of terms, a classi.cation system can be seen as a mapping tool, mapping one vector to another. Simple classi.cation systems can be based on polynomials or Gaussian functions. More complex systems, such as arti.cial neural networks and fuzzy logic, are capable of more complex non-linear mapping. Some classi.cation systems can be estimated, trained, through a set of marked training sets. I.e. input vectors where the output vector is known. Other classi.cation systems are best designed "by hand" using expert knowledge.
A commonly used non-linear mapping tool is the radial basis network. A radial
basis
layer,
left
part
of
.gure
A.2
[6],
consist
of
a
number
of
neurons
A, each with an R dimensional position in feature space. It accepts an R element feature vector as input, r, and computes the euclidean distance between the vector and each neuron. The A dimensional output, which re.ects the distance to each neuron, is multiplied with a bias and sent through a radial basis function. The radial basis function, of form f(x)= e.x2 , returns 1 for x =0 and converges quickly to 0 for input larger than 0. Consequently, the layer outputs 1 for neurons with coordinates matching the input vector, and a value between 1 and 0 for neurons further away. The rate of descent for is controlled by the bias. I.e. the bias controls the active radius, the area for which a neuron produces a signi.cant output.
A.5. CLASSIFICATION SYSTEMS
The active region of a neuron is a multidimensional sphere in input space. A class corresponds to region in input space, covered by the active region of one or more neurons. As some classes are covered by more than one neuron, the radial basis layer is often followed by a linear layer. The linear layer simply fuses together the outputs from the neurons corresponding to the same class, so that the number of network outputs corresponds to the number of classes.
　
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