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208 5 Neural Networks
Figure 5.41. An MLP2:2:1 with all its weights plus biases. These are considered
chromosome genes.
For this MLP2:2:1 device the chromosome can be expressed by an ordered
sequence of the genes, the so-called genotype g, such as:
In the representation of g we used a semi-colon to separate the weights of
individual neurons.
Imagine that we have a population, G, of a specified number of such devices
(individuals) represented by their chromosomes. Each device is characterized by a
fitnessfactor, which we may relate in some way with the error achieved with the
device. Using the sum of squares error E we can, for instance, define the fitness
factor for a device with genotype g, as:
where E,,,, is any upper bound of the error.
Inspired by the Darwinian theory of biological evolution, a genetic algorithm
generates a new population by repetition of the following two-step process:
I. Select the fittest individuals of the population (the so-called survival of the
fittest) for reproduction. A common selection process of parent individuals for
reproduction is based on the assignment of a probability of selection to an
individual, given by the individual's relative fitness:
This selection rule is also known as roulette-wheel selection.
2. Generate a new population based on the selected parent individuals by applying
the following operators to the parent chromosomes: