Domain-specific transposition is restricted to the NN-specific domains, Dw and Dt. Its mechanism is, however, similar to IS transposition
(Ferreira 2001). This operator randomly chooses the chromosome, the gene with its respective Dw plus Dt (if we use the same symbols to represent the weights and the thresholds, we can treat Dw and Dt as one big domain), the first position of the transposon, the transposon length, and the target site (also chosen within Dw plus
Dt).
Consider the chromosome below with h = 4 (Dw and Dt are shown in different
colors):
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0123456789012345678901234567890123456 |
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DTQaababaabbaabba05717457362846682867 |
(3.1) |
where “T” represents a function of three arguments and “Q” represents a function of four arguments. Suppose that the sequence “46682” was chosen as a transposon and that the insertion site was bond 4 in Dw (between positions 20 and 21). Then the following chromosome is obtained:
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0123456789012345678901234567890123456 |
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DTQaababaabbaabba05714668274573628466 |
(3.2) |
Note that the transposon might be any sequence in Dw or Dt, or even be part Dw and part Dt like in the example above. Note also that the insertion site might be anywhere in Dw or Dt as the symbols used to represent the weights and the thresholds are the same. Remember, however, that the values they represent are different for they are kept in different arrays. Suppose that the arrays below represent the weights and the thresholds of chromosome
(3.1) above:
W = {-1.64, -1.834, -0.295, 1.205, -0.807, 0.856, 1.702, -1.026, -0.417, -1.061}
T = {-1.14, 1.177, -1.179, -0.74, 0.393, 1.135, -0.625, 1.643, -0.029, -1.639} |
Although the new chromosome (3.2) obtained after transposition has the same topology and uses exactly the same arrays
of weights and thresholds for its expression, a different neural network is encoded in this chromosome
(Figure 1). Indeed, with domain-specific transposition the weights and thresholds are moved around and new combinations are tested.
Figure 1. Testing new combinations of existing weights and thresholds by domain-specific transposition.
a) The mother neural network. b) The daughter neural network created by domain-specific transposition. Note that the network architecture is the same for both mother and daughter and that
Wm = Wd and Tm = Td. However, mother and daughter are different because different combinations of weights and thresholds are expressed in these individuals.
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