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Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence

Inversion

The inversion operator randomly selects the chromosome, the multigene family to be modified, the inversion points in the MGF, and inverts the sequence between these points. Each chromosome can only be modified once by this operator.

Consider the chromosome below composed of two multigene families:

 01234567890123456780123456789012345678 snpbqhfgkicmjlaedorPRMDCNLEBQFGKJOHIAS (6.1)

Suppose, for instance, that genes 2 and 7 in MGF2 were chosen as inversion points. Then the sequence between these points is reversed, obtaining:

 01234567890123456780123456789012345678 snpbqhfgkicmjlaedorPRELNCDMBQFGKJOHIAS (6.2)

Note that with inversion the whole multigene family can be inverted. This happens whenever the first and last genes are chosen as inversion points. For instance, the inversion of MGF2 in chromosome (6.1) gives:

 01234567890123456780123456789012345678 snpbqhfgkicmjlaedorSAIHOJKGFKBELNCDMRP (6.3)

Note also that this operator allows small adjustments like, for instance, the permutation of two adjacent genes. For instance, if genes 7 and 8 in MGF1 of chromosome (6.3) were chosen as inversion points, these genes would be permuted, giving:

 01234567890123456780123456789012345678 snpbqhfkgicmjlaedorSAIHOJKGFKBELNCDMRP (6.4)

As shown in Figure 6.2, inversion is the most powerful of the combinatorial-specific genetic operators, causing populations to evolve with great efficiency even if used as the only source of genetic modification. Indeed, this operator alone produces better results than when combined with gene deletion/insertion or permutation. Inversion rates between 20% and 60% produce good results for most problems.

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