The restricted permutation operator appears as the “exchange mutation” operator in Larrañaga et al. (1998). It allows two genes occupying any positions within a particular multigene family to trade places. This operator might also be useful to make finer adjustments when combined with inversion, but it performs poorly if used as the only source of genetic variation (see Figure 1).

The restricted permutation operator randomly chooses the chromosome, the multigene family to be modified and the genes to be exchanged. Each chromosome is only modified once by this operator.

Consider another chromosome composed of two multigene families, each with 13 members:

01234567890120123456789012
ikmfghdeljcabljihgcdbkmfae	(3.7)

Suppose genes 5 and 9 in FMG₂ were chosen to be exchanged. Then the following chromosome is formed:

01234567890120123456789012
ikmfghdeljcabljihgMdbkCfae	(3.8)

Restricted permutation, when used at small rates and in combination with inversion, might be useful to make finer adjustments. However, for the problems analyzed in this work, when permutation is used in conjunction with inversion the success rate slightly decreases.