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The requirement raised at the beginning for mutations, according to which small changes should be more probable than large ones, is only inadequately fulfilled by the two permutation mutations presented, since the lengths of the partial lists and the number of shift positions are determined in an equally distributed manner. However, the longer the partial list and the shift, the greater the change in gene order.

This can be remedied by the following modifications. The end index j {\displaystyle j} of the partial lists is determined as the distance d {\displaystyle d} to the start index i {\displaystyle i} :

j = ( i + d ) mod | P 0 | {\displaystyle j=(i+d){\bmod {\left|P_{0}\right|}}}

where d {\displaystyle d} is determined randomly according to one of the two procedures for the mutation of real numbers from the interval [ 0 , | P 0 | − − 1 ] {\displaystyle \left[0,\left|P_{0}\right|-1\right]} and rounded.

For the rotation, k {\displaystyle k} is determined similarly to the distance d {\displaystyle d} , but the value 0 {\displaystyle 0} is forbidden.

For the inversion, note that i ≠ ≠ j {\displaystyle i\neq j} must hold, so for d {\displaystyle d} the value 0 {\displaystyle 0} must be excluded.

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