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One possible form of changing the value of a gene while taking its value range [ x min , x max ] {\displaystyle [x_{\min },x_{\max }]} into account is the mutation relative parameter change of the evolutionary algorithm GLEAM (General Learning Evolutionary Algorithm and Method),cite-ref-17[17] in which, as with the mutation presented earlier, small changes are more likely than large ones.

First, an equally distributed decision is made as to whether the current value x {\displaystyle x} should be increased or decreased and then the corresponding total change interval is determined. Without loss of generality, an increase is assumed for the explanation and the total change interval is then [ x , x max ] {\displaystyle [x,x_{\max }]} . It is divided into k {\displaystyle k} sub-areas of equal size with the width δ δ {\displaystyle \delta } , from which k {\displaystyle k} sub-change intervals of different size are formed:

i {\displaystyle i} -th sub-change interval: [ x , x + δ δ ⋅ ⋅ i ] {\displaystyle [x,x+\delta \cdot i]} with

δ δ = ( x max − − x ) k {\displaystyle \delta ={\frac {(x_{\text{max}}-x)}{k}}} and i = 1 , … … , k {\displaystyle i=1,\dots ,k}

Subsequently, one of the k {\displaystyle k} sub-change intervals is selected in equal distribution and a random number, also equally distributed, is drawn from it as the new value x ′ {\displaystyle x'} of the gene. The resulting summed probabilities of the sub-change intervals result in the probability distribution of the k {\displaystyle k} sub-areas shown in the adjacent figure for the exemplary case of k = 10 {\displaystyle k=10} . This is not a normal distribution as before, but this distribution also clearly favours small changes over larger ones.

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