Definition

Mutations are carried out on a gene-by-gene basis. Thus, in principle, the number of mutated genes can range from $0$ to $m$. We define the mutation probability as $p_{mut}$ which is typically set as $\frac{c}{m}$ where $c$ is a constant of order $1$ and $m$ is the Chromosome or Genotype length.

Binary Encoding

Here we just flip bits.

Real Encoding

Here we select a random number in the allowed range (i.e. $[0,1]$). The mutated value (allele) of a gene is centred on the previous value, and the creep rate determines how far the mutation may take the new value. The value $g$ of the gene changes according to $$g'=\psi(g)$$where $\psi$ is a suitable distribution, for instance a uniform distribution. In this case we get $$g\leftarrow g-\frac{C_{r}}{2}+C_{r}r$$where $r$ is the uniform random number in $[0,1]$ and $C_{r}$ is the creep rate (i.e. the width of the distribution).