Fig. 3.

Different optimal mutation rate control functions derived mathematically to optimise different criteria in Hamming space ${\mathcal{H}}_4^{10}$: step function minimising expected distance to optimum in one generation, linear function maximising probability of mutating directly into optimum, a function maximising conditional probability $P(m<n\mid n)$ that an offspring is closer to optimum than its parent, cumulative distribution function $P_0(m<n)={\sum }_{m=0}^{n-1}\left(\genfrac{}{}{0pt}{}{l}{m}\right)\frac{{(\mathit{\alpha }-1)}^m}{{\mathit{\alpha }}^l}$ minimising expected distance to optimum subject to an information constraint (Belavkin 2012)