Mutation

As mutation operator we have chosen the non-uniform mutation with parameter $b=5$ [Mic92] as its dynamical nature makes it very suitable for a wide variety of problems [HL00].

The individuals $\beta^m$ generated by this mutation are obtained as follows:

$$\beta^m_i=\left\{ \begin{array}{lll} \beta_i + \triangle(t,b_i-\b... ...u = 0 \\ \beta_i - \triangle(t,\beta_i-a_i) & si & \tau = 1 \end{array} \right.$$ (12)

being

$$\triangle(t,y)=y(1-r^{(1-{t \over g_{max}})^b})$$ (13)

where $t$ is the generation, $g_{max}$ is the maximum number of generations, $\tau$ is a random value, $\tau \in \{0,1\}$, $r$ is a random number in the interval $[0, 1]$ and $b$ is a parameter that determines the degree of dependence of the mutation with regards to the number of iterations. Equation 13 gives values in the interval $[0, y]$. The probability of obtaining a value near 0 increases as the algorithm progresses. This operator performs a uniform search in the initial stages of the evolution, and a very localized search in the final stages.