Crossover and Conditioned Mutation

While the crossover operation tends to keep or even to improve a given set of values (see below for the theoretical argument) can mutation destroy the given 'level' of values. Thus it is an interesting question how one can 'manage' mutation in a way which keeps the negative effect at a minimum.

Because crossover and mutation are only 'better' than pure chance in the presence of fitness values one could exploit this information for the management of mutation. If one can compute the approximate time $n$ for the crossover operator to move a given population $\cal{G}$$^{i}$ to a new population $\cal{G}$$^{i+n}$ with a relative maximum applying crossover to $\cal{G}$$^{i}$, and if this population $\cal{G}$$^{i+n}$ with the relative maximum is less than the theoretical maximum, then one could trigger a conditioned mutation operator to try to escape this relative maximum, but only then.

This would deviate from nature because natural evolution has no 'pre-knowledge' about fitness. There mutation has to be guided by pure chance just to try another variant because at the point of a mutation a 'real' biological systems does not 'know' what will be the final outcome in the future. Especially because the environment can have changed dramatically.

A simple form of conditioned mutation could be realized by only monitoring the level of the maximal fitness. If this does not change for $n$-many cycles while being below the theoretical maximum then this could be used as a trigger to apply restricted mutation.