I'm implementing a genetic algorithm to optimise $x$ so as to minimise the RMSD error $r(x)$ between my model and experimental data.
During the selection stage of recombination, I wish to select 'chromosomes' for breeding using fitness proportionate selection. This means that each chromosome $x$ is selected with a probability that is proportional to some fitness function $f(x)$. Clearly, $f$ should be large for good fits and small for bad fits, which is the inverse behaviour of the RMSD function $r(x)$.
So my question is: What is the standard way of constructing $f(x)$ from $r(x)$?
One obvious solution would be $f(x)=1/r(x)$ but I'm concerned that if $r$ is small enough then $f$ may be enormous which could harm genetic diversity.