I have some doubts about how the selection process and genetic modification work. Is the entire set of new individuals selected at once and then mutation, inversion, etc. applied by selecting from this new population? And how are the rates applied? For example, are they picked up randomly n times (where n is the number of individuals in this selected population)... then apply mutation, inversion etc and then put back into the population? And for the combination operators, are they chosen 2 at a time and put the 2 new children back into the population, removing the parents?
The selection and reproduction processes are done as shown in the GEP flowchart, that is, first, individuals are selected by roulette-wheel to be reproduced (so, in your words, they are all selected at once). And when they reproduce, depending on the rates and number of the genetic operators being used, their genomes might get modified or not.
There are, however, basically two different kinds of modification rates: (1) rates like mutation rates which relate to points (or individual targets) in the chromosomes; and (2) rates like inversion or transposition rates which relate to individual chromosomes.
This means that when you are applying the mutation rate (the first kind of modification rate) the probability of mutation is evaluated relatively to the number of points in the chromosome. But since chromosomes in artificial evolutionary systems are usually very small (comparatively to chromosomes in nature), it is advisable to use all the chromosomes in the population in order to determine the number of points to mutate. For instance, for 30 chromosomes of size 50, there are a total of 1500 potential targets, so, in this case, a mutation rate of say 0.05 means that a total of 75 points are randomly mutated each generation.
When, for example, you are evaluating a transposition rate or an inversion rate (the second type of modification rate), the probability of transposition/inversion is evaluated relatively to the number of chromosomes in the population. For instance, for a population with 30 individuals, a transposition rate of 0.3 means that, in this case, a total of 9 different chromosomes are randomly chosen to undergo transposition.
Recombination is similar to the latter, with the difference that in this case you’ll need an even number of chromosomes to recombine (if, for instance, the total number of chromosomes to recombine gives 9, only 8 are in truth recombined). And in all cases, when a chromosome is modified, say chromosome 2, the new version replaces the old one (recombination is no different and, for instance, if chromosomes 5 and 8 were selected to undergo recombination, then the two new versions would replace the old chromosomes 5 and 8).
So, as you can see, different modifications might accumulate on a chromosome during its reproduction or, in other words, a chromosome might be modified more than once by different genetic operators during its reproduction.