Genetic Algorithms Through Structures

I've noticed that it is possible to describe the genetic operators of Genetic Algorithms (and other evolutionary algorithms) though simple data structures. This does not seem to be any advantage in speed or even simplicity, but I like to think about GAs in different ways and try to decouple all the parts from each other, and this is a way to decouple the randomness from the action of a genetic operator.

First off- mutation. There are many ways to do mutation, but the simplest is to test for each symbol on each individual, and with a certain probability replace that symbol with a random one from the symbol set. In particular you often will simply flip a bit. The knowledge needed to change a symbol is whether or not you need to change it, therefore a boolean contains enough information to make this decision. For an individual of some structure, that same structure containing boolean values is enough to perform mutation so given, say, a vector of bits (the individual) and another vector of bits (the mutations), we can deterministically flips the bits in the individual that correspond to the 1s in the mutation vector (by xoring then in this case).

For crossover all we need is a single number (for one point crossover) to indicate the cut point. To crossover a whole population we need a structure containing numbers, and a structure containing pairs of individuals, and we can create a structure containing paired individuals that are crossed. We can then unpair them and get a population. We could also create some selection structure, like pairs of indices into the original population indicating who to cross. For uniform crossover, or crossover with multiple individuals, we could create a list of individuals and a list of number where each number indicates which individual the position it is in should be filled from. In other words, each index's symbol is chosen from that index in the individual indicated by the number in our crossover number list.

Selection is no harder then any other mechanism. We can do tournament selection by a structure of pairs of numbers, the indices into the population to pick the individuals for the tournament from. Notice that this means that, like all the other operators, the genetic operator structure can be determined without looking at the population at all. These pairs would have to be tagged with a boolean indicating whether the more or less fit individual should be chosen when the selection structure is applied.

In RGEP and PGEP there is a genetic operator called rotation, which is basically a shift with wraparound. Clearly this can be indicated by the number of positions to shift by, which is a single natural number.

So those are the ones I can think of right now, but it does seem like any genetic operator can be decomposed into a random part which generates the data for a deterministic part. Given the structure generated and the population you can perform the operator without generating random number.