From a theoretical point of view one is interested to compare different tasks with regard to the applied genetic algorithm (e.g. to find a solution needs 'more time' for than for ). One strategy to enable such comparisons is to translate all tasks into a common format. One very useful format is the binary format representing all information as binary strings. Because it can be proven that any kind of alphabet can be translated into a binary representation this requirement of a binary representation will no be a reduction of the general character of the approach.

From this follows that the only 'real work' which has to be done to apply a GA is the encoding of a task into a binary representation accompanied by the provision of an appropriate fitness function ^{5.1}. The fitness function has to encode the 'nearness' of a given (measurable) property to the set of 'good' properties
where the working set shall be 'processed' by in a way that there will be a point in time where ideally
. Every fitness function has to obey some ordering thus that for any
we have
.

Example:

Figure 5.10 shows the example of the 5-Queens-Problem as a 2-dimensional space with objects in a grid required not to collide according to the 'queens rule' of the chess game^{5.2}. This spatial situation is first encoded into a vector of numbers representing the columns with queens following the direction from 'top' to down'. This encoding is then further encoded into a binary representation. The primary information string has then the length , which allows many different strings; this gives us the ideal set . The simple fitness function counts the number of queens involved in a 'collision' according to the queens rule.

Gerd Doeben-Henisch 2013-01-14