Reproduction

  The heart of this operation is the objective function or the so called `fitness function'. The fitness function is a mapping from the chromosome domain into . This function evaluates a chromosome, a candidate DFA, grading it on the following aspects and returns a weighted sum of them. These aspects are:

• . Each member of , namely each example string is considered for testing. The Candidate DFA (encoded as the chromosome) is started from its start state and all the successful transitions are counted. The sum of these individual counts is the measure of the success of acceptance rate of that DFA. A perfect DFA, in this sense, will have an acceptance count equal to the sum of the lengths of all the examples (length of an example string is the count of tokens that make up the string).
• . Simplicity requires as less states and transitions as possible. Therefore, a penalty value directly proportional to the count of elements different than is introduced.
• . It has been discovered that the GA has a tendency to introduce transitions that leave the state unaltered. Considering the application field of NLP, this tendency is undesired. Therefore, a penalty value directly proportional to the count of such transitions is introduced.

The reproduction operator first evaluates all the chromosomes of a new generation and then replaces a certain proportion of the worst with the bests of the previous generation (provided that the replacing ones are better than the replaced ones).