The normalized edit distance is one of the distances derived from the edit distance. It is useful in some applications because it takes into account the lengths of the two strings compared. The normalized edit distance is not defined in terms of edit operations but rather in terms of the edit path. In this paper we propose a new derivative of the edit distance that also takes into consideration the lengths of the two strings, but the new distance is related directly to the edit distance. The particularity of the new distance is that it uses the genetic algorithms to set the values of the parameters it uses. We conduct experiments to test the new distance and we obtain promising results.