Comparing Evolutionary Computation Techniques via Their Representation

In the current paper a rigorous mathematical language for comparing evolutionary computation techniques via their representation is developed. A binary semi-genetic algorithm is introduced, and it is proved that in a certain sense any reasonable evolutionary search algorithm can be re-encoded by a binary semi-genetic algorithm (see corollaries 15 and 16). Moreover, an explicit bijection between the set of all such re-encodings and the collection of certain n-tuples of invariant subsets is constructed (see theorem 14). Finally, all possible re-encodings of a given heuristic search algorithm by a classical genetic algorithm are entirely classified in terms of invariant subsets of the search space in connection with Radcliffe’s forma (see [9] and theorem 20).