Automatic algebraic evolutionary algorithms

Motivated from the previously proposed algebraic framework for combinatorial optimization, here we introduce a novel formal languages-based perspective on discrete search spaces that allows to automatically derive algebraic evolutionary algorithms. The practical effect of the proposed approach is that the algorithm designer does not need to choose a solutions encoding and implement algorithmic procedures. Indeed, he/she only has to provide the group presentation of the discrete solutions of the problem at hand. Then, the proposed mechanism allows to automatically derive concrete implementations of a chosen evolutionary algorithms. Theoretical guarantees about the feasibility of the proposed approach are provided.