Algebraic perspectives of solutions spaces in combinatorial optimization

Motivated from the algebraic evolutionary algorithms proposed in [4] and [1], here we introduce novel algebraic perspectives for the search space of a large class of combinatorial optimization problems. By moving from some simple concepts of group theory, we propose a framework that allows: (i) to use algebraic concepts in order to formally define what is a search move on a discrete space of solutions, (ii) to provide a rationale of the algebraic concepts by means of simple geometric arguments, and (iii) to derive a formal languages point-of-view in order to link algebraic and geometric views, other than to extend the framework to more general search spaces.