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.

Algebraic perspectives of solutions spaces in combinatorial optimization

Valentino Santucci
2017

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12071/12803
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