The new classes of the genetic algorithms are defined by nonassociative groupoids

TL;DR

This paper introduces a new class of genetic algorithms based on nonassociative groupoids, generalizing classical genetic algorithms through the concept of genetic products derived from DNA recombination theory.

Contribution

It defines genetic groupoids and characterizes three-element cases, providing a foundation for developing novel genetic algorithms beyond traditional models.

Findings

Full classification of three-element genetic groupoids

Framework for constructing new genetic algorithms

Open problems in genetic groupoid theory

Abstract

The genetic product of the groupoids, originating in the theory of DNA recombination, is introduced. It permits a natural generalization of the classical genetic algorithm. The full characterization of all three-element genetic groupoids gives an approach to construct the new classes of genetic algorithms. In the conclusion, we formulate some open problems in the theory of the genetic groupoids.