Reciprocally induced coevolution: A computational metaphor in Mathematics

TL;DR

This paper introduces reciprocally induced coevolution as a novel mechanism to enhance genetic algorithms, demonstrated through solving Diophantine equations, which are historically and practically significant in mathematics and computer science.

Contribution

It proposes a new coevolutionary approach inspired by biological reciprocity to improve optimization in genetic algorithms for solving Diophantine equations.

Findings

Improved solution accuracy for Diophantine equations.

Effective handling of equations with multiple variables.

Demonstrated potential of coevolution in mathematical optimization.

Abstract

Natural phenomenon of coevolution is the reciprocally induced evolutionary change between two or more species or population. Though this biological occurrence is a natural fact, there are only few attempts to use this as a simile in computation. This paper is an attempt to introduce reciprocally induced coevolution as a mechanism to counter problems faced by a typical genetic algorithm applied as an optimization technique. The domain selected for testing the efficacy of the procedure is the process of finding numerical solutions of Diophantine equations. Diophantine equations are polynomial equations in Mathematics where only integer solutions are sought. Such equations and its solutions are significant in three aspects-(i) historically they are important as Hilbert's tenth problem with a background of more than twenty six centuries; (ii) there are many modern application areas of Diophantine equations like public key cryptography and data dependency in super computers (iii) it has been proved that there does not exist any general method to find solutions of such equations. The proposed procedure has been tested with Diophantine equations with different powers and different number of variables.