An Approach to Solve Linear Equations Using a Time-Variant Adaptation Based Hybrid Evolutionary Algorithm

TL;DR

This paper introduces a novel hybrid evolutionary algorithm with a time-variant adaptation technique for efficiently solving large systems of linear equations, improving upon existing uniform adaptation methods.

Contribution

It proposes a new TVA-based hybrid evolutionary algorithm for linear equations, with proven convergence and superior performance over UA-based methods.

Findings

TVA-based algorithm outperforms UA-based in efficiency

Theoretical convergence of the proposed method is established

Experimental results demonstrate improved solution speed

Abstract

For small number of equations, systems of linear (and sometimes nonlinear) equations can be solved by simple classical techniques. However, for large number of systems of linear (or nonlinear) equations, solutions using classical method become arduous. On the other hand evolutionary algorithms have mostly been used to solve various optimization and learning problems. Recently, hybridization of evolutionary algorithm with classical Gauss-Seidel based Successive Over Relaxation (SOR) method has successfully been used to solve large number of linear equations; where a uniform adaptation (UA) technique of relaxation factor is used. In this paper, a new hybrid algorithm is proposed in which a time-variant adaptation (TVA) technique of relaxation factor is used instead of uniform adaptation technique to solve large number of linear equations. The convergence theorems of the proposed algorithms are proved theoretically. And the performance of the proposed TVA-based algorithm is compared with the UA-based hybrid algorithm in the experimental domain. The proposed algorithm outperforms the hybrid one in terms of efficiency.