For Solving Linear Equations Recombination is a Needless Operation in Time-Variant Adaptive Hybrid Algorithms

TL;DR

This paper introduces modified hybrid evolutionary algorithms for solving large linear equations that omit the recombination operation, demonstrating comparable or improved efficiency and effectiveness over existing methods.

Contribution

The paper proposes recombination-free hybrid evolutionary algorithms with time-variant adaptive techniques for solving linear equations, showing they are more efficient and easier to implement.

Findings

Modified algorithms require less computational time.

Number of generations needed is comparable to existing algorithms.

Recombination-free algorithms are more efficient and easier to implement.

Abstract

Recently hybrid evolutionary computation (EC) techniques are successfully implemented for solving large sets of linear equations. All the recently developed hybrid evolutionary algorithms, for solving linear equations, contain both the recombination and the mutation operations. In this paper, two modified hybrid evolutionary algorithms contained time-variant adaptive evolutionary technique are proposed for solving linear equations in which recombination operation is absent. The effectiveness of the recombination operator has been studied for the time-variant adaptive hybrid algorithms for solving large set of linear equations. Several experiments have been carried out using both the proposed modified hybrid evolutionary algorithms (in which the recombination operation is absent) and corresponding existing hybrid algorithms (in which the recombination operation is present) to solve large set of linear equations. It is found that the number of generations required by the existing hybrid algorithms (i.e. the Gauss-Seidel-SR based time variant adaptive (GSBTVA) hybrid algorithm and the Jacobi-SR based time variant adaptive (JBTVA) hybrid algorithm) and modified hybrid algorithms (i.e. the modified Gauss-Seidel-SR based time variant adaptive (MGSBTVA) hybrid algorithm and the modified Jacobi-SR based time variant adaptive (MJBTVA) hybrid algorithm) are comparable. Also the proposed modified algorithms require less amount of computational time in comparison to the corresponding existing hybrid algorithms. As the proposed modified hybrid algorithms do not contain recombination operation, so they require less computational effort, and also they are more efficient, effective and easy to implement.