For Solving Linear Equations Recombination is a Needless Operation in Time-Variant Adaptive Hybrid Algorithms
This work addresses computational efficiency for researchers and practitioners using evolutionary algorithms to solve linear equations, but it is incremental as it modifies existing hybrid techniques by removing a component.
The paper tackles the problem of solving large sets of linear equations by proposing modified hybrid evolutionary algorithms that omit the recombination operation, finding that these new algorithms achieve comparable performance in terms of generations required while reducing computational time compared to existing methods.
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.