Improvement in Performance of GMRES(m) Method by Applying a Genetic Algorithm to the Restart Process

This paper presents an approach for improving the efficiency of solving linear systems by applying a genetic algorithm (GA) to the GMRES(m) method, which is one of the most powerful solvers of large-scale asymmetric sparse matrices. For each restart process in GMRES(m), the initial vectors are regarded as chromosomes. When the restart process stagnates, the GA process performs a crossover on chromosomes to create new chromosomes for the next restart stage. An algorithm, which was inspired by the look-back type of the GMRES(m) method, was developed to effectively perform the crossover process. The proposed method was tested on five example matrices selected from the University of Florida sparse matrix collection. The results show that improvements in execution time ranged from 15% to 600%, depending on the nature of the matrix.