  Large set of linear equations, especially for sparse and structured
coefficient (matrix) equations, solutions using classical methods become
arduous. And evolutionary algorithms have mostly been used to solve various
optimization and learning problems. Recently, hybridization of classical
methods (Jacobi method and Gauss-Seidel method) with evolutionary computation
techniques have successfully been applied in linear equation solving. In the
both above hybrid evolutionary methods, uniform adaptation (UA) techniques are
used to adapt relaxation factor. In this paper, a new Jacobi Based Time-Variant
Adaptive (JBTVA) hybrid evolutionary algorithm is proposed. In this algorithm,
a Time-Variant Adaptive (TVA) technique of relaxation factor is introduced
aiming at both improving the fine local tuning and reducing the disadvantage of
uniform adaptation of relaxation factors. This algorithm integrates the Jacobi
based SR method with time variant adaptive evolutionary algorithm. The
convergence theorems of the proposed algorithm are proved theoretically. And
the performance of the proposed algorithm is compared with JBUA hybrid
evolutionary algorithm and classical methods in the experimental domain. The
proposed algorithm outperforms both the JBUA hybrid algorithm and classical
methods in terms of convergence speed and effectiveness.
