Brain storm optimization algorithms for solving equations systems

Abstract

This chapter refers to the use of Brain Storm Optimization (BSO) algorithms in solving equations systems (ES). BSO algorithm is a swarm intelligence algorithm, which simulates the human brainstorming process, a form of human collective creativity. Mainly, in this chapter, two algorithms are proposed: the first for ES preconditioning and second for solving ES. First, is proposed a BSO method aiming the bandwidth reduction of sparse matrices, a process that can improve a lot of computing processes, such as solving large systems of linear equations. The other one proposes a method for solving equations systems that uses BSO. For the second problem, a new crossover strategy as well as a hybridization of BSO with graph theory elements are proposed. Serial and parallel variants of both algorithms are presented. Experimental results obtained illustrate the fact that the proposed algorithms lead to good results, with respect to other methods.