A probabilistic computation of artificial neural network and genetic algorithm in finding the minimum-norm residual solution to linear systems of equations

Artificial neural network and genetic algorithm have been extensively used in solving many real-world engineering problems. In this work these computational methods are used to solve linear systems of equations in finding the minimum-norm-residual solution, using a probabilistic approach. This work will show the efficacy of probabilistic artificial neural network and probabilistic genetic algorithm in finding solutions to determined, overdetermined, and undertermined systems. This work does not claim superiority over other neural network or genetic algorithm computational implementations, nor superiority over other linear solvers, but is presented as an alternative approach in solving root-finding or optimization problems. Experimental results for randomly generated matrices with increasing matrix sizes will be presented and analyzed. This work will be the basis in modeling and identifying the dynamics parameters of a humanoid robot through response optimization at excitatory motions