Using Metaheuristic Computations to Find the Minimum-Norm-Residual Solution to Linear Systems of Equations

This work will present metaheuristic computations,
namely, probabilistic artificial neural network, simulated annealing,
and modified genetic algorithm in finding the minimumnorm-residual
solution to linear systems of equations. By demonstrating
a set of input parameters, the objective function, and the
expected results solutions are computed for determined, overdetermined,
and underdetermined linear systems. In addition, this
work will present a version of genetic algorithm modified in
terms of reproduction and mutation. In this modification, every
reproduction cycle is performed by matching each individual with
the rest of the individuals in the population. Further, the offspring
chromosomes result from crossover of parent chromosomes
without mutation. The selection process only selects the best fit
individuals in the population. Mutation is only performed when
the desired level of fitness cannot be achieved, and all the possible
chromosome combinations were already exhausted. Experimental
results for randorrly generated matrices with increasing matrix
sizes will be presented and analyzed. It will be the basis in
modeling and identifying the dynamics parameters of a humanoid
robot through response optimization at excitatory motions.