Using metaheuristic computations to find the minimum-norm-residual solution to linear systems of equations

• Main Authors: Jamisola, Rodrigo S., Jr., Dadios, Elmer P., Ang, Marcelo H.
• Format: text
• Published: Animo Repository 2009
• Subjects: Metaheuristics; Neural networks (Computer science); Simulated annealing (Mathematics); Linear systems; Genetic algorithms; Electrical and Computer Engineering
• Online Access: https://animorepository.dlsu.edu.ph/faculty_research/7122
• Institution: De La Salle University

This work will present metaheuristic computations, namely, probabilistic artificial neural network, simulated annealing, and modified genetic algorithm in finding the minimum-norm-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.