### Abstract

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.

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.

Original language | English |
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Pages (from-to) | 1-9 |

Number of pages | 9 |

Journal | Philippine Computing Journal |

Volume | 4 |

Issue number | 2 |

Publication status | Published - 2009 |

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## Cite this

Jamisola, R., Dadios, E. P., & Ang, M. H. (2009). Using Metaheuristic Computations to Find the Minimum-Norm-Residual Solution to Linear Systems of Equations.

*Philippine Computing Journal*,*4*(2), 1-9. https://www.researchgate.net/profile/Rodrigo_Jamisola/publication/236651249_Using_Metaheuristic_Computations_to_Find_the_Minimum-Norm-Residual_Solution_to_Linear_Systerns_of_Equations/links/0deec518aedd2ac8f7000000/Using-Metaheuristic-Computations-to-Find-the-Minimum-Norm-Residual-Solution-to-Linear-Systerns-of-Equations.pdf