A Sharp Fitness Function for the Problem of Finding Roots of Polynomial Equations Systems

Cruz E. Borges, José L. Montaña, Luis M. Pardo

2014

Abstract

We experiment with several evolutionary algorithms for solving systems of polynomial equations with real coefficients. As a main difference with previous work, our algorithms can certify the correctness of the solutions they provide. This achievement is made possible by incorporating results from the field of numerical analysis to their fitness functions. We have performed an experimental comparison between the various proposed algorithms. The results of this comparison show that evolutionary and other local search algorithms can deal with the problem of solving systems of polynomial equations even for systems having many variables and high degree. Our main contribution is a nontrivial fitness function adjusted to the problem to be solved. This function is not based on any heuristics but on the fundamentals of numerical computation.

Paper Citation

in Harvard Style

Borges C., Montaña J. and Pardo L. (2014). A Sharp Fitness Function for the Problem of Finding Roots of Polynomial Equations Systems . In Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2014) ISBN 978-989-758-052-9, pages 294-301. DOI: 10.5220/0005140002940301

in Bibtex Style

@conference{ecta14,
author={Cruz E. Borges and José L. Montaña and Luis M. Pardo},
title={A Sharp Fitness Function for the Problem of Finding Roots of Polynomial Equations Systems},
booktitle={Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2014)},
year={2014},
pages={294-301},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005140002940301},
isbn={978-989-758-052-9},
}

in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2014)
TI - A Sharp Fitness Function for the Problem of Finding Roots of Polynomial Equations Systems
SN - 978-989-758-052-9
AU - Borges C.
AU - Montaña J.
AU - Pardo L.
PY - 2014
SP - 294
EP - 301
DO - 10.5220/0005140002940301