Hime Aguiar e O. Jr., "Diophantine Equations and Fuzzy Adaptive Simulated Annealing," WSEAS Transactions on Mathematics, vol. 13, pp. 48-58, 2014, DOI:
Hime Aguiar e O. Jr.. Diophantine Equations and Fuzzy Adaptive Simulated Annealing.
WSEAS Transactions on Mathematics. 2014;13:48-58.
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 13, 2014
Diophantine Equations and Fuzzy Adaptive Simulated Annealing
Author:
Abstract: This work uses the Fuzzy Adaptive Simulated Annealing algorithm to solve many examples of Diophantine equations, offering a global optimization alternative for those ones that did not have a general method or even a closed form for their solution. The proposed method uses the built-in integer programming capabilities of Fuzzy ASA and the candidate solutions evolve in Z^n, in contrast to the best known applications of ASA, exposing an almost unexplored feature of that paradigm. Some significant numerical results are introduced, and empirical relationships between number of independent variables and necessary number of cost function evaluations to get to solutions are presented.
Keywords:
Global optimization, Equation solving, Diophantine equations, Adaptive Simulated Annealing
Pages: 48-58 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 13, 2014, Art. #6 DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
**The DOI link will be activated in the first midst of January 2026.
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