Diophantine equations and Fuzzy Adaptive Simulated Annealing

This work uses the Fuzzy Adaptive Simulated Annealing algorithm to solve many examples of Dio-phantine 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 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.