Global Optimization on Topological Manifolds with Fuzzy Adaptive Simulated Annealing

This paper introduces a new approach that makes it possible to globally optimize real valued functions defined on topological manifolds. The functions under study don’t need to be differentiable or even continuous, and it is shown that the optimization task may be executed so that candidate points remain on the manifolds that contain their domains, evolving on them during the whole optimization process. Although the proposed paradigm is adequate for use with an extensive family of already established metaheuristics, the algorithm known as Fuzzy Adaptive Simulated Annealing is used in order to exemplify the overall global optimization mechanism.