Global optimization using dimensional jumping and fuzzy adaptive simulated annealing

This paper proposes a new multi-start, stochastic global optimization algorithm that uses dimensional reduction techniques based upon approximations of space-filling curves, simulated annealing and particle swarm optimization, aiming at finding global minima of real-valued functions that are not necessarily well behaved, that is, are not required to be differentiable, continuous, or even satisfying Lipschitz conditions. The overall idea is as follows: given a real-valued function F with a multidimensional and compact domain D, the method builds an equivalent one-dimensional problem by composing F with a linearization of D, searches for a small population of candidates and returns to the original high-dimensional domain, this time with a small set of promising starting points.