An algorithm is developed to statistically find the best global fit of a nonlinear non-convex cost-function over a D-dimensional space. It is argued that this algorithm permits an annealing schedule for ''temperature'' T decreasing exponentially in annealing-time k, T = T 0 exp(−ck 1/D ). The introduction of re-annealing also permits adaptation to changing sensitivities in the multidimensional parameter-space. This annealing schedule is faster than fast Cauchy annealing, where T = T 0 /k, and much faster than Boltzmann annealing, where T = T 0 / ln k. Applications are being made to fit empirical data to Lagrangians representing nonlinear Gaussian-Markovian systems.

Simulated annealing (SA) presents an optimization technique with several striking positive and negative features. Perhaps its most salient feature, statistically promising to deliver an optimal solution, in current practice is often spurned to use instead modified faster algorithms, "simulated quenching" (SQ). Using the author's Adaptive Simulated Annealing (ASA) code, some examples are given which demonstrate how SQ can be much faster than SA without sacrificing accuracy.

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We compare Genetic Algorithms (GA) with a functional search method, Very Fast Simulated Reannealing (VFSR), that not only is efficient in its search strategy, but also is statistically guaranteed to find the function optima. GA previously has been demonstrated to be competitive with other standard Boltzmann-type simulated annealing techniques. Presenting a suite of six standard test functions to GA and VFSR codes from previous studies, without any additional fine tuning, strongly suggests that VFSR can be expected to be orders of magnitude more efficient than GA.