Mathematics – Probability
Scientific paper
May 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007aas...210.4502m&link_type=abstract
American Astronomical Society Meeting 210, #45.02; Bulletin of the American Astronomical Society, Vol. 39, p.159
Mathematics
Probability
Scientific paper
Numerical experiments have been carried out with a Simulated Annealing program incorporated into the light curve modeling package WD2007, the latest version of this package initially called WD95, developed and maintained by JK. Simulated annealing (SA) is one a number of metaheuristic methods that have been used in various scientific, economic, and business applications, to seek the absolute minimum of functions in multi-dimensional parameter space. SA draws on an analogue from metallurgy that makes use of an optimum cooling process. The search is conducted, as with other optimization procedures, by following a course toward the deepest minimum, but permits jumps to less optimum solutions by a quasi-random procedure using the "Metropolis criterion," involving a probability that decreases with the 'temperature," a quantity that describes the annealing state over time. It is this capability of escaping from a local minimum that allows wider sampling of parameter solution space.
We used as test data a simulated light-curve, based loosely on light curves of the over-contact system V781 Tau. In this work we tested the goodness of fit and the efficiency of the SA algorithm we employed, against our damped least squares and simplex programs, also located in WD2007. Although we find that SA as coded here, is far less efficient than DLS (a purely-down-hill gradient program) and simplex, it appears sufficiently robust to avoid getting stuck in a local minimum, for the most part, if the initial "temperature" is high enough. It is, however, hardly fool-proof. Nevertheless, for initial model exploration, and as a check on solutions found by the other methods, simulated annealing appears to offer another useful test in the search for true global minima.
This work was supported in part by grants to EFM from the Canadian Natural Sciences and Engineering Research Council.
Kallrath Josef
Milone Eugene F.
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