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Applications of simulated annealing in the estimation of statistical models

Kastrinakis Evangelos

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Summary

This work deals with the study of complex global optimization problems. Global optimization is of major importance in various fields in science and engineering. Solving complex optimization problems with multiple local extrema is particularly difficult when using conventional methods of local optimization. On the other hand, global optimization methods can address convergence problems and lead to improvement performance. Specifically, the thesis examines the methods of simulated annealing and global search in the solution of two distinct problems. The first problem refers to finding the global optimum of high dimensional control functions (in 10 and 30 dimensional spaces) with multiple local extrema. The second problem involves maximizing the likelihood of a set of spatial data (a sample of a spatial stochastic process) in terms of the parameters of the so-called stochastic local interaction model. Both synthetic and real (coal thickness) spatial data are examined. A four-dimensional parametric space is used in this case. The present study aims to examine the performance of the above optimization methods in terms of global optimum localization accuracy and computational time. The results of applying the two optimization techniques to the two problems (i.e., the control functions and the likelihood of the stochastic local interactions model) are presented. More specifically, the comparison concerns the computational optimization time, the accuracy of the achieved solution, and the sensitivity of each method to various parameterizations. Regarding the optimization of the control functions, it is evident that the global search method is more efficient in terms of computational time and finds the global optimum more consistently regardless of the parameterization. Regarding the optimization of the likelihood, it is observed that the simulated annealing is more efficient in terms of computational time. For the synthetic spatial data, both methods achieve similar solutions for maximum likelihood. For the coal thickness data, global search does not converge over a period longer than two hours. However, for the spatial datasets neither method significantly improves the likelihood compared to local optimization.

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