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- A global optimization approach based on adaptive populationsPublication . Silva, Tiago A. N.; Loja, Amélia; Carvalho, Alda; Maia, Nuno M. M.; Barbosa, JoaquimThe solution of inverse problems based on experimental data is itself an important research issue. In this context and assuming that an experimental sample is available, rather than trying to find a specific deterministic solution for the inverse problem, one aims to determine the probabilistic distribution of the modelling parameters, based on the minimization of the dissimilarity between the empirical cumulative distribution function of an experimental solution and its simulation counterpart. The present paper presents na innovative framework, where Differential Evolution is extended in order to estimate not only an optimal set of modelling parameters, but to estimate their optimal probabilistic distributions. Additionally, the Adaptive Empirical Distributions optimization scheme is here introduced. Both schemes rely on the two samples Kolmogorov-Smirnov goodness-offit test in order to evaluate the resemblance between two empirical cumulative distribution functions. A numerical example is considered in order to assess the performance of the proposed strategies and validity of their solutions.
- Adaptive empirical distributions in the framework of inverse problemsPublication . Silva, Tiago; Loja, Amélia; Carvalho, Alda; Maia, Nuno. M.; Barbosa, JoaquimThis article presents an innovative framework regarding an inverse problem. One presents the extension of a global optimization algorithm to estimate not only an optimal set of modeling parameters, but also their optimal distributions. Regarding its characteristics, differential evolution algorithm is used to demonstrate this extension, although other population-based algorithms may be considered. The adaptive empirical distributions algorithm is here introduced for the same purpose. Both schemes rely on the minimization of the dissimilarity between the empirical cumulative distribution functions of two data sets, using a goodness-of-fit test to evaluate their resemblance.