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Global Optimization Methods (global + optimization_methods)

Distribution by Scientific Domains

Engineering	50%
Chemistry	50%

Selected Abstracts

A reduced-order simulated annealing approach for four-dimensional variational data assimilation in meteorology and oceanography

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2008
I. Hoteit
Abstract Four-dimensional variational data assimilation in meteorology and oceanography suffers from the presence of local minima in the cost function. These local minima arise when the system under study is strongly nonlinear. The number of local minima further dramatically increases with the length of the assimilation period and often renders the solution to the problem intractable. Global optimization methods are therefore needed to resolve this problem. However, the huge computational burden makes the application of these sophisticated techniques unfeasible for large variational data assimilation systems. In this study, a Simulated Annealing (SA) algorithm, complemented with an order-reduction of the control vector, is used to tackle this problem. SA is a very powerful tool of combinatorial minimization in the presence of several local minima at the cost of increasing the execution time. Order-reduction is then used to reduce the dimension of the search space in order to speed up the convergence rate of the SA algorithm. This is achieved through a proper orthogonal decomposition. The new approach was implemented with a realistic eddy-permitting configuration of the Massachusetts Institute of Technology general circulation model (MITgcm) of the tropical Pacific Ocean. Numerical results indicate that the reduced-order SA approach was able to efficiently reduce the cost function with a reasonable number of function evaluations. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Diffusion-equation method for crystallographic figure of merits

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2010
Anders J. Markvardsen
Global optimization methods play a significant role in crystallography, particularly in structure solution from powder diffraction data. This paper presents the mathematical foundations for a diffusion-equation-based optimization method. The diffusion equation is best known for describing how heat propagates in matter. However, it has also attracted considerable attention as the basis for global optimization of a multimodal function [Piela et al. (1989). J. Phys. Chem.93, 3339,3346]. The method relies heavily on available analytical solutions for the diffusion equation. Here it is shown that such solutions can be obtained for two important crystallographic figure-of-merit (FOM) functions that fully account for space-group symmetry and allow the diffusion-equation solution to vary depending on whether atomic coordinates are fixed or not. The resulting expression is computationally efficient, taking the same order of floating-point operations to evaluate as the starting FOM function measured in terms of the number of atoms in the asymmetric unit. This opens the possibility of implementing diffusion-equation methods for crystallographic global optimization algorithms such as structure determination from powder diffraction data. [source]

Parameter identification for leaky aquifers using global optimization methods

HYDROLOGICAL PROCESSES, Issue 7 2007
Hund-Der Yeh
Abstract In the past, graphical or computer methods were usually employed to determine the aquifer parameters of the observed data obtained from field pumping tests. Since we employed the computer methods to determine the aquifer parameters, an analytical aquifer model was required to estimate the predicted drawdown. Following this, the gradient-type approach was used to solve the nonlinear least-squares equations to obtain the aquifer parameters. This paper proposes a novel approach based on a drawdown model and a global optimization method of simulated annealing (SA) or a genetic algorithm (GA) to determine the best-fit aquifer parameters for leaky aquifer systems. The aquifer parameters obtained from SA and the GA almost agree with those obtained from the extended Kalman filter and gradient-type method. Moreover, all results indicate that the SA and GA are robust and yield consistent results when dealing with the parameter identification problems. Copyright © 2006 John Wiley & Sons, Ltd. [source]

On the equivalence of the Rietveld method and the correlated integrated intensities method in powder diffraction

JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 4 2004
William I. F. David
The Rietveld method is the most straightforward and statistically correct approach for the refinement of crystal structure parameters from powder diffraction data. The equivalent two-stage approach, involving the refinement of structural parameters based on integrated intensities extracted using the Pawley method, is extremely useful in circumstances such as the global optimization methods of structure determination, where a great many refinements need to be performed very quickly. The equivalence is emphasized in a simple mathematical relationship between the goodness of fits obtained in Rietveld, Pawley and correlated integrated intensities refinements. A rationale is given for determining the estimated standard deviations for structural variables from powder diffraction data. [source]