A Comparison of Several Current Optimization Methods, and the use of Transformations in Constrained Problems
ABSTRACT The performances of eight current methods for unconstrained optimization are evaluated using a set of test problems with up to twenty variables. The use of optimization techniques in the solution of simultaneous non-linear equations is also discussed. Finally transformations whereby inequality constraints of certain forms can be eliminated from the formulation of an optimization problem are described, and examples of their use compared with other methods for handling such constraints.
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ABSTRACT: Direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives. Direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked coherent mathematical analysis. Nonetheless, users remained loyal to these methods, most of which were easy to program, some of which were reliable. In the past fifteen years, these methods have seen a revival due, in part, to the appearance of mathematical analysis, as well as to interest in parallel and distributed computing. This review begins by briefly summarizing the history of direct search methods and considering the special properties of problems for which they are well suited. Our focus then turns to a broad class of methods for which we provide a unifying framework that lends itself to a variety of convergence results. The underlying principles allow generalization to handle bound constraints andSIAM Review. 01/2003; 45(3):385-482.
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ABSTRACT: Mathematical simulation of flow toward drains is an important and indispensable stage in drainage design and management. Many related models have been developed, but most of them simulate the saturated flow toward drains without a due consideration of the unsaturated zone. In this study, the two dimensional differential equation governing saturated and unsaturated flow in porous media is numerically solved and water table variations between drains predicted. By introducing and linking a proper optimization model to the numerical one, saturated and unsaturated soil hydrodynamic parameters were estimated within the inverse problem technique context. Data for calibration and verification were provided through a conduction of laboratory experimentation. Other laboratory data were also employed for the proposed model evaluation. The results indicated that in addition to a prediction of the water table variations between drains, the inverse problem model can be employed to estimate the unsaturated soil hydrodynamic parameters with a high degree of precision.J. Agric. Sci. Technol. 01/2009; 11:199-210.
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ABSTRACT: The paper presents an optimization routine especially developed for the identification of model parameters in soil plasticity on the basis of different soil tests. Main focus is put on the mathematical aspects and the experience from application of this optimization routine. Mathematically, for the optimization, an objective function and a search strategy are needed. Some alternative expressions for the objective function are formulated. They capture the overall soil behaviour and can be used in a simultaneous optimization against several laboratory tests. Two different search strategies, Rosenbrock's method and the Simplex method, both belonging to the category of direct search methods, are utilized in the routine. Direct search methods have generally proved to be reliable and their relative simplicity make them quite easy to program into workable codes. The Rosenbrock and simplex methods are modified to make the search strategies as efficient and user-friendly as possible for the type of optimization problem addressed here. Since these search strategies are of a heuristic nature, which makes it difficult (or even impossible) to analyse their performance in a theoretical way, representative optimization examples against both simulated experimental results as well as performed triaxial tests are presented to show the efficiency of the optimization routine. From these examples, it has been concluded that the optimization routine is able to locate a minimum with a good accuracy, fast enough to be a very useful tool for identification of model parameters in soil plasticity. Copyright © 2001 John Wiley & Sons, Ltd.International Journal for Numerical and Analytical Methods in Geomechanics 04/2001; 25(5):435 - 472. · 1.06 Impact Factor