Number Of Objective Function Evaluations Research Articles

Circuit performance optimization and model fitting based on simulated annealing

An efficient new method, based on the coupling between an enhanced simulated annealing algorithm and the SPICE-PAC ‘open’ circuit simulator, is proposed for minimizing objective functions describing circuit performance optimization problems or component model fitting to experimental data. To keep the number of objective function evaluations and CPU times to the lowest possible level, we focus our attention on two features: first, we build an original partitioning technique for splitting large n-dimensional problems; then we carefully study variables discretization, (which is necessary for applying the simulated annealing method to continuous problems). To illustrate the efficiency of our method, we show how to determine the 40 MOS transistor model parameters, through fitting the model to experimental data.

A Fibonacci search technique for model parameter selection

A sequential Fibonacci search technique that includes an objective function sensitivity criterion is used to optimise model parameter selection within a specified search interval. The technique can reduce by about half the number of objective function evaluations that is required by the standard Fibonacci search and includes an automatic parameter range selection. The present technique is ideally suited to complex and nonlinear ecological models for which many parameter sets may fit the data provided the modelling aim is to predict the system's response to external stimuli rather than to determine precisely the optimal values of the individual parameters. Sample applications are given for two nonlinear hydrological models, one with a fairly smooth system output profile and the other with a highly irregular output profile. A test case is also given involving a simple analytical model for in vitro dissolution of uranium in lung fluid.

The Gauss optimization method for problems with general nonlinear constraints

A new algorithm is presented for finding the minimum of a nonnegative objective function subject to general nonlinear constraints. This algorithm, based of Gauss’ method for unconstrained problems, is developed as an extension to the Gauss constrained technique for linear constraints. The derivation of the algorithm, using a Lagrange multiplier approach, is based on the Kuhn-Tucker conditions so that, when the iteration process terminates, these conditions are automatically satisfied. A feasible design is maintained throughout the iteration process. The solution of preliminary examples indicate excellent results in terms of the number of objective function evaluations required by the algorithm to obtain an optimal design.

TESTING THE EFFICIENCY OF ALGORITHMS AND STRATEGIES FOR AUTOMATIC CALIBRATION OF RAINFALL-RUNOFF MODELS / Essais de l'efficacité des algorithms et des stratégies pour l'étalonnage des modèles pluie-écoulement

Abstract This paper examines the efficiency of various methods of calibrating a rainfall-runoff model. The model used is a 12 parameter version of the Boughton model which has been developed for large tropical basins. Attempts were made to improve the efficiency of calibration in three areas: selection of the best nonlinear programming algorithms; reduction of the number of objective functions required for calibration; and simplification of the model structure. The best algorithms were found to be those of Powell, Rosenbrock, and the simplex method of Nelder and Mead. The Davidon method did not perform well. The number of objective function evaluations can be reduced by performing a sensitivity analysis on the model and selecting a small group of parameters which are not interdependent and which the objective function is sensitive to. This may yield a substantial reduction in the computer time required to calibrate the model. Simplification of the model structure can also yield substantial savings, especi...

Application of the Complex Method for Constrained Optimization to Oilfield Problems

Abstract In the application of optimization techniques, considerable difficulty is often encountered in determining the most applicable or effective method for solving a particular problem. In an attempt to solve this dilemma, M. J. Box developed the Complex Method, which can be used in solving a broad spectrum of problems. The method is a multivariable, direct-search technique that is efficient and convenient in optimizing problems with nonlinear objective functions subject to inequality constraints on explicit or implicit variables. This method has been applied successfully to many problems in the chemical industry; however, the applicability of this method for solving oilfield problems apparently has not been recognized. In this paper, two oilfield problems, a push-pull steam stimulation process problems, a push-pull steam stimulation process and a well-drilling schedule, were optimized using the Complex Method. The results were compared with those obtained by other optimization techniques reported in the literature. For both problems, the Complex Method was as efficient as other methods and probably was more efficient in obtaining the global optimum, both in terms of the number of objective-function evaluations required and of computing time. The solution to the constrained push-pull steam stimulation process was obtained push-pull steam stimulation process was obtained in one-fourth the number of evaluations required with the Hooke and Jeeves search technique; the solution to the drilling problem with 48 variables was obtained in only 2,123 objective-function evaluations, or 29 seconds of computing time on an IBM 370/165. Through the solution of two problems, the Complex Method was demonstrated to be easily applied and effective in obtaining optimum solutions as compared with other methods. This method should be implemented easily in obtaining optimum solutions as compared with other methods. This method should be implemented easily in obtaining optimum solutions to other oilfield problems. Introduction In recent years, the application of optimization techniques to oilfield problems has become widespread because of the possibility of increased profits or reduced costs with implementation of such studies. Several types of oilfield problems have been optimized using a wide variety of optimization techniques. E. L. Dougherty conducted an extensive review of the major applications of optimization techniques to oilfield problems. in these studies, the authors used a variety problems. in these studies, the authors used a variety of optimization techniques because of the difficulty of selecting an effective method for a particular problem. The Complex Method is a general optimization technique that can be applied directly to a variety of nonlinear problems with inequality constraints. The method is a problems with inequality constraints. The method is a multivariable direct-search technique; thus, the application of this method is especially convenient when derivatives of the objective function are difficult to obtain. The broad applicability of the Complex Method has been demonstrated in the chemical industry by successfully optimizing problems ranging from absorber-strippers to nonisothermal polymerization reactors. The method is implemented easily and is efficient in obtaining the global optimum while imposing inequality constraints on explicit and implicit variables. The objective of this paper is to demonstrate the usefulness and effectiveness of the Complex Method in obtaining the optimum values for oilfield problems, as compared with other methods. Two oilfield problems that previously have been solved by other methods were optimized using the Complex Method. The sample problems were the following:the optimum cycle length and the amount of steam injected in successive cycles are determined for a push-pull steam stimulation process such that the cumulative discounted net income is maximized; andthe optimum set of rotary speeds and weights on a bit is determined such that the drilling cost per foot is minimized in a drilling operation. These problems were selected to illustrate the wide range of mathematical formulations for which the Complex Method is applicable. The variable weight-speed schedule was selected for optimization rather than the constant weight-speed schedule because of the complexity of the variable weight-speed problem. SPEJ p. 123

Multivariable monotonic optimization over multivalued logics and rectangular design lattices

A minimum dichotomous direct search procedure is given for finding the optimum combination of N variables, each having M( n) possible values, when a certain monotonicity condition is satisfied. The least upper bound on the number of objective function evaluations is 1 + Σ N n=1 Q( n), where Q( n) is defined by 2 Q( n)-1 < M( n) < 2 Q( n) , whereas the total number of possibilities is Π N R=1 M( n). An example shows where the procedure applies to restricted problems in multivalued logic and engineering design.