Home About us Contact
|
Home About us Contact | ||
|
|
||
Simplex Method (simplex + method)
Selected AbstractsOptimization routine for identification of model parameters in soil plasticityINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2001Hans Mattsson 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. [source] Optimization of Rosmarinic Acid Production by Lavandula vera MM Plant Cell Suspension in a Laboratory BioreactorBIOTECHNOLOGY PROGRESS, Issue 2 2005Atanas I. Pavlov The all-round effect of dissolved oxygen concentration, agitation speed, and temperature on the rosmarinic acid production by Lavandula veraMM cell suspension was studied in a 3-L laboratory bioreactor by means of the modified Simplex method. Polynomial regression models were elaborated for description of the process of rosmarinic acid production (Y) in the bioreactor as a consequence of the variation of the dissolved oxygen (X1) concentration between 10% and 50%; agitation (X2) between 100 and 400 rpm; and temperature (X3) between 22 and 30 °C. The optimization made it possible to establish the optimal conditions for the biosynthesis of rosmarinic acid by L. veraMM: dissolved oxygen (X1*), 50% of air saturation; agitation (X2*), 400 rpm; and temperature (X3*), 29.9 °C, where maximal yield (Ymax) of 3489.4 mg/L of rosmarinic acid was achieved (2 times higher compared with the shake-flasks cultivation). [source] Note on the determination of the ignition point in forest fires propagation using a control algorithmINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2008M. Bergmann Abstract This paper is devoted to the determination of the origin point in forest fires propagation using a control algorithm. The forest fires propagation are mathematically modelled starting from a reaction diffusion model. A volume of fluid (V.O.F.) formulation is also used to determine the fraction of the area which is burnt. After having developed the objective functional and its derivative, results from an optimization process based on the simplex method is presented. It is shown that the ignition point and the final time of the fire propagation are precisely recovered, even for a realistic, non-horizontal, terrain. Copyright © 2007 John Wiley & Sons, Ltd. [source] Utilisation de la méthode du cubic simplex pour l'optimisation de la formulation a froid d'une emulsion de thioglycolate de calciumINTERNATIONAL JOURNAL OF COSMETIC SCIENCE, Issue 5 2003N. Moulai-Mostefa Synopsis The aim of this work relates to the optimization of a cold formulation of a depilatory emulsion containing thioglycolate of calcium, which presents the same characteristics as a reference product. To lead to this objective, a cubic simplex method was used. A preliminary formulation was preformed to evaluate the influence of each factor on the process formulation. The depilatory creams carried out present a rheological behaviour described by the model of Hershell,Bulkely, whose parameters are considered as responses of the optimizing system. This strategy allows both reducing and optimizing the number of experiments. The rheological measurements and the tests of stability showed that the use of an emulsifying polymer led to obtain a stable depilatory cream with a good effectiveness at a strong pH value. Résumé L'objectif principal de ce travail concerne l'optimisation de la formulation à froid d'une émulsion dépilatoire à base de thioglycolate de calcium, présentant les mêmes caractéristiques qu'un produit de référence. Pour aboutir à cet objectif, on a utilisé la méthode du cubic simplex. L'étude de préformulation a permis d'évaluer avec précision l'influence des différents facteurs sur le processus de formulation. Les crèmes dépilatoires réalisées présentent un comportement rhéologique décrit par le modèle de Hershell,Bulkley dont les deux paramètres sont considérés comme réponses du système à optimiser. Les plans d'expériences utilisés ont permis de restreindre le nombre d'essais à réaliser. Les résultats expérimentaux de l'analyse rhéologique et les tests de stabilité ont montré que l'utilisation d'un polymère émulsifiant conduit à l'obtention d'une crème dépilatoire stable possédant une bonne efficacité aux fortes valeurs du pH. [source] Parameter optimization for a PEMFC model with a hybrid genetic algorithmINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 8 2006Zhi-Jun Mo Abstract Many steady-state models of polymer electrolyte membrane fuel cells (PEMFC) have been developed and published in recent years. However, models which are easy to be solved and feasible for engineering applications are few. Moreover, rarely the methods for parameter optimization of PEMFC stack models were discussed. In this paper, an electrochemical-based fuel cell model suitable for engineering optimization is presented. Parameters of this PEMFC model are determined and optimized by means of a niche hybrid genetic algorithm (HGA) by using stack output-voltage, stack demand current, anode pressure and cathode pressure as input,output data. This genetic algorithm is a modified method for global optimization. It provides a new architecture of hybrid algorithms, which organically merges the niche techniques and Nelder,Mead's simplex method into genetic algorithms (GAs). Calculation results of this PEMFC model with optimized parameters agreed with experimental data well and show that this model can be used for the study on the PEMFC steady-state performance, is broader in applicability than the earlier steady-state models. HGA is an effective and reliable technique for optimizing the model parameters of PEMFC stack. Copyright © 2005 John Wiley & Sons, Ltd. [source] Derivative Free Optimization in Higher DimensionINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 3 2001Shamsuddin Ahmed Non-linear optimizations that do not require explicit or implicit derivative information of an objective function are an alternate search strategy when the derivative of the objective function is not available. In factorial design, the number of trials for experimental identification method in Em is about (m+ 1). These (m+ 1) equally spaced points are allowed to form a geometry that is known as regular simplex. The simplex method is attributed to Spendley, Hext and Himsworth. The method is improved by maintaining a set of (m+ 1) points in m dimensional space to generate a non-regular simplex. This study suggests re-scaling the simplex in higher dimensions for a restart phase. The direction of search is also changed when the simplex degenerates. The performance of this derivative free search method is measured based on the number of function evaluations, number of restart attempts and improvements in function value. An algorithm that describes the improved method is presented and compared with the Nelder and Mead simplex method. The performance of this algorithm is also tested with artificial neural network (ANN) problem. The numbers of function evaluations are about 40 times less with the improved method against the Nelder and Mead (1965) method to train an ANN problem with 36 variables. [source] A scenario-based stochastic programming model for water supplies from the highland lakesINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 3 2000D.W. Watkins Jr Abstract A scenario-based, multistage stochastic programming model is developed for the management of the Highland Lakes by the Lower Colorado River Authority (LCRA) in Central Texas. The model explicitly considers two objectives: (1) maximize the expected revenue from the sale of interruptible water while reliably maintaining firm water supply, and (2) maximize recreational benefits. Input data can be represented by a scenario tree, built empirically from a segment of the historical flow record. Thirty-scenario instances of the model are solved using both a primal simplex method and Benders decomposition, and results show that the first-stage (,here and now') decision of how much interruptible water to contract for the coming year is highly dependent on the initial (current) reservoir storage levels. Sensitivity analysis indicates that model results can be improved by using a scenario generation technique which better preserves the serial correlation of flows. Ultimately, it is hoped that use of the model will improve the LCRA's operational practices by helping to identify flexible policies that appropriately hedge against unfavorable inflow scenarios. [source] Modeling of Slurry Polymerization of Ethylene Using a Soluble Cp2ZrCl2/MAO Catalytic SystemMACROMOLECULAR THEORY AND SIMULATIONS, Issue 5 2007Mostafa Ahmadi Abstract The slurry homopolymerization of ethylene catalyzed by a Cp2ZrCl2/MAO catalytic system was studied. A simple kinetic model including initiation, propagation, transfer to monomer and cocatalyst, spontaneous transfer and spontaneous deactivation was developed to predict dynamic yield of polymerization and molecular weight of final products. Kinetic constants were estimated by numerical solution of polymerization kinetic model, combined with Nelder-Mead simplex method. The model predicts that the propagation reaction has the lower activation energy in relation to chain transfer reactions which leads to decrease of molecular weight at elevated temperatures. The initiation reaction has however, the highest activation energy that results in raising the peak of reaction rate at higher temperatures. [source] On,off minimum-time control with limited fuel usage: near global optima via linear programmingOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2006Brian J. Driessen Abstract A method for finding a global optimum to the on,off minimum-time control problem with limited fuel usage is presented. Each control can take on only three possible values: maximum, zero, or minimum. The simplex method for linear systems naturally yields nearly such a solution for the re-formulation presented herein because the simplex method always produces an extreme point solution to the linear program. Numerical examples for the benchmark linear flexible system are presented. Copyright © 2006 John Wiley & Sons, Ltd. [source] The Random-Facet simplex algorithm on combinatorial cubes,RANDOM STRUCTURES AND ALGORITHMS, Issue 3 2002Bernd Gärtner The RANDOM -FACET algorithm is a randomized variant of the simplex method which is known to solve any linear program with n variables and m constraints using an expected number of pivot steps which is subexponential in both n and m. This is the theoretically fastest simplex algorithm known to date if m , n; it provably beats most of the classical deterministic variants which require exp(,(n)) pivot steps in the worst case. RANDOM -FACET has independently been discovered and analyzed ten years ago by Kalai as a variant of the primal simplex method, and by Matous,ek, Sharir, and Welzl in a dual form. The essential ideas and results connected to RANDOM -FACET can be presented in a particularly simple and instructive way for the case of linear programs over combinatorialn - cubes. I derive an explicit upper bound of (1) on the expected number of pivot steps in this case, using a new technique of "fingerprinting" pivot steps. This bound also holds for generalized linear programs, similar flavors of which have been introduced and studied by several researchers. I then review an interesting class of generalized linear programs, due to Matous,ek, showing that RANDOM -FACET may indeed require an expected number of pivot steps in the worst case. The main new result of the paper is a proof that all actual linear programs in Matous,ek's class are solved by RANDOM -FACET with an expected polynomial number of pivot steps. This proof exploits a combinatorial property of linear programming which has only recently been discovered by Holt and Klee. The result establishes the first scenario in which an algorithm that works for generalized linear programs "recognizes" proper linear programs. Thus, despite Matous,ek's worst-case result, the question remains open whether RANDOM -FACET (or any other simplex variant) is a polynomial-time algorithm for linear programming. Finally, I briefly discuss extensions of the combinatorial cube results to the general case. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 20:353,381, 2002 [source] | ||||||||||