Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Partial spectral projected gradient method with active-set strategy for linearly constrained optimization

A method for linearly constrained optimization which modifies and generalizes recent box-constraint optimization algorithms is introduced. The new algorithm is based on a relaxed form of Spectral Projected Gradient iterations. Intercalated with these projected steps, internal iterations restricted to faces of the polytope are performed, which enhance the efficiency of the algorithm. Convergence proofs are given and numerical experiments are included and commented. Software supporting this paper is available through the Tango Project web page: http://www.ime.usp.br/similar to egbirgin/tango/.

A linear optimization approach to the combined production planning model

Two fundamental processes usually arise in the production planning of many industries. The first one consists of deciding how many final products of each type have to be produced in each period of a planning horizon, the well-known lot sizing problem. The other process consists of cutting raw materials in stock in order to produce smaller parts used in the assembly of final products, the well-studied cutting stock problem. In this paper the decision variables of these two problems are dependent of each other in order to obtain a global optimum solution. Setups that are typically present in lot sizing problems are relaxed together with integer frequencies of cutting patterns in the cutting problem. Therefore, a large scale linear optimizations problem arises, which is exactly solved by a column generated technique. It is worth noting that this new combined problem still takes the trade-off between storage costs (for final products and the parts) and trim losses (in the cutting process). We present some sets of computational tests, analyzed over three different scenarios. These results show that, by combining the problems and using an exact method, it is possible to obtain significant gains when compared to the usual industrial practice, which solve them in sequence. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Optimization of the physical refining of sunflower oil concerning the final contents of trans-fatty acids

The final contents of total and individual trans-fatty acids of sunflower oil, produced during the deacidification step of physical refining were obtained using a computational simulation program that considered cis-trans isomerization reaction features for oleic, linoleic, and linolenic acids attached to the glycerol part of triacylglycerols. The impact of process variables, such as temperature and liquid flow rate, and of equipment configuration parameters, such as liquid height, diameter, and number of stages, that influence the retention time of the oil in the equipment was analyzed using the response-surface methodology (RSM). The computational simulation and the RSM results were used in two different optimization methods, aiming to minimize final levels of total and individual trans-fatty acids (trans-FA), while keeping neutral oil loss and final oil acidity at low values. The main goal of this work was to indicate that computational simulation, based on a careful modeling of the reaction system, combined with optimization could be an important tool for indicating better processing conditions in industrial physical refining plants of vegetable oils, concerning trans-FA formation.

Elaboration and optimization of (Y,Er)Al(3)(BO(3))(4) glassy planar waveguides through the sol-gel process

In this work, a sol-gel route was used to prepare Y(0.9)Er(0.1)Al(3)(BO(3))(4) glassy thin films by spin-coating technique looking for the preparation and optimization of planar waveguides for integrated optics. The films were deposited on silica and silicon substrates using stable sols synthesized by the sol-gel process. Deposits with thicknesses ranging between 520 and 720 nm were prepared by a multi-layer process involving heat treatments at different temperatures from glass transition to the film crystallization and using heating rates of 2 degrees C/min. The structural characterization of the layers was performed by using grazing incidence X-ray diffraction and Raman spectroscopy as a function of the heat treatment. Microstructural evolution in terms of annealing temperatures was followed by high resolution scanning electron microscopy and atomic force microscopy. Optical transmission spectra were used to determine the refractive index and the film thicknesses through the envelope method. The optical and guiding properties of the films were studied by m-line spectroscopy. The best films were monomode with 620 nm thickness and a refractive index around 1.664 at 980 nm wavelength. They showed good waveguiding properties with high light-coupling efficiency and low propagation loss at 632.8 and 1550 nm of about 0.88 dB/cm. (C) 2009 Elsevier B.V. All rights reserved.

Synthesis optimization, structural evolution and optical properties of Y(0.9)Er(0.1)Al(3)(BO(3))(4) nanopowders obtained by soft chemistry methods

This paper describes the structural evolution of Y(0.9)Er(0.1)Al(3)(BO(3))(4) nanopowders using two soft chemistry routes, the sol-gel and the polymeric precursor methods. Differential scanning calorimetry, differential thermal analyses, thermogravimetric analyses, X-ray diffraction, Fourier-transform infrared, and Raman spectroscopy techniques have been used to study the chemical reactions between 700 and 1200 degrees C temperature range. From both methods the Y(0.9)Er(0.1)Al(3)(BO(3))(4) (Er:YAB) solid solution was obtained almost pure when the powdered samples were heat treated at 1150 degrees C. Based on the results, a schematic phase formation diagram of Er:YAB crystalline solid solution was proposed for powders from each method. The Er:YAB solid solution could be optimized by adding a small amount of boron oxide in excess to the Er:YAB nominal composition. The nanoparticles are obtained around 210 nm. Photoluminescence emission spectrum of the Er:YAB nanocrystalline powders was measured on the infrared region and the Stark components of the (4)I(13/2) and (4)I(15/2) levels were determined. Finally, for the first time the Raman spectrum of Y(0.9)Er(0.1)Al(3)(BO(3))(4) crystalline phase is also presented. (C) 2008 Elsevier Masson SAS. All rights reserved.

Continuous GRASP with a local active-set method for bound-constrained global optimization

Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic-based on the CGRASP and GENCAN methods-for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP-GENCAN on a set of benchmark multimodal test functions.

Second-order negative-curvature methods for box-constrained and general constrained optimization

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Convergence proofs under weak constraint qualifications are given. Numerical examples showing that the new method converges to second-order stationary points in situations in which first-order methods fail are exhibited.

Outer Trust-Region Method for Constrained Optimization

Given an algorithm A for solving some mathematical problem based on the iterative solution of simpler subproblems, an outer trust-region (OTR) modification of A is the result of adding a trust-region constraint to each subproblem. The trust-region size is adaptively updated according to the behavior of crucial variables. The new subproblems should not be more complex than the original ones, and the convergence properties of the OTR algorithm should be the same as those of Algorithm A. In the present work, the OTR approach is exploited in connection with the ""greediness phenomenon"" of nonlinear programming. Convergence results for an OTR version of an augmented Lagrangian method for nonconvex constrained optimization are proved, and numerical experiments are presented.

U-curve: A branch-and-bound optimization algorithm for U-shaped cost functions on Boolean lattices applied to the feature selection problem

This paper presents the formulation of a combinatorial optimization problem with the following characteristics: (i) the search space is the power set of a finite set structured as a Boolean lattice; (ii) the cost function forms a U-shaped curve when applied to any lattice chain. This formulation applies for feature selection in the context of pattern recognition. The known approaches for this problem are branch-and-bound algorithms and heuristics that explore partially the search space. Branch-and-bound algorithms are equivalent to the full search, while heuristics are not. This paper presents a branch-and-bound algorithm that differs from the others known by exploring the lattice structure and the U-shaped chain curves of the search space. The main contribution of this paper is the architecture of this algorithm that is based on the representation and exploration of the search space by new lattice properties proven here. Several experiments, with well known public data, indicate the superiority of the proposed method to the sequential floating forward selection (SFFS), which is a popular heuristic that gives good results in very short computational time. In all experiments, the proposed method got better or equal results in similar or even smaller computational time. (C) 2009 Elsevier Ltd. All rights reserved.

Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.

Molecular analysis of maltotriose active transport and fermentation by Saccharomyces cerevisiae reveals a determinant role for the AGT1 permease

Incomplete and/or sluggish maltotriose fermentation causes both quality and economic problems in the ale-brewing industry. Although it has been proposed previously that the sugar uptake must be responsible for these undesirable phenotypes, there have been conflicting reports on whether all the known alpha-glucoside transporters in Saccharomyces cerevisiae (MALx1, AGT1, and MPH2 and MPH3 transporters) allow efficient maltotriose utilization by yeast cells. We characterized the kinetics of yeast cell growth, sugar consumption, and ethanol production during maltose or maltotriose utilization by several S. cerevisiae yeast strains (both MAL constitutive and AM inducible) and by their isogenic counterparts with specific deletions of the AGT1 gene. Our results clearly showed that yeast strains carrying functional permeases encoded by the MAL21, MAL31, and/or MAL41 gene in their plasma membranes were unable to utilize maltotriose. While both high-and low-affinity transport activities were responsible for maltose uptake from the medium, in the case of maltotriose, the only low-affinity (K-m, 36 +/- 2 mM) transport activity was mediated by the AGT1 permease. In conclusion, the AGT1 transporter is required for efficient maltotriose fermentation by S. cerevisiae yeasts, highlighting the importance of this permease for breeding and/or selection programs aimed at improving sluggish maltotriose fermentations.

Optimization of the ultrasound-assisted synthesis of allyl 1-naphthyl ether using response surface methodology

Allyl 1-naphthyl ethers are useful compounds for different purposes, but reported methods to synthesize them require long reaction times. In this work, we have obtained allyl 1-naphthyl ether in good yield using ultrasonic-assisted methodology in a 1-h reaction. A central composite design was used to obtain a statistical model and a response surface (p < 0.05; R(2) = 0.970; R(adj)(2) = 0.949; R(pred)(2) = 0.818) that can predict the optimal conditions to maximize the yield, validated experimentally. (C) 2010 Elsevier B.V. All rights reserved.

Optimization of incubation time of protein Tc85 in the construction of biosensor: Is the EIS a good tool?

Electrochemical impedance spectroscopy (EIS) in pH 6.9 phosphate buffer solution was used to investigate each step of the procedure employed to modify a screen-printed electrode (SPE). The SPE was modified with self-assembled monolayers (SAMs) of cystamine (CYS, deposited from 20 mM solution), followed by glutaraldehyde (GA, 0.3 M solution). The Trypanosoma cruzi antigen was immobilized using different deposition times. The influence of incubation time (2-18 h) of protein was also investigated. The topography of modified electrode with this protein was investigated by atomic force microscopy (AFM). Interpretation of impedance data was based on physical and chemical adsorption, and degradation of the layer at high and meddle frequencies, and charge transfer reaction involving mainly the reduction of oxygen at low frequencies. EIS studies on modified electrodes with Tc85 protein immobilized for different incubation times indicated that the optimum incubation time was 6-8 h. It was demonstrated that EIS is a good technique to evaluate the different steps and the integrity of the surface modifications, and to optimize the incubation time of protein in the development of biosensors. (C) 2010 Elsevier B.V. All rights reserved.

Synthesis Optimization of Hydroxymethylnitrofurazone, an Antichagasic Candidate, Using 3(2) Factorial Design

Hydroxymethylnitrofurazone presents in vitro activity against Trypanosoma cruzi. The optimization of the synthesis of this compound was performed through a 3(2) factorial statistical design. Quadratic model produced the best response surface predicting a maximum yield (82%) close to the center design point with a seven hours reaction and a 1:1.5 (NF:K(2)CO(3)) ratio.