Unconstrained Optimization Procedure Research Articles

Electric train energy consumption modeling

The paper develops an electric train energy consumption modeling framework considering instantaneous regenerative braking efficiency in support of a rail simulation system. The model is calibrated with data from Portland, Oregon using an unconstrained non-linear optimization procedure, and validated using data from Chicago, Illinois by comparing model predictions against the National Transit Database (NTD) estimates. The results demonstrate that regenerative braking efficiency varies as an exponential function of the deceleration level, rather than an average constant as assumed in previous studies. The model predictions are demonstrated to be consistent with the NTD estimates, producing a predicted error of 1.87% and −2.31%. The paper demonstrates that energy recovery reduces the overall power consumption by 20% for the tested Chicago route. Furthermore, the paper demonstrates that the proposed modeling approach is able to capture energy consumption differences associated with train, route and operational parameters, and thus is applicable for project-level analysis. The model can be easily implemented in traffic simulation software, used in smartphone applications and eco-transit programs given its fast execution time and easy integration in complex frameworks.

Optimizing the geometrical accuracy of curvilinear meshes

This paper presents a method to generate valid high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a linear mesh, that is subsequently curved without taking care of the validity of the high order elements. An optimization procedure is then used to both untangle invalid elements and optimize the geometrical accuracy of the mesh. Standard measures of the distance between curves are considered to evaluate the geometrical accuracy in planar two-dimensional meshes, but they prove computationally too costly for optimization purposes. A fast estimate of the geometrical accuracy, based on Taylor expansions of the curves, is introduced. An unconstrained optimization procedure based on this estimate is shown to yield significant improvements in the geometrical accuracy of high order meshes, as measured by the standard Haudorff distance between the geometrical model and the mesh. Several examples illustrate the beneficial impact of this method on CFD solutions, with a particular role of the enhanced mesh boundary smoothness.

Morphologic, structural, and optical characterization of sol‐gel derived TiO2 thin films for memristive devices

AbstractSol‐gel derived TiO2 thin films were prepared by spin‐ coating from an alcoholic solution of titanium isopropoxide. With the aim to develop titania layers suitable for memristive devices, the films were deposited onto test structures based on fused silica quartz substrates patterned with a Ti (5nm)/Pt (50nm) layer. The reported fabrication protocol is suitable for the development of a memristive device. Optical, structural, and morphological features of the samples were investigated with complementary techniques, such as scanning electron microscopy (SEM), prism coupling m‐line and micro‐Raman spectroscopy as well as transmittance and profilometry measurements. The quality of the surface of the obtained films was evaluated by SEM technique, and the morphology of samples deposited with different fabrication protocols was investigated. Additionally, a computer code for the refractive index and thickness estimation from the transmittance spectra was developed by unconstrained optimization procedure. The results of simulation were in good agreement with the experimental data obtained by m‐line measurements. Moreover, the porosity of a specific set of test unannealed films has been estimated. TiO2 films exhibit thickness of tens of nm, and micro‐Raman spectroscopy in conjunction with SEM indicate the presence of anatase phase after thermal annealing at 400 °C. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Optimizing the Geometrical Accuracy of 2D Curvilinear Meshes

This paper presents a method to generate valid 2D high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a straight sided mesh. High order points are initially snapped to the real geometry without taking care of the validity of the high order elements. An optimization procedure that both allow to untangle invalid elements and to optimize the geometrical accuracy of the mesh is presented. An area based distance is proposed to compute the geometrical discrepancy between the mesh and its underlying geometry. This area based distance is shown to be strongly related to standard distance measures such as the Hausdorff distance, while being largely faster to compute.The new distance is minimized through an unconstrained optimization procedure, allowing significant improvements of the geometrical accuracy of high order meshes. A simple computational example shows that geometrically optimized meshes allow smooth CFD solutions.

LOUDSPEAKER ARRAY DESIGN

Sound signals to be output from a loudspeaker array are modified by a plurality of filters designed according to an unconstrained optimization procedure to improve overall performance (e.g., power, directivity) of the loudspeaker array. More particularly, respective filters are configured to receive a signal to be output to a plurality of loudspeakers. Upon receiving the signal, the respective filters individually modify the received signal according to the results of the unconstrained optimization procedure and then output the individually modified signals to respective loudspeakers. The unconstrained optimization procedure takes into account manufacturing tolerances and individually enhances the signal output to each of a plurality of individual loudspeakers within an array to achieve an overall improvement in performance. In one example, a speaker system utilizes the unconstrained optimization procedure to enable a user to hear an output sound clearly, while adjacent people experience the output sound at lower volume, if at all.

Mathematical modeling and numerical analysis of the growth of non-O157 Shiga toxin-producing Escherichia coli in spinach leaves

This study was conducted to investigate the growth of non-O157 Shiga toxin-producing Escherichia coli (STEC) in spinach leaves and to develop kinetic models to describe the bacterial growth. Six serogroups of non-O157 STEC, including O26, O45, O103, O111, O121, and O145, were used in the growth studies conducted isothermally at 4, 8, 15, 20, 25, 30, and 35°C. Both STEC and background microflora were enumerated to develop kinetic models. Growth of STEC in spinach leaves was observed at elevated temperatures (15–35°C), but not at 4 and 8°C.This study considered the dynamic interactions between the STEC cells and the background microflora. A modified Lotka–Volterra and logistic equation was used to simulate the bacterial growth. In combination with an unconstrained optimization procedure, the differential growth equations were solved numerically to evaluate the dynamic interactions between the STEC cells and the background microflora, and to determine the kinetic parameters by fitting each growth curve to the growth equations. A close agreement between the experimental growth curves and the numerical analysis results was obtained.The analytical results showed that the growth of STEC in spinach leaves was unhindered when the population was low, but the growth was suppressed by the background microflora as the STEC population approached the maximum population density. The effect of temperature on the growth of both STEC and background microflora was also evaluated. Secondary models, evaluating the effect of temperature on growth rates, were also developed. The estimated apparent minimum growth temperature for STEC was 11°C in commercial spinach leaves. The methodology and results of this study can be used to examine the dynamic interactions and growth between different bacteria in foods, and to conduct risk assessments of STEC in spinach leaves.

Analysis of Laminar Flow in a Channel with One Porous Bounding Wall

Computer extended series solution is used to analyse the problem of laminar flow in a channel with one porous bounding wall. The objective is to study the effect of non-zero tangential slip velocity on the velocity field, pressure gradient and mass transfer. The problem is also studied using power series method in conjunction with an unconstrained optimization procedure. The domain and rate of convergence of the series so generated are further increased by Pade’ approximants. The coupled diffusion equation in the boundary layer is solved using a finite difference scheme. The solution presented here is valid for much larger Reynolds number compared with earlier investigation.

A validation and verification tool for global optimization solvers

Linearly constrained optimization models based on a systems description often possess multiple local optima. Therefore, there are a broad variety of problems in which the property of unique solution cannot be simply postulate or verified. The aim of global optimization (GO) is to find the best possible solution of multi-extremal problems. This paper illustrates the applicability of GO modeling techniques and solution strategies to real-world problems. In this paper we propose an enumeration approach for solving the linearly constrained optimization problem with continuous but general objective function. The method uses a parametric but unconstrained representation of the problem in terms of the vertices (and the extreme rays) of the feasible region. The unconstrained problem is then solved by the classical unconstrained continuous optimization procedure. Our aim is to propose a new introduction to optimization, the design of a general solution algorithm that is easy for the user to understand and provides useful information such as global bounding of the objective function. For illustrative and comparative purposes, the algorithm and its applications are presented in the context of applied problems solved by other solution algorithms.

Layup Optimization for Buckling of Laminated Composite Shells with Restricted Layer Angles

The layup optimization for maximizing buckling loads of long laminated composite cylindrical shells subjected to combinations of axial compression, external lateral pressure, and torsion is carried out on the basis of Flugge's theory. The layer angles, that is, fiber orientation angles, of the laminated composite cylindrical shells are restricted to the values of 0, 45, -45, and 90 deg, and then nine lamination parameters are used as design variables for the layup optimization. Explicit expressions relating the nine lamination parameters are derived and used to describe the feasible region in the design space of lamination parameters. Thus, the layup optimization problem becomes a constrained nonlinear optimization problem, and the optimum lamination parameters are determined by a mathematical programming method. The laminate configurations aiming to realize the optimum lamination parameters are obtained by analytic formulas or by an unconstrained optimization procedure. It is observed that, for the laminated composite cylindrical shells with the layer angles restricted to the values of 0, 45, -45, and 90 deg, the optimum buckling loads are less than 10% lower than the optimum buckling loads obtained for unrestricted laminate configurations.

Combining Routing and Buffer Allocation Problems in Series-Parallel Queueing Networks

Given a series-parallel queueing network topology with exponential servers of finite capacity, a systematic design methodology is presented that approximately solves the optimal routing and buffer space allocation problems within the network. The multi-objective stochastic nonlinear programming problem in integer variables is described and a two-stage iterative optimization procedure is presented which interconnects the routing and buffer space allocation problems. The algorithmic procedure couples the Expansion method, a decomposition method for computing performance measures in queueing networks with finite capacity, along with Powell's unconstrained optimization procedure which allocates the buffers and a multi-variable search procedure for determining the routing probabilities. The effectiveness and efficiency of the resulting two-stage design methodology is tested and evaluated in a series of experimental designs along with simulations of the network topologies.

From linear to non-linear optimization: the missing chapter

Linear global optimization is the task of finding the absolute set of decision variables to optimize a given continuous function. In general, there might be several local optimal solutions and global solutions. Consequently, global optimization problems such as non-convex cases are quite difficult to solve exactly. This paper proposes an enumeration approach for solving the linearly constrained optimization problem with continuous but general objective function. This method uses a parametric but unconstrained representation of the problem in terms of the vertices (and the extreme rays) of the feasible region. The unconstrained problem is then solved by the classical unconstrained continuous optimization procedure. The aim is to propose a new introduction to optimization, the design of a general solution algorithm that is easy for the user to understand and provides useful information such as global bounding of the objective function. For illustrative and comparative purposes, the algorithm and its applications are presented in the context of numerical problems solved by other methods.

Dirichlet series solution of equations arising in boundary layer theory

The differential equation F′'' + AFF′'+ BF′ 2 = 0, where A and B are arbitrary constants subject to different types of boundary conditions, is considered. This class of equations frequently occurs in boundary-layer theory. The proposed Dirichlet series method, in conjunction with an unconstrained optimization procedure, is found useful in analyzing these problems. The series so generated is analyzed using Euler transformation and Padé approximants.

Design of insensitive multirate aircraft control using optimized eigenstructure assignment

This paper presents a new method for the design of constant-gain controllers for digital aircraft systems monitored and updated at multiple frequencies. It addresses two main problems associated with such a scheme: the adverse effects of intersample cross coupling and the high-amplitude control signals that normally result from a multirate feedback structure. An examination of the problem indicates that the two objectives present conflicting design criteria. Thus, a solution must seek to achieve an acceptable compromise between the minimization of control effort and the assignment of a prescribed modal structure. An unconstrained numerical optimization procedure, based on eigenstructur e assignment using full-state feedback, has been developed to provide for this compromise. A suitable choice of weighting factors, introduced into the scalar cost function defined for the optimization, allows for the computation of two alternative control laws. They differ only in the emphasis placed on the two conflicting design objectives. The lateral motion of a light aircraft is the test system employed to illustrate the application of the method. The controllers are evaluated using a fully nonlinear simulation of the aircraft. The results fully demonstrate the eigeninsensitivity of the multirate feedback solution and the flexibility offered by the eigenstructure-assignment optimization approach in both cases.

Parallel-vector computation for linear structural analysis and non-linear unconstrained optimization problems

Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve, is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14–16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for non-linear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on non-linear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.

Generalized non-linear elastic inversion with constraints in model and data spaces

SUMMARY Seismic data are non-linearly related to model parameters such as seismic velocities. However, seismic inversion is usually considered in a linear approximation. Such techniques as the Born inversion were recently applied to seismic data. Non-linear inversion is more complicated and involves extensive calculations. Non-linear inversion was developed in the frame work of an unconstrained optimization procedure. It uses as a priori information an initial model and probability distribution functions in the data and model spaces (This a priori information is called ‘soft’ bounds). In this paper, we propose a new technique for solving a constrained non-linear inversion. This technique will allow us to use a priori information not only in terms of ‘soft’ bounds, but ‘hard’ bounds as well (usually giving more stable and accurate solutions). Non-linear inversion is considered as an iterative procedure which involves a dual transform at each iteration. A dual transform allows for considering the problem in terms of the Lagrangian multipliers. The number of Lagrangian multipliers is equal to the number of available data and thus, significantly reduces the dimension of the problem (this is true for underdetermined problems only). However, the most important property of the dual transform is that it allows us to consider a constrained problem as an unconstrained problem. Another important property is that proper constraints incorporate small-wave numbers in the generalized inversion. It is shown that conventional (unconstrained non-linear inversion) is a special case of the constrained non-linear inversion developed in this paper if the truncation operator is represented by the identity matrix.

Buffer Space Allocation in Automated Assembly Lines

Automated assembly lines are modeled as finite open queueing networks and a heuristic for buffer space allocation within these lines is presented. The Expansion Method, an analytical technique for modeling finite open queueing networks and Powell's unconstrained optimization procedure are integrated in a design methodology, which evaluates alternative line topologies, system throughputs, and their optimal buffer sizes. The resulting design methodology is demonstrated for series, merging and splitting topologies of automated assembly lines with balanced and unbalanced service rates.

ESR determination of lipid translational diffusion coefficients at low spin-label concentrations in biological membranes, using exchange broadening, exchange narrowing, and dipole-dipole interactions

Spin-spin interactions between phosphatidylcholine nitroxide spin labels in fluid-phase dimyristoyl phosphatidylcholine bilayers have been studied in the concentration range 0.1–2.0 mol%. The total line broadening has been separated into its Gaussian and Lorentzian components. The Gaussian linewidth exhibits exchange narrowing of the unresolved proton hyperfine structure, with an approximate quadratic concentration dependence for the square of the linewidth, over this spin-label concentration range. The Lorentzian linewidth has a linear dependence on the spin-label concentration over the same range. The temperature dependence of the gradient of the Lorentzian broadening with respect to spin-label concentration is biphasic over the range 30–80°C, indicating a dominant contribution from magnetic dipole-dipole broadening at the lower temperatures. The contributions from the dipole-dipole and exchange interactions to the Lorentzian broadening have been separated by fitting the temperature dependence using an unconstrained optimization procedure and assuming a single effective activation energy for both diffusion-controlled processes. The lipid lateral diffusion coefficient has been determined from the concentration dependence of both the exchange broadening of the nitrogen hyperfine structure and the exchange narrowing of the proton hyperfine structure using a two-dimensional lattice diffusion model, and also from the concentration dependence of the dipole-dipole interaction using a three-dimensional Fick's law diffusion model. All three methods yield consistent values for the diffusion coefficient, although because of the approximate nature of some of the theoretical models the exchange broadening is expected to give the most reliable results. An experimental protocol for determining the actual spin concentration in the membrane sample is also presented.

Free volume model for lipid lateral diffusion coefficients. Assessment of the temperature dependence in phosphatidylcholine and phosphatidylethanolamine bilayers

The lipid lateral diffusion coefficients, D T, in fluid-phase phosphatidylcholine and phosphatidylethanolamine bilayers have been analysed in terms of the free-volume diffusion model by fitting the expression: D T = ATexp[- B/ T- T O to the observed temperature dependence, where A, B and T o are the parameters to be optimized. Application of an unconstrained optimization procedure to data obtained from excimer formation (Galla et al (1979) J. Membrane Biol. 48, 215–236) and from fluorescence photobleaching (Vaz et al. (1985) Biochemistry 24, 781–786) provides statistical evidence for a free-volume model as opposed to a simple Stokes-Einstein model ( T o = 0), only in certain cases. In the instances for which the parameter T o can be determined with a reasonable degree of accuracy, it is found that this characteristics temperature at which the free volume extrapolates to zero lies below the bilayer gel-to-fluid phase transition temperature and does not coincide with the pre-transition temperature for phosphatidylcholines.

Theory of inhomogeneous quantum systems. IV. Variational calculations of metal surfaces.

We present results of variational calculations for the jellium model of metal surfaces. The ground-state wave function is represented by a product of local one- and two-body functions and a model Slater function. The correlation functions and the single-particle orbitals entering the Slater determinant are calculated by an unconstrained optimization procedure. Results for the surface energy and the work function are somewhat higher than previously published values.

Some aspects of placement optimization of thermal significant components in thick film high-power hybrid integrated circuits

A fast method for calculation of the temperature map in thick film, high-power hybrid IC's is presented. Based upon the method, a way of automatic placement of the elements which decide the reliability of the circuit is put forward. This approach ensures the minimum failure rate of the IC using the modified unconstrained Powell's static optimization procedure in cooperation with the penalty function shifting method. The presented approach is an improvement and development of methods described earlier. The proposed procedure is very fast, as well as being a very efficient one, as illustrated by the computation examples included. At the end of the paper the conclusions from implementation of the method for computer-aided hybrid IC design are presented.