Optimization Method In Order Research Articles

Global optimization using a multipoint type quasi-chaotic optimization method

This paper proposes a new global optimization method called the multipoint type quasi-chaotic optimization method. In the proposed method, the simultaneous perturbation gradient approximation is introduced into a multipoint type chaotic optimization method in order to carry out optimization without gradient information. The multipoint type chaotic optimization method, which has been proposed recently, is a global optimization method for solving unconstrained optimization problems in which multiple search points which implement global searches driven by a chaotic gradient dynamic model are advected to their elite search points (best search points among the current search histories). The chaotic optimization method uses a gradient to drive search points. Hence, its application is restricted to a class of problems in which the gradient of the objective function can be computed. In this paper, the simultaneous perturbation gradient approximation is introduced into the multipoint type chaotic optimization method in order to approximate gradients so that the chaotic optimization method can be applied to a class of problems for which only the objective function values can be computed. Then, the effectiveness of the proposed method is confirmed through application to several unconstrained multi-peaked, noisy, or discontinuous optimization problems with 100 or more variables, comparing to other major meta-heuristics.

Identification of phosphorus emission hotspots in agricultural catchments

An enhanced transport-based management approach is presented, which is able to support cost-effective water quality management with respect to diffuse phosphorus pollution. Suspended solids and particulate phosphorus emissions and their transport were modeled in two hilly agricultural watersheds (Wulka River in Austria and Zala River in Hungary) with an improved version of the catchment-scale PhosFate model. Source and transmission areas were ranked by an optimization method in order to provide a priority list of the areas of economically efficient (optimal) management alternatives. The model was calibrated and validated at different gauges and for various years. The spatial distribution of the emissions shows that approximately one third of the catchment area is responsible for the majority of the emissions. However, only a few percent of the source areas can transport fluxes to the catchment outlet. These effective source areas, together with the main transmission areas are potential candidates for improved management practices. In accordance with the critical area concept, it was shown that intervention with better management practices on a properly selected small proportion of the total area (1–3%) is sufficient to reach a remarkable improvement in water quality. If soil nutrient management is also considered in addition to water quality, intervention on 4–12% of the catchment areas can fulfill both aspects.

Identification of the Jiles-Atherton Model Parameters Using Simulated Annealing Method

This paper presents a method and the experimental measurement system for the determination of Jiles-Atherton model parameters of the 30ZH120 electrical steel sheet. The paper utilizes Epstein Square devices to proceed with the experiment and measurement on a group of hysteresis loops of some certain transformers which use the 30ZH120 electrical steel sheet under two different lap ways. The approach relies on the simulated annealing optimization method in order to minimize the error between the measured and modeled hysteresis curves and yield the best five Jiles-Atherton model parameters. A convenient program, based on the Simulink platform, that can identify the J-A model parameters automatically from the experimental saturated hysteresis loop which is used to model the nonlinear characteristics of the electrical steel sheet, is developed. Research shows that the simulated annealing optimization method gets satisfactory results.

A Gradient-Less Shape Optimization for Elastic Contact Problems

A shape optimization method for solving elastic contact problems is proposed based on gradient-less idea(a zero order optimization method). It is found that the contact stress on the elastic contact surface can be smoothed and reduced effectively by both changing the contact surface shape and changing the shape of non-contact surface. To avoid mesh distortion that results in undesirable shape, a move stratrgy for nodal movement has been used in the finite element model. Two examples are presented to show the effectiveness of the proposed method in dealing with elastic contact problems.

Structure design and optimization of a new type of subsea pipeline connector

The basic configuration of a new type of subsea pipeline connector was proposed based on the press-fitting principle, and a parametric finite element model was created using APDL language in ANSYS. Combining the finite element model and optimization technology, the dimension optimization aiming at obtaining the minimum loading force and the optimum sealing performance was designed by the zero order optimization method. Experiments of the optimized connector were carried out. The results indicate that the optimum structural design significantly improved the indicators of the minimum loading force and sealing performance of the connector.

On optimal fourth-order iterative methods free from second derivative and their dynamics

In this paper new fourth order optimal root-finding methods for solving nonlinear equations are proposed. The classical Jarratt’s family of fourth-order methods are obtained as special cases. We then present results which describe the conjugacy classes and dynamics of the presented optimal method for complex polynomials of degree two and three. The basins of attraction of existing optimal methods and our method are presented and compared to illustrate their performance.

Structural Optimization Research on Girder of 200t Bridge Crane Based on ANSYS

According to the practical production of 200t bridge crane, the structure and operating conditions of the main girder were studied and the optimal mathematical model was established. Through determining the objective function and boundary constraint conditions, the finite element model was established based on ANSYS and the analysis results were obtained. Using the first order optimization method to optimize the calculating results and comparing with the initial sequence, it shows that the total volume of girder is decreased by about 19.4%. The structural optimization of the main girder gets a preferable economic benefit and provides a foundation for designing the bridge crane girder.

Optimum design of laminated composite plates under dynamic excitation

An integrated model for optimum weight design of symmetrically laminated composite plates subjected to dynamic excitation is presented in this work. Optimum design procedure based on flexibility and strength criteria is presented. The objective is to determine the optimum thicknesses of the laminate layers and its optimum orientations without exhibiting any failure according to Tsai-Wu failure criterion. The finite element method, based on Mindlin plate theory, is used in conjunction with an optimization method in order to determine the optimum design. Newmark algorithm, as an implicit time integration scheme, is used to discretize the time domain and calculate the transient response of the laminated composite plate. Exterior penalty method is exploited for the constrained minimization procedure. Fletcher–Powell algorithm is used for the unconstrained minimization process. To verify the capability and efficiency of the proposed model, three examples are solved. The examples deal with flexibility and stress constraints for different boundary conditions under various dynamic excitations.

궤도 차량용 MR 현수장치의 최적 설계

This paper presents optimal design of controllable magnetorheological suspension unit for a tracked vehicle. As a first step, a double-rod type MR suspension unit is designed on the basis of the Bingham model of commercially available MR fluid, and its damping characteristics are evaluated with respect to the intensity of the magnetic field. Subsequently, the governing equation of motion of the MR suspension system featuring the MR valve is established. Then, the optimization problem to find optimal geometric dimensions of the MR supension unit is formulated by considering an objective function which is related to damping torque and control energy. The first order optimization method intergrated with a commercial finite element method(FEM) software is adopted to obtain optimal solution of the system. The performance characteristics of the optimized MR susepnsion unit is then evaluated and compared with initial one.

Effect of loading and lamination parameters on the optimum design of laminated plates

This paper illustrates the effect of loading conditions and lamination parameters on the optimum design of the laminated composite plates. Optimum design procedure based on the flexibility criterion is presented in this paper. The objective is to determine the optimum thickness of the laminate layers and its optimum orientations without exhibiting any failure. The finite element method based on Mindlin plate theory is used in conjunction with an optimization method in order to determine the optimum design. Newmark implicit time integration scheme is used to discretize the time domain and calculate the transient response of the laminated plate. Exterior penalty method is exploited as a constrained minimization technique. For this purpose, four numerical examples are presented to figure out the effects of dynamic loading profile, boundary conditions, number of layers, and degree of orthotropy on the optimum weight design.

Two numerical methods for a Cauchy problem for modified Helmholtz equation

We consider a Cauchy problem for the modified Helmholtz equation. A conditional stability estimate is proved. Two order optimal regularization methods and error estimates are investigated. Numerical experiment shows that these methods work well.

Study of Parameters Optimization on Seismic Isolated Railway Bridges

Based on optimization theories, considering soil-structure interaction and running safety, the optimal design model of the seismic isolation system with lead-rubber bearings (LRB) for a simply supported railway beam bridge is established by using the first order optimization method in ANSYS, which the parameters of the isolation bearing are taken as design variables and the maximum moments at the bottom of bridge piers are taken as objective functions. The optimal calculations are carried out under the excitation of three practical earthquake waves respectively. The research results show that the ratio of the stiffness after yielding to the stiffness before yielding has important effect on the structural seismic responses. Through the optimal analysis of isolated bridge system, the optimal design parameters of isolation bearing can be determined properly, and the seismic forces can be reduced maximally as meeting with the limits of relative displacement between pier top and beam, which provides efficient paths and beneficial references for dynamic optimization design of seismic isolated bridges.

On the similarity of some three-point methods for solving nonlinear equations

In this short note we discuss certain similarities between some three-point methods for solving nonlinear equations. In particular, we show that the recent three-point method published in [R. Thukral, A new eighth-order iterative method for solving nonlinear equations, Appl. Math. Comput. 217 (2010) 222–229] is a special case of the family of three-point methods proposed previously in [R. Thukral, M.S. Petković, Family of three-point methods of optimal order for solving nonlinear equations, J. Comput. Appl. Math. 233 (2010) 2278–2284].

A family of two-point methods with memory for solving nonlinear equations

An efficient family of two-point derivative free methods with memory for solving nonlinear equations is presented. It is proved that the convergence order of the proposed family is increased from 4 to at least 2 + ?6 ? 4.45, 5, 1/2 (5 + ?33) ? 5.37 and 6, depending on the accelerating technique. The increase of convergence order is attained using a suitable accelerating technique by varying a free parameter in each iteration. The improvement of convergence rate is achieved without any additional function evaluations meaning that the proposed methods with memory are very efficient. Moreover, the presented methods are more efficient than all existing methods known in literature in the class of two-point methods and three-point methods of optimal order eight. Numerical examples and the comparison with the existing two-point methods are included to confirm theoretical results and high computational efficiency. 2010 Mathematics Subject Classification. 65H05

A Zero-Stable Optimal Order Method for Direct Solution of Second Order Differential Equations

Problem statement: In this study, a numerical method for direct solution of general second order differential equations was considered in order to circumvent the problems of computational burden and computer time wastage associated with method of reduction to system of first order equations. The issue of zero stability of higher order methods is considered in the development of the method. Approach: The method was developed based on collocation and interpolation approach using power series as the basis function to the solution of the problem. The basic properties of the method were considered. A consistent symmetric and zero stable main predictor of order five was also developed for the evaluation of the implicit scheme. The accuracy of the developed method is tested with test problems. Results: The method was zero-stable, consistent and normalized. The order of accuracy was found to be optimal. Both the main method and the predictor were obtained to be normalized and zero-stable. Conclusion/Recommendations: Comparison of the derived method with an existing method of the same order of accuracy showed a higher accuracy of the derived method. In the later research, this accuracy will be improved by developing the main predictor of the same order of accuracy with the main method.

Numerical solutions for optimal control of monodomain equations

AbstractWe present the numerical solutions of optimality systems corresponding to optimal control problems governed by the mono‐domain equations which are widely used for describing the electrical activity of the cardiac tissue. This mono‐domain model is based on a parabolic equation and a system of stiff ordinary differential equations. The space discretization of the state variables and dual variables is done using piecewise linear finite elements and the time discretization is based on linearly implicit Runge‐Kutta methods. The main goal of this work is to study the optimal control behavior of the electrical potentials under the influence of extracellular ionic currents as control variables. The numerical results presented are based on first and second order optimization methods. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A family of three-point methods of optimal order for solving nonlinear equations

A family of three-point iterative methods for solving nonlinear equations is constructed using a suitable parametric function and two arbitrary real parameters. It is proved that these methods have the convergence order eight requiring only four function evaluations per iteration. In this way it is demonstrated that the proposed class of methods supports the Kung–Traub hypothesis (1974) [3] on the upper bound 2 n of the order of multipoint methods based on n + 1 function evaluations. Consequently, this class of root solvers possesses very high computational efficiency. Numerical examples are included to demonstrate exceptional convergence speed with only few function evaluations.

Updating of a lumped model for an experimental web tension control system using a multivariable optimization method

The modelling and the control of web handling systems have been studied for a long time; correct modelling is necessary in order to design a better control system or to identify the plant parameters experimentally. On the web dynamics itself, lumped parameters expressions may be used to designate a web section between two adjacent drive rolls, and there is the necessity of incorporating the property of viscoelasticity to the web. In this paper the lumped model of a new web tension experimental system is updated; the model is based on the conservation mass, torque balance and viscoelasticity (Voigt approach). The experimental system consists of four sections each of which is driven by a servomotor; the speed and tension feedback, by using encoders and tension sensors, drives simultaneously the four servomotors through a real time C programmed D/A board. Usually, as described in the literature, these kinds of models are developed in the Laplace domain and the block scheme gives a graphical interpretation of the interaction between different sections. The transformation of the block scheme in a differential equation system in the time domain is fully described in this paper; it is not a simple step and it requires the introduction of not null initial condition for the derivative of physical variables. Moreover, the problem of validation has been dealt with in detail in this paper, considering simultaneously 2 different combinations of input data in open loop and a multivariable optimization method in order to estimate a certain number of unknown parameters. The results will show the accuracy of this kind of lumped parameters model for the complex experimental systems and useful information for successively designing an efficient control strategy.

CAD of RF Windows Using Multiobjective Particle Swarm Optimization

In this paper, computer-aided design (CAD) of two types of RF windows, namely, double-disk RF window and pillbox-type RF window, is presented for use in high-power microwave/millimeter-wave sources. The design of double-disk RF window was carried out for 42-GHz band (TE0,3 mode) and 170-GHz band (Gaussian mode), while the design of pillbox-type RF window was carried out for 2.856-GHz band. The requirement for the design of RF window is to minimize the reflections with exact matching at desired resonant frequency. In the present approach, a scattering-matrix code was invoked with recently developed particle swarm optimization (PSO) method in order to optimize the geometrical parameters of the window. Multiobjective optimizations using PSO have been used to achieve optimized tradeoff between matching of desired resonant frequency and minimizing the power reflections in the desired band of operation.

Optimal design of a magnetorheological fluid suspension for tracked vehicle

This paper presents optimal design of controllable magnetorheological suspension system (MRSS) for a tracked vehicle. As a first step, a double-rod type MRSS is designed on the basis of the Bingham model of commercially available MR fluid, and its damping characteristics are evaluated with respect to the intensity of the magnetic field. Subsequently, the governing equation of motion of the MRSS featuring the MR valve is established Then, the optimization problem to find optimal geometric dimensions of the MRSS is formulated by considering an objective function which is related to damping torque and control energy. The first order optimization method intergrated with a commercial finite element method(FEM) software is adopted to obtain optimal solution of the system. The performance characteristics of the optimized MRSS are then evaluated and compared with initial ones.