基于动态度的回溯算法求解大值域约束满足问题

针对一个具有精确可满足性相变现象的大值域随机约束满足问题,提出了两种启发式动态回溯算法,即基于动态度的ddeg-MAC（dynamic degree-maintaining arc consistency）回溯算法和基于值域与动态度比值的dom/ddeg-MAC（dom/dynamic degree-maintaining arc consistency）回溯算法。这两种算法分别基于ddeg和dom/ddeg挑选变量,利用维持弧相容（MAC）技术为挑选的变量进行赋值。当赋值无法进行时,再执行动态回溯修正变量的赋值。数值实验结果表明：在控制参数非常接近理论相变点时,算法仍然能够有效地找到问题的解。与经典回溯算法相比,这两种启发式动态回溯算法具有显著的优越性。     

Evolutionary structural optimization for stress minimization problems by discrete thickness design

Stress minimization is a major aspect of structural optimization in a wide range of engineering designs. This paper presents a new evolutionary criterion for the problems of variable thickness design whilst minimizing the maximum stress in a structure. On the basis of finite element analysis, a stress sensitivity number is derived to estimate the stress change in an element due to varying the thickness of other elements. Following the evolutionary optimization procedure, an optimal design with a minimum maximum stress is achieved by gradually removing material from those elements, which have the lowest stress sensitivity number or adding material onto those elements, which have the highest stress sensitivity number. The numerical examples presented in this paper demonstrate the capacity of the proposed method for solving stress minimization problems. The results based on the stress criterion are compared with traditional ones based on a stiffness criterion, and an optimization scheme based on the combination of both the stress minimization and the stiffness maximization criteria is presented.     

一种求解多阶段多目标优化问题的算法

为了高效地求解"最优路由"、"Web Service及网格资源调度"等多阶段、多目标优化组合问题,提出结合AHP(Analytic Hierarchy Process)方法和遗传算法的求解算法,可以高效地完成多阶段的优化组合以及合理地确定多目标中各目标权重,实验结果表明了算法的有效性。     

Fully discrete potential-based finite element methods for a transient eddy current problem

Fully discrete potential-based finite element methods called methods are used to solve a transient eddy current problem in a three-dimensional convex bounded polyhedron. Using methods, fully discrete coupled and decoupled numerical schemes are developed. The existence and uniqueness of solutions for these schemes together with the energy-norm error estimates are provided. To verify the validity of both schemes, some computer simulations are performed for the model from TEAM Workshop Problem 7. This work was supported by Postech BSRI Research Fund-2009, National Basic Research Program of China (2008CB425701), NSFC under the grant 10671025 and the Key Project of Chinese Ministry of Education (No. 107018).     

Finite element approximation of nonlinear transient magnetic problems involving periodic potential drop excitations

This paper deals with the computation of nonlinear 2D transient magnetic fields when the data concerning the electric current sources involve potential drop excitations. In the first part, a mathematical model is stated, which is solved by an implicit time discretization scheme combined with a finite element method for space approximation. The second part focuses on developing a numerical method to compute periodic solutions by determining a suitable initial current which avoids large simulations to reach the steady state. This numerical method leads to solve a nonlinear system of equations which requires to approximate several nonlinear and linear magnetostatic problems. The proposed methods are first validated with an axisymmetric example and sinusoidal source having an analytical solution. Then, we show the saving in computational effort that this methodology offers to approximate practical problems specially with pulse-width modulation (PWM) voltage supply.     

Multilevel projection algorithm for solving obstacle problems

Obstacle problems are nonlinear free boundary problems and the computation of approximate solutions can be difficult and expensive. Little work has been done on effective numerical methods of such problems. This paper addresses some aspects of this issue. Discretizing the problem in a continuous piecewise linear finite element space gives a quadratic programming problem with inequality constraints. A new method, called the multilevel projection (MP) method, is established in this paper. The MP algorithm extends the multigrid method for linear equations to nonlinear obstacle problems. The convergence theorems of this method are also proved. A numerical example presented shows our error estimate is sharp and the MP algorithm is robust.     

An efficient algorithm to solve the small sample size problem for LDA

In this paper, we present an efficient algorithm to solve the most discriminant vectors of LDA for high-dimensional data set. The experiments on ORL face database confirm the effectiveness of the proposed method.     

Topology optimization for transient wave propagation problems in one dimension

Structures exhibiting band gap properties, i.e., having frequency ranges for which the structure attenuates propagating waves, have applications in damping of acoustic and elastic wave propagation and in optical communication. A topology optimization method for synthesis of such structures, employing a time domain formulation, is developed. The method is extended to synthesis of pulse converting structures with possible applications in optical communication.     

An approximation to solve regression problems with a genetic fuzzy rule ordinal algorithm

Regression problems try estimating a continuous variable from a number of characteristics or predictors. Several proposals have been made for regression models based on the use of fuzzy rules; however, all these proposals make use of rule models in which the irrelevance of the input variables in relation to the variable to be approximated is not taken into account. Regression problems share with the ordinal classification the existence of an explicit relationship of order between the values of the variable to be predicted. In a recent paper, the authors have proposed an ordinal classification algorithm that takes into account the detection of the irrelevance of input variables. This algorithm extracts a set of fuzzy rules from an example set, using as the basic model a sequential covering strategy along with a genetic algorithm. In this paper, a proposal for a regression algorithm based on this ordinal classification algorithm is presented. The proposed model can be interpreted as a multiclassifier and multilevel system that learns at each stage using the knowledge gained in previous stages. Due to similarities between regression and ordinal problems as well as the use of a set of ordinal algorithms, an error interval can be returned with the regression output value. Experimental results show the good behavior of the proposal as well as the results of the error interval.     

THERMIC: a 2-D finite-element tool to solve conductive and advective heat transfer problems in Earth Sciences

We present a C-language program, THERMIC, that solves the 2-dimensional (pseudo 3D for axi-symmetric cases) conductive and advective heat-transfer equation. THERMIC uses a finite-element method that takes into account realistic geometries, heterogeneous material properties and various boundary and initial conditions. As it also allows for latent heat (heat production due to crystallisation) and for thermal properties, such as thermal conductivity, to be dependent on temperature, it is particularly suited to heat transfer problems encountered in the Earth Sciences. We present sample applications from the various problems already treated by THERMIC (cooling of magma chambers and dykes, the study of a granitic magma ascent or of pore water flow in sedimentary basins).Successfully tested on SUN® and SGI® UNIX workstations and on Microsoft Windows 95®, 98® and NT® 4.0 system based PCs, the THERMIC package can be downloaded from the web (THERMIC home page: http://www.ipgp.jussieu.fr/UFP/thermic/html/Thermic_home.html) and contains source files, makefiles and environment files as well as executable files for both systems and an html directory with help and example files.     

An integrated approach to solving mechanical problems on parallel computers

Possibilities of a programming environment that integrates the specificity of the different types of parallel computers are presented in the framework of computational structural mechanics. An extension of the development environment of the Finite Element code CASTEM 2000 has been realized to offer the user a global vision on all objects of the parallel application. To facilitate the implementation of parallel applications, this system hides data transfers between processors and allows a direct reuse of modules of the original sequential code. It is an object-based shared virtual memory system which allows a parallelism by data distribution (for non-structured data) or by control distribution; it is therefore well suited to “mechanic” parallelism. To validate this programming environment, domain decomposition techniques well suited to parallel computation have been used.     

A stable time advancing scheme for solving fluid-structure interaction problem at small structural displacements

A semi-implicit time advancing scheme for transient fluid-structure interaction problem is presented. At every time step, a least squares problem is solved by partitioned procedures, such that the continuity of the velocity as well as the continuity of the stress hold at the interface. During the iterative method for solving the optimization problem, the fluid mesh does not move, which reduces the computational effort. The stability of the algorithm is derived. The numerical results presented in this paper show that the computed solution is similar to the one obtained by the implicit algorithm, but the computational time is reduced.     

Efficient iterative solvers for structural dynamics problems

Direct solvers are commonly used in implicit finite element codes for structural dynamics problems. This study explores an alternative approach to solving the resulting linear systems by using preconditioned iterative schemes such as the preconditioned conjugate gradient algorithm and its variants. Preconditioners used in this study include approximate Cholesky factorization, block Jacobi, and the symmetric Gauss-Seidel over-relaxation scheme. The effects of various preconditioners and ordering schemes on the solution time and required storage are investigated. Performance results of these iterative solver are compared against the MA57 direct solver routine of the commercial Harwell Software Library.     

Hybrid numerical methods to solve shallow water equations for hurricane induced storm surge modeling

In this paper an efficient numerical method based on hybrid finite element and finite volume techniques to solve hurricane induced storm surge flow problem is presented. A segregated implicit projection method is used to solve the 2D shallow water equations on staggered unstructured meshes. The governing equations are written in non-conservation form. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centered finite volume method. The nonlinear wave equation is solved by the node-based Galerkin finite element method. This staggered-mesh scheme is distinct from other conventional approaches in that the velocity components and auxiliary variables are stored at cell centers and vertices, respectively. The present model uses an implicit method, which is very efficient and can use a large time step without losing accuracy and stability.The hurricane induced wind stress and pressure, bottom friction, Coriolis effect, and tidal forcing conditions are implemented in this model. The levee overtopping option is implemented in the model as well. Hurricane Katrina (2005) storm surge has been simulated to demonstrate the robustness and applicability of the model.     

An efficient method for solving elliptic boundary element problems with application to the tokamak vacuum problem

A method for regularizing ill-posed Neumann Poisson-type problems based on applying operator transformations is presented. This method can be implemented in the context of the finite element method to compute the solution to inhomogeneous Neumann boundary conditions; it allows to overcome cases where the Neumann problem otherwise admits an infinite number of solutions. As a test application, we solve the Grad–Shafranov boundary problem in a toroidally symmetric geometry. Solving the regularized Neumann response problem is found to be several orders of magnitudes more efficient than solving the Dirichlet problem, which makes the approach competitive with the boundary element method without the need to derive a Green function. In the context of the boundary element method, the operator transformation technique can also be applied to obtain the response of the Grad–Shafranov equation from the toroidal Laplace n=1 response matrix using a simple matrix transformation.     

A parallel finite element procedure for contact-impact problems

An efficient parallel finite element procedure for contact-impact problems is presented within the framework of explicit finite element analysis with thepenalty method. The procedure concerned includes a parallel Belytschko-Lin-Tsay shell element generation algorithm and a parallel contact-impact algorithm based on the master-slave slideline algorithm. An element-wise domain decomposition strategy and a communication minimization strategy are featured to achieve almost perfect load balancing among processors and to show scalability of the parallel performance. Throughout this work, a prototype code, named GT-PARADYN, is developed on the IBM SP2 to implement the procedure presented, under message-passing paradigm. Some examples are provided to demonstrate the timing results of the algorithms, discussing the accuracy and efficiency of the code.     

An efficient hybrid genetic algorithm to solve assembly line balancing problem with sequence-dependent setup times

In this paper the setup assembly line balancing and scheduling problem (SUALBSP) is considered. Since this problem is NP-hard, a hybrid genetic algorithm (GA) is proposed to solve the problem. This problem involves assigning the tasks to the stations and scheduling them inside each station. A simple permutation is used to determine the sequence of tasks. To determine the assignment of tasks to stations, the algorithm is hybridized using a dynamic programming procedure. Using dynamic programming, at any time a chromosome can be converted to an optimal solution (subject to the chromosome sequence).     

Analytical derivatives technology for structural shape design

The ability to perform and evaluate the effect of shape changes on the stress and modal responses of components is an important ingredient in the “design” of aircraft engine components. The classical design of experiments (DOE)-based approach that is motivated from statistics (for physical experiments) is one of the possible approaches for the evaluation of the component response with respect to design parameters [Myers, Montgomery. Response surface methodology, process and product optimization using design of experiments. John Wiley and Sons, NY (1995)]. As the underlying physical model used for the component response is deterministic and understood through a computer simulation model, one needs to re-think the use of the classical DOE techniques for this class of problems. In this paper, we explore an alternate sensitivity-analysis-based technique where a deterministic parametric response is constructed using exact derivatives of the complex finite-element (FE)-based computer models to design parameters. The method is based on a discrete sensitivity analysis formulation using semi-automatic differentiation (Griewank, SIAM (2000), ADIFOR, Automatic Differentiation of FORTRAN codes ) to compute the Taylor series or its Pade equivalent for finite-element-based responses. Shape design or optimization in the context of finite element modeling is challenging because the evaluation of the response for different shape requires the need for a meshing consistent with the new geometry. This paper examines the differences in the nature and performance (accuracy and efficiency) of the analytical derivatives approach against other existing approaches with validation on several benchmark structural applications. The use of analytical derivatives for parametric analysis is demonstrated to have accuracy benefits on certain classes of shape applications.     

A note on a linear time algorithm for constructing adjacency graphs of 3D FEA data

In this paper, we present an algorithm for constructing adjacency graphs of 3D finite element analysis (FEA) data. Adjacency graphs are created to represent the connectivities of FEA data cells. They are used in most visualization methods for FEA data. We stress that in many engineering applications FEA data sets do not contain the adjacency information. This is opposite to computer-aided geometric design where, e.g., the winged edge geometrical representation is usually generated and utilized. By establishing intermediate data structures and using bin-sorting, we developed an efficient algorithm for constructing such graphs. The total time complexity of the algorithm is linear in the number of data cells.