RDS-NSGA-II: a memetic algorithm for reference point based multi-objective optimization

Reference point based optimization offers tools for the effective treatment of preference based multi-objective optimization problems, e.g. when the decision-maker has a rough idea about the target objective values. For the numerical solution of such problems, specialized evolutionary strategies have become popular, despite their possible slow convergence rates. Hybridizing such evolutionary algorithms with local search techniques have been shown to produce faster and more reliable algorithms. In this article, the directed search (DS) method is adapted to the context of reference point optimization problems, making this variant, called RDS, a well-suited option for integration into evolutionary algorithms. Numerical results on academic test problems with up to five objectives demonstrate the benefit of the novel hybrid (i.e. the same approximation quality can be obtained more efficiently by the new algorithm), using the state-of-the-art algorithm R-NSGA-II for this coupling. This represents an advantage when treating costly-to-evaluate real-world engineering design problems.     

Numerical inversion of the Laplace–Carson transform applied to homogenization of randomly reinforced linear viscoelastic media

Homogenization of linear viscoelastic materials is possible using the viscoelastic correspondence principle (VCP) and homogenization solutions obtained for linear elastic materials. The VCP involves a Laplace–Carson Transform (LCT) of the material phases constitutive theories and in most cases, the time domain solution must be obtained through numerical inversion of the LCT. The objective of this paper is to develop and test numerical algorithms to invert LCT which are encountered in the context of homogenization of linear viscoelastic materials. The homogenized properties, as well as the stress concentration and strain localization tensors, are considered. The algorithms suggested have the following two key features: (1) an acceptance criterion which allows to reject solutions of unacceptable accuracy and (2) some algorithms lead to solutions for the homogenized properties where the thermodynamics restrictions imposed on linear viscoelastic materials are encountered. These two features are an improvement over the previous algorithms. The algorithms are tested on many examples and the accuracy of the inversion is excellent in most cases.     

Finite element formulation of viscoelastic sandwich beams using fractional derivative operators

This paper presents a finite element formulation for transient dynamic analysis of sandwich beams with embedded viscoelastic material using fractional derivative constitutive equations. The sandwich configuration is composed of a viscoelastic core (based on Timoshenko theory) sandwiched between elastic faces (based on Euler–Bernoulli assumptions). The viscoelastic model used to describe the behavior of the core is a four-parameter fractional derivative model. Concerning the parameter identification, a strategy to estimate the fractional order of the time derivative and the relaxation time is outlined. Curve-fitting aspects are focused, showing a good agreement with experimental data. In order to implement the viscoelastic model into the finite element formulation, the Grünwald definition of the fractional operator is employed. To solve the equation of motion, a direct time integration method based on the implicit Newmark scheme is used. One of the particularities of the proposed algorithm lies in the storage of displacement history only, reducing considerably the numerical efforts related to the non-locality of fractional operators. After validations, numerical applications are presented in order to analyze truncation effects (fading memory phenomena) and solution convergence aspects.     

Weakly singular stress‐BEM for 2D elastostatics

A weakly singular stress‐BEM is presented in which the linear state regularizing field is extended over the entire surface. The algorithm employs standard conforming C⁰ elements with Lagrangian interpolations and exclusively uses Gaussian integration without any transformation of the integrands other than the usual mapping into the intrinsic space. The linear state stress‐BIE on which the algorithm is based has no free term so that the BEM treatment of external corners requires no special consideration other than to admit traction discontinuities. The self‐regularizing nature of the Somigliana stress identity is demonstrated to produce a very simple and effective method for computing stresses which gives excellent numerical results for all points in the body including boundary points and interior points which may be arbitrarily close to a boundary. A key observation is the relation between BIE density functions and successful interpolation orders. Numerical results for two dimensions show that the use of quartic interpolations is required for algorithms employing regularization over an entire surface to show comparable accuracy to algorithms using local regularization and quadratic interpolations. Additionally, the numerical results show that there is no general correlation between discontinuities in elemental displacement gradients and solution accuracy either in terms of unknown boundary data or interior solutions near element junctions. Copyright © 1999 John Wiley & Sons, Ltd.     

Generalized viscoelastic model for creep analysis coupled with plastic deformation

A creep analysis capability, using a generalized viscoelastic model, is introduced to process the creep behaviour coupled with elastoplastic deformation. The formulation is based on the step-by-step time integration of the Kelvin-Maxwell rheological model with non-constant parameters. The concept of a rheological model is extended to the multiaxial stresses by the Prandtl-Reuss stress-strain relationship, from which the tangential stiffness matrix is formed for Newton's iteration. If the plastic deformation is coupled with creep, the algorithm will seek a solution in two distinct steps. Various choices of empirical creep laws are available and small variations in temperature are allowed as implemented in the general purpose finite element analysis program.     

A new hybrid imperialist competitive algorithm on data clustering

Clustering is a process for partitioning datasets. This technique is very useful for optimum solution. k-means is one of the simplest and the most famous methods that is based on square error criterion. This algorithm depends on initial states and converges to local optima. Some recent researches show that k-means algorithm has been successfully applied to combinatorial optimization problems for clustering. In this paper, we purpose a novel algorithm that is based on combining two algorithms of clustering; k-means and Modify Imperialist Competitive Algorithm. It is named hybrid K-MICA. In addition, we use a method called modified expectation maximization (EM) to determine number of clusters. The experimented results show that the new method carries out better results than the ACO, PSO, Simulated Annealing (SA), Genetic Algorithm (GA), Tabu Search (TS), Honey Bee Mating Optimization (HBMO) and k-means.     

FINITE ELEMENT ALGORITHMS FOR DYNAMIC SIMULATIONS OF VISCOELASTIC COMPOSITE SHELL STRUCTURES USING CONJUGATED GRADIENT METHOD ON COARSE GRAINED AND MASSIVELY PARALLEL MACHINES

Recently much attention has been paid to high-performance computing and the development of parallel computational strategies and numerical algorithms for large-scale problems. In this present study, a finite element procedure for the dynamic analyses of anisotropic viscoelastic composite shell structures by using degenerated 3-D elements has been studied on vector and coarse grained and massively parallel machines. CRAY hardware performance monitors such as Flowtrace and Perftrace tools are used to obtain performance data for subroutine program modules and specified code segments. The performances of conjugated gradient method, the Cray sparse matrix solver and the Feable solver are evaluated. SIMD and MIMD parallel implementation of the finite element algorithm for dynamic simulation of viscoelastic composite structures on the CM-5 is also presented. The performance studies have been conducted in order to evaluate efficiency of the numerical algorithm on this architecture versus vector processing CRAY systems. Parametric studies on the CM-5 as well as the CRAY system and benchmarks for various problem sizes are shown. The second study is to evaluate how effectively the finite element procedures for viscoelastic composite structures can be solved in the Single Instruction Multiple Data (SIMD) parallel environment. CM-FORTRAN is used. A conjugate gradient method is employed for the solution of systems. In the third study, we propose to implement the finite element algorithm in a scalable distributed parallel environment using a generic message passing library such as PVM. The code is portable to a range of current and future parallel machines. We also introduced the domain decomposition scheme to reduce the communication time. The parallel scalability of the dynamic viscoelastic finite element algorithm in data parallel and scalable distributed parallel environments is also discussed. © 1997 by John Wiley & Sons, Ltd.     

A time‐integration method for the viscoelastic–viscoplastic analyses of polymers and finite element implementation

The present study introduces a time‐integration algorithm for solving a non‐linear viscoelastic–viscoplastic (VE–VP) constitutive equation of isotropic polymers. The material parameters in the constitutive models are stress dependent. The algorithm is derived based on an implicit time‐integration method (Computational Inelasticity. Springer: New York, 1998) within a general displacement‐based finite element (FE) analysis and suitable for small deformation gradient problems. Schapery's integral model is used for the VE responses, while the VP component follows the Perzyna model having an overstress function. A recursive‐iterative method (Int. J. Numer. Meth. Engng 2004; 59 :25–45) is employed and modified to solve the VE–VP constitutive equation. An iterative procedure with predictor–corrector steps is added to the recursive integration method. A residual vector is defined for the incremental total strain and the magnitude of the incremental VP strain. A consistent tangent stiffness matrix, as previously discussed in Ju (J. Eng. Mech. 1990; 116 :1764–1779) and Simo and Hughes (Computational Inelasticity. Springer: New York, 1998), is also formulated to improve convergence and avoid divergence. Available experimental data on time‐dependent and inelastic responses of high‐density polyethylene are used to verify the current numerical algorithm. The time‐integration scheme is examined in terms of its computational efficiency and accuracy. Numerical FE analyses of microstructural responses of polyethylene reinforced with elastic particle are also presented. Copyright © 2009 John Wiley & Sons, Ltd.     

Enhancing particle swarm optimization algorithm using two new strategies for optimizing design of truss structures

This work develops an augmented particle swarm optimization (AugPSO) algorithm using two new strategies,: boundary-shifting and particle-position-resetting. The purpose of the algorithm is to optimize the design of truss structures. Inspired by a heuristic, the boundary-shifting approach forces particles to move to the boundary between feasible and infeasible regions in order to increase the convergence rate in searching. The purpose of the particle-position-resetting approach, motivated by mutation scheme in genetic algorithms (GAs), is to increase the diversity of particles and to prevent the solution of particles from falling into local minima. The performance of the AugPSO algorithm was tested on four benchmark truss design problems involving 10, 25, 72 and 120 bars. The convergence rates and final solutions achieved were compared among the simple PSO, the PSO with passive congregation (PSOPC) and the AugPSO algorithms. The numerical results indicate that the new AugPSO algorithm outperforms the simple PSO and PSOPC algorithms. The AugPSO achieved a new and superior optimal solution to the 120-bar truss design problem. Numerical analyses showed that the AugPSO algorithm is more robust than the PSO and PSOPC algorithms.     

求解约束优化问题的退火遗传算法

针对基于罚函数遗传算法求解实际约束优化问题的困难与缺点,提出了求解约束优化问题的退火遗传算法。对种群中的个体定义了不可行度,并设计退火遗传选择操作。算法分三阶段进行,首先用退火算法搜索产生初始种群体,随后利用遗传算法使搜索逐渐收敛于可行的全局最优解或较优解,最后用退火优化算法对解进行局部优化。两个典型的仿真例子计算结果证明该算法能极大地提高计算稳定性和精度。     

A Direct Data-Cluster Analysis Method Based on Neutrosophic Set Implication

Raw data are classified using clustering techniques in a reasonable manner to create disjoint clusters. A lot of clustering algorithms based on specific parameters have been proposed to access a high volume of datasets. This paper focuses on cluster analysis based on neutrosophic set implication, i.e., a k-means algorithm with a threshold-based clustering technique. This algorithm addresses the shortcomings of the k-means clustering algorithm by overcoming the limitations of the threshold-based clustering algorithm. To evaluate the validity of the proposed method, several validity measures and validity indices are applied to the Iris dataset (from the University of California, Irvine, Machine Learning Repository) along with k-means and threshold-based clustering algorithms. The proposed method results in more segregated datasets with compacted clusters, thus achieving higher validity indices. The method also eliminates the limitations of threshold-based clustering algorithm and validates measures and respective indices along with k-means and thresholdbased clustering algorithms.     

Registration of motion-distorted interlaced images captured by a scanning vector imaging sensor

We present an algorithm to realign images distorted by motion and vibrations captured in cameras that use a scanning vector sensor with an interlaced scheme. In particular, the method is developed for images captured by a staggered time delay and integration camera distorted by motion. The algorithm improves the motion-distorted image by adjusting its fields irrespective of the type of motion that occurs during the exposure. The algorithm performs two tasks: estimation of the field relative motion during the exposure by a normal least-squares estimation technique and improvement of the degraded image from such motion distortion. The algorithm uses matrix computations; therefore it has a computation advantage over algorithms based on the technique of searching for a match. The algorithm is successfully demonstrated on both simulated and real images.     

Implicit–explicit time integration DRBEM for generalized magneto-thermoelasticity problems of rotating anisotropic viscoelastic functionally graded solids

A numerical computer model based on the dual reciprocity boundary element method (DRBEM) is extended to study the generalized theories of magneto-thermoelasticity problems in a rotating anisotropic viscoelastic functionally graded solid placed in a constant primary magnetic field acting in the direction of the z-axis and rotating about this axis with a constant angular velocity. In the case of plane deformation, a predictor–corrector implicit–explicit time integration algorithm was developed and implemented for use with the DRBEM to obtain the solution for the displacement and temperature fields in the context of the Green and Naghdi theory of type III. A comparison of the results is presented graphically in the absence and presence of magnetic field. Numerical results that demonstrate the validity of the proposed method are also presented graphically.     

Weighting parameters for time‐step integration algorithms with predetermined coefficients

In this paper, the effect of using the predetermined coefficients in constructing time‐step integration algorithms is investigated. Both first‐ and second‐order equations are considered. The approximate solution is assumed to be in a form of polynomial in the time domain. It can be related to the truncated Taylor's series expansion of the exact solution. Therefore, some of the coefficients can be predetermined from the known initial conditions. If there are m predetermined coefficients and r unknown coefficients in the approximate solution, the unknowns can be solved by the weighted residual method. The weighting parameter method is used to investigate the resultant algorithm characteristics. It is shown that the formulation is consistent with a minimum order of accuracy m+r. The maximum order of accuracy achievable is m+2r. Unconditionally stable algorithms exist if m⩽r for first‐order equations and m+1⩽r for second‐order equations. Hence, the Dahlquist's theorem is generalized. Algorithms equivalent to the Padé approximations and unconditionally stable algorithms equivalent to the generalized Padé approximations are constructed. The corresponding weighting parameters and weighting functions for the Padé and generalized Padé approximations are given explicitly. Copyright © 2000 John Wiley & Sons, Ltd.     

Dynamic stability of a viscoelastic cylindrical panel with concentrated masses

We discuss the problem of the dynamic stability of a viscoelastic cylindrical panel with concentrated masses in a geometrically nonlinear formulation that is based on the Kirchhoff-Love hypothesis. The effect of the action of concentrated masses is introduced into the equation of motion of a cylindrical panel using the Dirac δ-function. The problem is solved by the Bubnov-Galerkin method based on a polynomial approximation of deflections together with a numerical method based on the use of quadrature formulas. The choice of the Koltunov-Rzhanitsyn singular kernel is justified. Comparisons between the results obtained from different theories are presented. The Bubnov-Galerkin method convergence is investigated for all problems. The effect of the material viscoelastic properties and concentrated masses on the process of the dynamic stability of a cylindrical panel is shown. __________ Translated from Problemy Prochnosti, No. 4, pp. 132–147, July–August, 2008.     

Performance measures of a make-to-orderinventory-production system

This paper develops two algorithms for computing the average total cost per product and other performance measures for a make-to-order inventory-production system. The two algorithms are developed by using matrix analytic methods. The first algorithm is based on the matrix-geometric solution of the Quasi-Birth-and-Death (QBD) Markov process. The second algorithm is based on the fundamental period of the QBD Markov process. The advantages and disadvantages of the two algorithms are discussed     

基于分数导数模型的粘弹性桩振动分析

研究成果表明混凝土桩具有粘弹性性质,为了准确分析粘弹性桩的振动特性,必须建立准确的本构模型。在分数导数理论、粘弹性理论、应力波理论基础上建立了基于分数导数模型的粘弹性桩的振动方程,利用Zhang-Shimizu分数导数数值积分法得到基于分数导数模型的粘弹性桩的振动方程数值解。分析结果表明分数导数微分算子的阶数和粘弹比对粘弹性桩桩端速度衰减的快慢和衰减周期等有很大的影响。     

Efficient techniques for predicting viscoelastic behavior of sublaminates

Even for linear elastic behavior, stress analysis of thick laminated composites can be very computation intensive if every lamina is modeled discretely. In such cases, modeling of individual lamina is impractical and the homogenization method for sublaminates becomes essential. In the current work, 3D homogenization formulas for an elastic sublaminate, which were derived by the authors in previous work, were utilized to determine the 3D effective properties for a viscoelastic sublaminate. The properties were determined by three methods that exploited the 3D elastic homogenization formulas: (i) quasi-elastic method, (ii) correspondence principle, and (iii) direct time integration of the incremental viscoelastic equations. The finite element method with discrete modeling of the plies was used to obtain reference solutions. The effective viscoelastic properties obtained using the three methods based on the elastic homogenization formulas were in very good agreement with the reference solution. Among these methods, the quasi-elastic method was found to be both accurate and the simplest method in determining the effective properties. The methods were also used to predict the stress response of a sublaminate to different strain histories. The direct time integration method using the 3D elastic homogenization formulas performs accurately and efficiently for this problem.     

Mixed mode fracture separation in viscoelastic orthotropic media: numerical and analytical approach by the <Emphasis Type="Italic">M</Emphasis>θ<Emphasis Type="Italic">v</Emphasis> -integral

An analytical and numerical procedure based on an independent integral path and finite element analysis for mixed-mode fracture in viscoelastic orthotropic media is developed. The separated method employs virtual mechanics fields induced by the classical singular analytical forms. The viscoelastic generalization uses a thermodynamic approach by defining an energy release rate only taking into account a perfect uncoupling between free and viscous energies. The implementation of the Mθ-integral in finite element software and its integration into the viscoelastic incremental formulation are presented. As results, the analytical and numerical solutions are compared by the way of the energy release rate in pure mode I, pure mode II and mixed modes. In shows that, the developed model lead to accurate and efficient separated fracture mode in viscoelastic materials.