Compact Mathematical Formulation for Graph Partitioning

The graph partitioning problem consists of dividing the vertices of a graph into clusters, such that the weight of the edges crossing between clusters is minimized. We present a new compact mathematical formulation of this problem, based on the use of binary representation for the index of clusters assigned to vertices. This new formulation is almost minimal in terms of the number of variables and constraints and of the density of the constraint matrix. Its linear relaxation brings a very fast computational resolution, compared with the standard one.Experiments were conducted on classical large benchmark graphs designed for comparing heuristic methods. On one hand, these experiments show that the new formulation is surprisingly less time efficient than expected on general k-partitioning problems. On the other hand, the new formulation applied on bisection problems allows to obtain the optimum solution for about ten instances, where only best upper bounds were previously known.     

基于多尺度模型的RC框架撞击倒塌响应数值分析

为了在保证计算精度的同时提高撞击荷载作用下RC框架结构连续倒塌分析的计算效率,本文基于有限元软件LS-DYNA,建立了撞击响应分析的多尺度模型。针对该模型分别采用拆除构件法和撞击全过程分析法分析了撞击荷载下框架结构的连续倒塌动力响应。结果表明：拆除构件法在分析撞击作用下结构的连续倒塌时,由于忽略了撞击力及其对周围结构造成的初始损伤、初始位移和初始速度,低估了结构的动力响应,不能合理反映撞击作用下框架结构的破坏模式;多尺度模型能够准确模拟撞击作用下框架结构的动力响应和破坏模式,同时计算时间仅为精细模型的三分之一,满足整体结构系统撞击倒塌分析的需要。     

Enhanced balancing Neumann–Neumann preconditioning in computational fluid and solid mechanics

In this work, we propose an enhanced implementation of balancing Neumann–Neumann (BNN) preconditioning together with a detailed numerical comparison against the balancing domain decomposition by constraints (BDDC) preconditioner. As model problems, we consider the Poisson and linear elasticity problems. On one hand, we propose a novel way to deal with singular matrices and pseudo‐inverses appearing in local solvers. It is based on a kernel identification strategy that allows us to efficiently compute the action of the pseudo‐inverse via local indefinite solvers. We further show how, identifying a minimum set of degrees of freedom to be fixed, an equivalent definite system can be solved instead, even in the elastic case. On the other hand, we propose a simple implementation of the algorithm that reduces the number of Dirichlet solvers to only one per iteration, leading to similar computational cost as additive methods. After these improvements of the BNN preconditioned conjugate gradient algorithm, we compare its performance against that of the BDDC preconditioners on a pair of large‐scale distributed‐memory platforms. The enhanced BNN method is a competitive preconditioner for three‐dimensional Poisson and elasticity problems and outperforms the BDDC method in many cases. Copyright © 2013 John Wiley & Sons, Ltd.     

Multi-objective lot splitting for a single product m-machine flowshop line

In this paper, the mean flowtime and the makespan objectives are simultaneously investigated in a single product, m-machine, flowshop system. For this purpose, an efficiency frontier approach is applied and an optimal algorithm for generating all efficient solutions is developed. A comprehensive computational experiment is performed for analyzing the tradeoff between the two objectives and evaluating the proposed algorithm performance. The most-balanced-solution, MinMax, is defined and recommended as a desirable alternative for either the flowtime or the makespan optimal solutions. Results show that when the system is optimized for either the mean flowtime or the makespan, a significant loss in the nonoptimized objective value is observed. On the other hand, adopting the MinMax solution obtains a close to optimal solution in both objectives.     

Optimage central organised image quality control including statistics and reporting

Quality control of medical imaging systems is performed using dedicated phantoms. As the imaging systems are more and more digital, adequate image processing methods might help to save evaluation time and to receive objective results. The developed software package OPTIMAGE is focusing on this with a central approach: On one hand, OPTIMAGE provides a framework, which includes functions like database integration, DICOM data sources, multilingual user interface and image processing functionality. On the other hand, the test methods are implemented using modules which are able to process the images automatically for the common imaging systems. The integration of statistics and reporting into this environment is paramount: This is the only way to provide these functions in an interactive, user-friendly way. These features enable the users to discover degradation in performance quickly and document performed measurements easily.     

Iterative reanalysis approximation-assisted moving morphable component-based topology optimization method

An Iterative Reanalysis Approximation- (IRA) assisted Moving Morphable Components- (MMCs) based topology optimization is developed (IRA-MMC) in this study. Compared with other classical topology optimization methods, Finite Element-based solver is replaced with the suggested IRA. In this way, the expensive computational cost can be significantly saved by several nested iterations. In the suggested algorithm, a hybrid optimizer based on Method of Moving Asymptotes approach and Globally Convergent version of Method of Moving Asymptotes is suggested to improve convergence ratio and avoid local optimum. Finally, the proposed approach is evaluated by some classical benchmark problems in topology optimization. The results show significant time saving without compromising accuracy.     

Binary Fruit Fly Swarm Algorithms for the Set Covering Problem

Currently, the industry is experiencing an exponential increase in dealing with binary-based combinatorial problems. In this sense, metaheuristics have been a common trend in the field in order to design approaches to solve them successfully. Thus, a well-known strategy consists in the use of algorithms based on discrete swarms transformed to perform in binary environments. Following the No Free Lunch theorem, we are interested in testing the performance of the Fruit Fly Algorithm, this is a bio-inspired metaheuristic for deducing global optimization in continuous spaces, based on the foraging behavior of the fruit fly, which usually has much better sensory perception of smell and vision than any other species. On the other hand, the Set Coverage Problem is a well-known NP-hard problem with many practical applications, including production line balancing, utility installation, and crew scheduling in railroad and mass transit companies. In this paper, we propose different binarization methods for the Fruit Fly Algorithm, using S-shaped and V-shaped transfer functions and various discretization methods to make the algorithm work in a binary search space. We are motivated with this approach, because in this way we can deliver to future researchers interested in this area, a way to be able to work with continuous metaheuristics in binary domains. This new approach was tested on benchmark instances of the Set Coverage Problem and the computational results show that the proposed algorithm is robust enough to produce good results with low computational cost.     

An accelerated,convergent, and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics

Convergent and stable domain integration that is also computationally efficient remains a challenge for Galerkin meshfree methods. High order quadrature can achieve stability and optimal convergence, but it is prohibitively expensive for practical use. On the other hand, low order quadrature consumes much less CPU but can yield non‐convergent, unstable solutions. In this work, an accelerated, convergent, and stable nodal integration is developed for the reproducing kernel particle method. A stabilization scheme for nodal integration is proposed based on implicit gradients of the strains at the nodes that offers a computational cost similar to direct nodal integration. The method is also formulated in a variationally consistent manner, so that optimal convergence is achieved. A significant efficiency enhancement over a comparable stable and convergent nodal integration scheme is demonstrated in a complexity analysis and in CPU time studies. A stability analysis is also given, and several examples are provided to demonstrate the effectiveness of the proposed method for both linear and nonlinear problems. Copyright © 2015 John Wiley & Sons, Ltd.     

An explicit asynchronous contact algorithm for elastic body–rigid wall interaction

The use of multiple‐time‐step integrators can provide substantial computational savings over traditional one‐time‐step methods for the simulation of solid dynamics, while maintaining desirable properties, such as energy conservation. Contact phenomena generally require either the adoption of an implicit algorithm or the use of unacceptably small time steps to prevent large amount of numerical dissipation from being introduced. This paper introduces a new explicit dynamic contact algorithm that, by taking advantage of asynchronous time stepping, delivers an outstanding energy performance at a much more acceptable computational cost. We demonstrated the performance of the numerical method with several three‐dimensional examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Higher derivative explicit one step methods for non-linear dynamic problems. Part II: Practical calculations and comparisons with other higher order methods

A generalized explicit one step alogorithm developed in Part I of this paper is presented in the form of a predictor–corrector scheme suitable for arbitrary non-linear analyses of structural dynamics problems. Convergence results are checked through practical calculations on linear and non-linear systems. The generalized algorithm proposed is compared with other recently developed higher order one step algorithms. The slight amount of additional computational effort compared to second order methods pays off in linear and weakly non-linear systems. The behaviour of the methods is also tested on extreme stiffening and softening systems to investigate reliability and robustness of the algorithm.     

Hybrid-stress models for elastic–plastic analysis by the initial-stress approach

Two alternative numerical methods are presented, based on the assumed-stress hybrid finite element model and the initial-stress approach, for the elastic–plastic small-deflection analysis of structures under static loading. The use of the initial-stress approach results in a set of simultaneous linear algebraic incremental equations to be solved at each loading step, with the elastic stiffness matrix remaining unchanged throughout the loading process and the effects of plasticity included as equivalent element loads. The derivation of these alternative methods differs in the assigning of the incremental stress which satisfies equilibrium; in one case it is the actual stress increment while in the other it is a fictitious stress increment. An equilibrium imbalance correction is included in each of these methods to prevent drifting of the solution during the incremental process. Example solutions are presented which demonstrate the accuracy of the two methods and permit comparisons of the relative efficiencies of the two methods.     

Error evaluations for the computation of failure probability in static structural reliability problems

The determination of mathematical reliability in static structures is still a motivating field of research. On one hand, the failure probability values are of greater importance in engineering activities; on the other hand, the determination of this probability remains a time consuming computational task when real problems are examined. To obtain a significant value for the failure probability while preserving a reasonable computation cost is therefore an objective to be considered. One of the necessary conditions to reach this target is to design a method to determine the computational error. Knowing the error will then give the capacity to limit the computation time, in particular by avoiding a too accurate probability evaluation. This paper presents a method allowing one to deal with these factors. The RGMR method, presented at the ICASP'7 meeting (July 1995, Paris) was designed to make such an error evaluation possible. Examples of numerical error computations with the RGMR method, particularly when low significant variables are eliminated, are given. These new developments are a step towards the goal mentioned above.     

Hybrid algorithm of differential evolution and evolutionary programming for optimal reactive power flow

Differential evolution (DE) is a promising evolutionary algorithm for solving the optimal reactive power flow (ORPF) problem, but it requires relatively large population size to avoid premature convergence, which will increase the computational time. On the other hand, evolutionary programming (EP) has been proved to have good global search ability. Exploiting this complementary feature, a hybrid algorithm of DE and EP, denoted as DEEP, is proposed in this study to reduce the required population size. The hybridisation is designed as a novel primary-auxiliary model to minimise the additional computational cost. The effectiveness of DEEP is verified by the serial simulations on the IEEE 14-, 30-, 57-bus system test cases and the parallel simulations on the IEEE 118-bus system test case.     

Model order reduction for hyperelastic materials

In this paper, we develop a novel algorithm for the dimensional reduction of the models of hyperelastic solids undergoing large strains. Unlike standard proper orthogonal decomposition methods, the proposed algorithm minimizes the use of the Newton algorithms in the search of non‐linear equilibrium paths of elastic bodies. The proposed technique is based upon two main ingredients. On one side, the use of classic proper orthogonal decomposition techniques, that extract the most valuable information from pre‐computed, complete models. This information is used to build global shape functions in a Ritz‐like framework. On the other hand, to reduce the use of Newton procedures, an asymptotic expansion is made for some variables of interest. This expansion shows the interesting feature of possessing one unique tangent operator for all the terms of the expansion, thus minimizing the updating of the tangent stiffness matrix of the problem. The paper is completed with some numerical examples in order to show the performance of the technique in the framework of hyperelastic (Kirchhoff–Saint Venant and neo‐Hookean) solids. Copyright © 2009 John Wiley & Sons, Ltd.     

“依赖应变历史材料”结构动力松弛法静力分析中规避虚假应变历史的非线性弹性增量算法

针对SHDM结构（由依赖应变历史材料制成的结构）有限元非线性静力平衡方程组动力松弛法（DRM）迭代求解时的积分点应力更新步骤,提出非线性弹性增量算法,即在一个静力增量步内固定材料的加卸载路径,使之在该增量步内成为非线性弹性材料。该应力更新算法能使包括收敛解在内的迭代序列中不含虚假应变历史。此外,该算法还可避免静力解答精度依赖于静力增量步长的局限性。通过三个SHDM结构的数值试验对该算法进行了验证。该算法可望对SHDM结构非线性有限元静力问题DRM分析技术的发展起促进作用。     

Multi‐scale modeling of plastic deformations in nano‐scale materials; Transition to plastic limit

A large amount of research in computational mechanics has biased toward atomistic simulations. This trend, on one hand, is due to the increased demand to perform computations in nanoscale and, on the other hand, is due to the rather simple applications of pairwise potentials in modeling the interactions between atoms of a given crystal. The Cauchy–Born (CB) hypothesis has been used effectively to model the behavior of crystals under different loading conditions, in which the comparison with molecular dynamics simulations presents desirable coincidence between the results. A number of research works have been devoted to the validity of CB hypothesis and its application in post‐elastic limit. However, the range of application of CB hypothesis is limited, and it remains questionable whether it is still applicable beyond the validity limit. In this paper, a multi‐scale technique is developed for modeling of plastic deformations in nanoscale materials. The deformation gradient is decomposed into the plastic and elastic parts, i.e., F  =  F ^p F ^e. This decomposition is in contrast to the conventional decomposition, F  =  F ^e F ^p, generally encountered in continuum and crystal plasticity. It is shown that the former decomposition is more appropriate for the problem dealt within this work. Inspired by crystal plasticity, the plastic part is determined from the slip on potential slip systems. Based on the assumption that the CB hypothesis remains valid in the homogeneous deformation, the elastic deformation gradient resulting from the aforementioned decomposition is employed in conjunction with the CB hypothesis to update the state variables for face‐centered cubic crystals. The assumption of homogeneity of elastic deformation gradient is justified by the fact that elastic deformations are considerably smaller than the plastic deformations. The computational algorithms are derived in details, and numerical simulations are presented through several examples to demonstrate the capability of the proposed computational algorithm in the modeling of golden crystals under different loading conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

The design of composite adaptive morphological filter and applications to Rician noise reduction in MR images

Composite filters based on morphological operators are getting considerably attractive to medical image denoising. Most of such composite filters depend on classical morphological operators. In this article, an optimal composite adaptive morphological filter (F_CAMF) is developed through a genetic programming (GP) training algorithm by using new nonlocal amoeba morphological operators. On one hand, we propose a novel method for formulating and implementing nonlocal amoeba structuring elements (SEs) for input‐adaptive morphological operators. The nonlocal amoeba SEs in the proposed strategy is divided into two parts: one is the patch distance based amoeba center, and another is the geodesic distance based amoeba boundary, by which the nonlocal patch distance and local geodesic distance are both taken into consideration. On the other hand, GP as a supervised learning algorithm is employed for building the F_CAMF. In GP module, F_CAMF is evolved through evaluating the fitness of several individuals over certain number of generations. The proposed method does not need any prior information about the Rician noise variance. Experimental results on both standard simulated and real MRI data sets show that the proposed filter produces excellent results and outperforms existing state‐of‐the‐art filters, especially for highly noisy image. © 2015 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 25, 15–23, 2015     

A workload balancing genetic algorithm for the quay crane scheduling problem

This paper proposes a novel genetic algorithm to deal with the quay crane scheduling problem (QCSP), which is known to be one of the most critical tasks in terminal operations because its efficiency and the quality of the schedule directly influence the productivity of the terminal. QCSP has been studied intensively in recent years. Algorithms in this field are concerned in the solution quality obtained and the required computational time. As QCSP is known to be NP-hard, heuristic approaches are widely adopted. The genetic algorithm proposed is constructed with a novel workload balancing heuristics, which is capable of considering the loading conditions of different quay cranes (QCs) during the reassignment of task-to-QC. The idea is modelled as a fuzzy logic controller to guide the mutation rate and mutation mechanism of the genetic algorithm. As a result, the proposed algorithm does not require any predefined mutation rate. Meanwhile, the genetic algorithm can more adequately reassign tasks to QCs according to the QCs’ loading condition throughout the evolution. The proposed algorithm has been tested with the well-known benchmark problem sets in this field and produces some new best solutions in a much shorter computational time.     

Discrete and continuum methods for numerical simulations of non‐linear wave propagation in discontinuous media

The main objective of this paper is to develop a methodology to model dynamic loading of various discontinuous media. Two methods for modeling non‐linear waves in a media with multiple discontinuities are considered. The first one, a discrete method, is based on the Simple Common Plane contact algorithm. This method can be applied both to compliant contacts characterized by finite thickness and elastic moduli (such as joints in geomechanics) as well as to non‐compliant frictional contacts traditionally described by the slide lines in finite element/finite difference codes. The second one, a continuum method, assumes that the contacts are not compliant and can be modeled as one or several weakness planes cutting through the elements of the computational mesh. Both discrete and continuum methods described in the paper can be applied to derive equivalent continuum properties for media with multiple discontinuities. An example of such application for a randomly jointed media is given in the paper. Copyright © 2010 John Wiley & Sons, Ltd.     

An integrated load increment method for finite elasto–plastic stress analysis

A new computational scheme, named the ‘Integrated Load Increment’ method (ILI), has been developed to handle elasto–plastic analysis of solids by the finite element variational technique. This scheme allows considerably larger loading steps to be applied to the structure without deviating from its nonlinear, load-deformation relationship. It has been shown that these relationships can be evaluated by integrating the nonlinear constitutive equations within each load increment under certain conditions. A numerical example on a pressurized thick-walled cylinder indicates that a 240 per cent improvement in computational efficiency and substantial reduction of loading steps over the conventional load incremental method can be achieved by the ILI technique.