Solution Of Large-scale Problems Research Articles

Fuzzy LR linear systems: quadratic and least squares models to characterize exact solutions and an algorithm to compute approximate solutions

We first establish some necessary and sufficient conditions for solvability of fuzzy LR linear systems. We then propose a concept for an approximate solution when a fuzzy LR linear system lacks a solution. Recently, we have proposed an approximate solution for a fuzzy LR linear system under the condition that a corresponding crisp linear system was solvable. Here, we remove this condition by presenting a more general concept of an approximate solution based on a least squares model. We also develop the conditions for the uniqueness of the approximate solution. To compute an approximate solution, we propose an algorithm based on a quadratic programming model with bound constraints on some variables. Finally, we show numerically the appropriateness of our proposed approximate solution for large scale problems in comparison with other recently proposed approximate solutions. The numerical results show that our proposed algorithm produces significantly more accurate solutions.

Job Scheduling Problem with Fuzzy Neural Network by using the MapReduce Model in a Cloud Environment

Cloud computing is a solution for processing large amounts of data. Therefore, Google introduced map reduce as a programming model for large scale data applications in the cloud environment. Map reduce is used for data processing and parallel computing. The Apache Hadoop is an open source implementation of mapreduce. However job shop scheduling problem (JSSP) is an important issues that is one of the most popular NP hard, it is necessary to find a faster solution for large scale problems. For this purpose, fuzzy neural network must be use to solve this kind of optimization problem. In this paper, we proposed new novel method by using a fuzzy neural network with map reduce model to solve job shop scheduling problem, implementation and results are presented. The experiments of our proposed method are performed for well-known problem instances from job scheduling. The results show our method has high convergence speed and less execution time compared with Genetic algorithm.

A rolling horizon-based decomposition algorithm for the railway network train timetabling problem

This article presents the train timetabling problem in the complex railway network (including single-track line, double-track line, mixed-track line and terminal) and a solution algorithm. The problem is to determine the arrival, departure or through time of each train at each station on its predetermined route to satisfy several operational and safety requirements and minimise multiple objectives corresponding to train and engine time. The problem is formulated as a large-scale mixed integer nonlinear programming model with multiple objectives to simultaneously minimise the total train travel time, the total train connection time and the total engine turnaround time with several practical constraints. The model can be easily modified to simulate different scenarios of train timetabling problems. By aggregating the objectives and simplifying some constraints, a rolling horizon-based decomposition algorithm is developed based on the unique structure of the railway network and the characteristic of the train timetable. The algorithm decomposes the network into several single lines and progressively adds the train timetable of a new line into the current partial network train timetable until a complete network train timetable is obtained. The rolling horizon method is designed to determine the train timetable of each single line in iterations. Each iteration is restricted into a subregion of the feasible region, and the feasible solution to that subregion is determined by a timetable evaluation procedure and a boundary detection procedure. Lastly, computational test on real-world data shows that the presented approach can produce high-quality solutions for large-scale problems within a reasonable computation time.

On the stable solution of large scale problems over the doubly nonnegative cone

The recent approach of solving large scale semidefinite programs with a first order method by minimizing an augmented primal-dual function is extended to doubly nonnegative programs. A key point governing the convergence of this approach are regularity properties of the underlying problem. Regularity of the augmented primal-dual function is established under the condition of uniqueness and strict complementarity. The application to the doubly nonnegative cone is motivated by the fact that the cost per iteration does not increase by adding nonnegativity constraints. Numerical experiments indicate that a two phase approach based on the augmented primal-dual function results in a stable method for solving large scale problems.

Simulation of collapse and fragmentation phenomena in a sharp interface Eulerian setting

Sharp interface Eulerian methods are used to develop a technique for handling high speed material dynamics leading to collapse and fragmentation. Two problems are of primary interest, viz. void collapse in energetic materials and fragmentation of solids under impact; in the first case the sharp interface reconnects to itself, while in the second the sharp interface is torn apart. The challenge is to simulate using a sharp interface Eulerian approach through these topological changes and to apply boundary conditions on the immersed interfaces. Level set interface representations are combined with a modified Ghost Fluid Method to solve sharp interface dynamics in the presence of elasto-plastically deforming solid materials. A unified method of populating ghost field is developed using an adaptive least squares approach and demonstrated to be robust for severe interface deformations, including changes in topology. A parallel algorithm is used to enable solutions of large scale problems. The embedded material interfaces undergoing severe deformation while moving at a very high speed are handled efficiently and accurately in a multi-processor setting. Validation exercises, examples and benchmark calculations are presented to demonstrate the accuracy of the approach.

A new approach to generation scheduling in interconnected power systems using predictor-corrector proximal multiplier method

The purpose of this paper is to elaborate a new generation scheduling algorithm in the interconnected power systems. Typically, the generation scheduling problem as a mixed integer non-linear programming can be effectively solved by the generalized Benders decomposition technique which decouples an original problem into the master problem and subproblems to tremendously allow fast and accurate solutions of large-scale problems. In order to formulate efficient inter-temporal optimal power flow (OPF) subproblems, we will explore a regional decomposition framework based on predictor-corrector proximal multiplier method. In fact, this scheme can find the most economic generation schedules under the power transactions for a multi-utility system without the exchange of each utility’s own private information and major disruption to existing economic dispatch or OPF adopted by individual utilities.

An efficient differential evolution algorithm for multi-mode resource-constrained project scheduling problems

This paper considers a general resource-constrained project scheduling problem in which activities may be executed in more than one operating mode with both renewable and non-renewable resources. Each mode may have different durations and requires different amounts of renewable and non-renewable resources. To solve this NP-hard problem, an efficient differential evolution (eDE) algorithm is proposed with linear decreasing crossover factor and adaptive penalty cost. The purpose of these modifications is to enhance the ability of DE algorithm to quickly search for better solutions by encouraging solutions to escape from local solution and effectively evolve solutions in the search space. The performance of the proposed algorithm is compared with other algorithms in the literature and shows that the proposed algorithm is very efficient. It outperforms several heuristics in terms of lower average deviation from the optimal makespan. Moreover, it is capable of finding quality solutions for large-scale problems in reasonable computational time.

A new improved genetic algorithm approach and a competitive heuristic method for large-scale multiple resource-constrained project-scheduling problems

Article history: Received 6 May 2010 Received in revised form June, 28, 2011 Accepted 29 June 2011 Available online 30 June 2011 The aim of this paper is to present a new genetic algorithm approach for large scale multiple resource-constrained project-scheduling problems (RCPSP). It also presents a heuristic approach to achieve proper solutions for large scale problems. This research area is very common in industry especially when a set of activities needs to be finished as soon as possible subject to two sets of constraints, precedence constraints and resource constraints. The emphasis in this research is on investigating the complexity of scheduling problems and developing a new GA approach to solve this problem in such a way that the advantages of GA are appropriately utilized by applying a novel method to reduce the complexity of the problem. Computational results are also reported for the most famous classical problems taken from the operational research literature. © 2011 Growing Science Ltd. All rights reserved

PARALLEL MULTIDIMENSIONAL SCALING USING GRID COMPUTING: ASSESSMENT OF PERFORMANCE

Multidimensional scaling is a technique for visualization and exploratory analysis of multidimensional data aiming to discover a structure of sets of objects using information on similarities/dissimilarities between those objects. A difficult global optimization problem should be solved to minimize the error of visualization. A hybrid optimization algorithm has been constructed combining evolutionary global search with efficient local descent. A parallel version of the proposed optimization algorithm is implemented to enable solution of large scale problems in acceptable time. In the present paper we investigated the efficiency of the parallel version of the algorithm on PC clusters and computational grids.

The use of hybrid techniques at CERFACS for the solution of large problems on parallel machines

AbstractCurrent problems in scientific computing often require the solution of sets of sparse linear equations of very large order. Particularly for three dimensional problems, it may to be impractical to solve them using a direct method but equally iterative methods may not converge and often standard preconditioning techniques do not work.We thus propose using a hybrid method by which we mean that either a nearby problem or a subproblem is solved by a direct method with the overall problem being solved by an iterative method. We discuss two applications of this at CERFACS in the solution of large scale problems from industry. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Static Displacement Reanalysis of Modified Structures Using Epsilon Algorithm

I N THE optimization of structural systems, it is very important to compute the static displacements of the structures when the parameters of the structures are changed.One of themain obstacles is the high computational cost involved in the solution of large-scale problems. Therefore, the reanalysis problems excite the interest of many researchers and both approximate and exact reanalysis methods have been reported and reviewed [1]. In general, the following factors are considered in choosing an approximate behavior model for a specific optimal design problem [2]. 1) the accuracy of the calculations or the quality of the approximations; 2) the computational effort involved or the efficiency of the method, and 3) the ease of implementation. At present, the various approximations have been developed. Barthelemy, Kirsch, and Haftka et al. [3–5] developed the global approximation (also called multipoint approximations), such as polynomial fitting or reduced basis methods. These approximations are obtained by analyzing the structure at a number of design points, and they are valid for the whole design space. Local approximation is called single-point approximations, such as the Taylor series expansion or the binomial series expansion about a given point in the design space. Local approximations are based on information calculated at a single point. Thesemethods are effective only in cases of small changes in parameters of the structures. For large changes in the design, the accuracy of the approximations often deteriorates, and they may become meaningless [6]. Kirsch [7–12] discussed the combined approximations, which attempt to give global qualities to local approximations. Recently, the Pade approximation and Shanks transformation were used to improve the accuracy of the reanalysis [13,14]. It is shown that it can significantly improve the domain of convergence. In this study, we use the epsilon algorithm [15–17] to deal with the static displacement reanalysis. The main objectives are to preserve the ease of implementation and to improve significantly the domain of convergence and the quality of the results, such that the method can be used in problems with very large changes in the structural parameters. A numerical example is demonstrated and the method is compared with the Kirsch combined approximation.

Cache efficient data structures and algorithms for adaptive multidimensional multilevel finite element solvers

Due to the increasing gap between speed of CPU and speed of access to memory the latter is often the main bottleneck in modern high performance computing. Hierarchical cache architectures designed to avoid this problem conflict with the rather irregular memory access of modern adaptive multilevel algorithms which cause frequent cache misses. In this paper we present an algorithm for an adaptive multilevel FE solver that reduces random access and jumps in address space considerably. The grid is based on a fully adaptive space tree based on a d-dimensional hypercube where d is an arbitrary positive integer. The individual cells in the hierarchical space tree are ordered by a space-filling curve, the d-dimensional Peano curve, and the data processing is organized by a small set of stacks. Because access to a stack always stays local in memory, cache misses are very rare. The organizational overhead is very small. Only one bit per node to define the geometry of the domain and one bit per node to specify the refinement structure are needed allowing the solution of large-scale problems.

Multi-view correspondence by enforcement of rigidity constraints

Establishing the correct correspondence between features in an image set remains a challenging problem amongst computer vision researchers. In fact, the combinatorial nature of feature matching effectively hinders the solution of large scale problems, which have direct applications in important areas such as 3D reconstruction and tracking. The solution is obtained by imposing a geometric constraint – rigidity – that selects the matching solution resulting in a rank-4 observation matrix. Since this is a global criterion, issues usually associated to local matching algorithms (such as the aperture problem) do not present an obstacle in this case. The use of a geometric constraint of this type assumes that all feature points are visible in every image, so as to obtain a complete observation matrix. The rank of the observation matrix is a function of the matching solutions associated to each image and as such a simultaneous solution for all frames has to be found. For each frame, correspondence is modeled through a permutation matrix, which also allows for the rejection of wrong candidates. Although each image is matched individually, an iterative algorithm is used to integrate correspondence information associated to all remaining images. Each individual matching process results in a linear problem: the reduced computational complexity allows the solution of large problems in an acceptable time interval. Although the algorithm has intrinsically been designed for calibrated systems, some instances of the uncalibrated case can also be solved provided a convenient bootstrap is available.

Parallel hybrid algorithm for global optimization of problems occurring in MDS-based visualization

Multidimensional scaling is a widely used technique for visualization of multidimensional data. For the implementation of a multidimensional scaling technique a difficult global optimization problem should be solved. To attack such problems a hybrid global optimization method is developed combining evolutionary global search with local descent. A parallel version of the proposed method is implemented to enable solution of large scale problems in acceptable time. The results of the experimental investigation of the efficiency of the proposed method are presented.

Simulation of a free boundary problem using boundary element method and restarted re-analysis technique

In this work, we deal with the numerical approximation of a free boundary problem reformulated as an optimal shape design one. The boundary element method is used for the approximation of this problem. The iterative method used to solve the discrete problem requires the resolution of intermediate linear systems associated with the successive modification in the design process. In many cases one of the main obstacles is the high computational cost involved in the solution of large-scale problems. To reduce the computational cost, a restarted re-analysis technique is introduced to solve these systems. Numerical examples including comparison results are presented to show the efficiency of the proposed approach.

Parallel numerical simulation with domain decomposition for seismic response analysis of shield tunnel

The research presented in this paper deals with parallel explicit finite element simulation with domain decomposition for seismic response analysis of shield tunnel, which is the non-linear and time dependent behaviour of complex structures in engineering. Such simulations have to provide high accuracy in the prediction of deformations and stability, by taking into account the long-term influences of the non-linear behaviour of the material as well as the large deformation and contact conditions. The limiting factors of the computer simulation are the computer run time and the memory requirement during solution of large-scale problems. To overcome these problems, a domain decomposition method and dynamic-explicit time integration procedure are used, and the latter is used for the solution of the semi-discrete equations of motion, which is very suited for parallel processing. Using the high performance computer ShenWei-I, the seismic response of shield tunnel in Shanghai is processed, and the number of nodes and elements in final finite element model exceeded 4.0 million and 3.8 million, respectively. The results reveal the weak position in the shield tunnel under Shanghai seismic wave. The paper provides references for the antiseismic design of the shield tunnel.

Parallel programming in computational science: an introductory practical training course for computer science undergraduates at Aachen University

Parallel programming of high-performance computers has emerged as a key technology for the numerical solution of large-scale problems arising in computational science and engineering (CSE). The authors believe that principles and techniques of parallel programming are among the essential ingredients of any CSE as well as computer science curriculum. Today, opinions on the role and importance of parallel programming are diverse. Rather than seeing it as a marginal beneficial skill optionally taught at the graduate level, we understand parallel programming as crucial basic skill that should be taught as an integral part of the undergraduate computer science curriculum. A practical training course developed for computer science undergraduates at Aachen University is described. Its goal is to introduce young computer science students to different parallel programming paradigms for shared and distributed memory computers as well as to give a first exposition to the field of computational science by simple, yet carefully chosen sample problems.

Parallelization of EMAP3D based on element-by-element Jacobi preconditioned conjugate gradient method

The demand for more accurate analyses of electromechanical systems, such as electromagnetic launchers and pulsed rotating power supplies, requires an increase in the size of the finite-element model of these systems. It is not uncommon for the number of unknowns for such a model to reach a half million. A parallel computing system with multiple processors and distributed memory, such as a PC cluster, makes it possible to obtain solutions for large-scale problems in reasonable times. In order to utilize this parallel hardware architecture, the software needs to be parallelized accordingly. Electromechanical Analysis Program in Three Dimensions (EMAP3D) is parallelized based on the element-by-element Jacobi preconditioned conjugate gradient (EBEJPCG) method because it is easily adopted into a parallel scheme and has low memory requirements because the formation of the global matrix is not necessary. The details of this algorithm are described in this paper. A block armature railgun was used to investigate this parallel algorithm on the Institute for Advanced Technology's (IAT's) eight-node PC-based Beowulf cluster. The performance of the algorithm in terms of speed-up ratio is presented.

Finding all solutions of piecewise‐linear resistive circuits using the dual simplex method

AbstractAn efficient algorithm is proposed for finding all solutions of piecewise‐linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for non‐existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. However, this algorithm requires a very large number of pivotings because the simplex method is applied on many regions. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm could find all solutions of large‐scale problems, including those where the number of variables is 300 and the number of linear regions is 10300, in practical computation time. Copyright © 2002 John Wiley & Sons, Ltd.

A scalar damage model with a shear retention factor for the analysis of reinforced concrete structures: theory and validation

A local isotropic single parameter scalar model that can simulate the mechanical behaviour of quasi-brittle materials, such as concrete, is described. The constitutive law needs the mechanical characteristics and the fracture energy of concrete to be completely defined. The damage parameter is obtained directly from the value of an equivalent effective stress in order to reduce the computing effort. Due to the unique damage parameter, this model is suitable for the study of quasi-static problems involving monotonically increasing loads. The problem of localisation and mesh dependency have been partially overcome by using an enhanced local method in which a characteristic internal length related to the mesh dimension is employed instead of the characteristic fracture length. In this work, the model was enriched further with the introduction of a shear retention factor that accounts for the friction between the two surfaces of a crack. These new features assure a real improvement of the damage model, maintaining nevertheless its simplicity and low computing cost and making it suitable for the practical solution of large scale problems. Several numerical simulations of experimental tests, concerning fracture tests on concrete specimens and beams failing in shear, have been performed for the validation of the model. The main results from the numerical analyses are described and compared with the experimental ones.