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Heuristic Algorithms (heuristic + algorithms)

Distribution by Scientific Domains
Mathematics and Statistics28%

Selected Abstracts

Stencil reduction algorithms for the local discontinuous Galerkin method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010
Paul E. Castillo
Abstract The problem of reducing the stencil of the local discontinuous Galerkin method applied to second-order differential operator is discussed. Heuristic algorithms to minimize the total number of non-zero blocks of the reduced stiffness matrix are presented and tested on a wide variety of unstructured and structured grids in 2D and 3D. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Dispersion of Nodes Added to a Network

GEOGRAPHICAL ANALYSIS, Issue 4 2005
Michael Kuby
For location problems in which optimal locations can be at nodes or along arcs but no finite dominating set has been identified, researchers may desire a method for dispersing p additional discrete candidate sites along the m arcs of a network. This article develops and tests minimax and maximin models for solving this continuous network location problem, which we call the added-node dispersion problem (ANDP). Adding nodes to an arc subdivides it into subarcs. The minimax model minimizes the maximum subarc length, while the maximin model maximizes the minimum subarc length. Like most worst-case objectives, the minimax and maximin objectives are plagued by poorly behaved alternate optima. Therefore, a secondary MinSumMax objective is used to select the best-dispersed alternate optima. We prove that equal spacing of added nodes along arcs is optimal to the MinSumMax objective. Using this fact we develop greedy heuristic algorithms that are simple, optimal, and efficient (O(mp)). Empirical results show how the maximum subarc, minimum subarc, and sum of longest subarcs change as the number of added nodes increases. Further empirical results show how using the ANDP to locate additional nodes can improve the solutions of another location problem. Using the p-dispersion problem as a case study, we show how much adding ANDP sites to the network vertices improves the p-dispersion objective function compared with (a) network vertices only and (b) vertices plus randomly added nodes. The ANDP can also be used by itself to disperse facilities such as stores, refueling stations, cell phone towers, or relay facilities along the arcs of a network, assuming that such facilities already exist at all nodes of the network. [source]

A survey on vertex coloring problems

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 1 2010
Enrico Malaguti
Abstract This paper surveys the most important algorithmic and computational results on the Vertex Coloring Problem (VCP) and its generalizations. The first part of the paper introduces the classical models for the VCP, and discusses how these models can be used and possibly strengthened to derive exact and heuristic algorithms for the problem. Computational results on the best performing algorithms proposed in the literature are reported. The second part of the paper is devoted to some generalizations of the problem, which are obtained by considering additional constraints [Bandwidth (Multi) Coloring Problem, Bounded Vertex Coloring Problem] or an objective function with a special structure (Weighted Vertex Coloring Problem). The extension of the models for the classical VCP to the considered problems and the best performing algorithms from the literature, as well as the corresponding computational results, are reported. [source]

Identification and thermodynamic treatment of several types of large-amplitude motions

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 14 2005
Gernot Katzer
Abstract We present a partially automated method for the thermodynamic treatment of large-amplitude motions. Starting from the molecular geometry and the Hessian matrix, we evaluate anharmonic partition functions for selected vibrational degrees of freedom. Supported anharmonic vibration types are internal rotation and inversion (oscillation in a double-well potential). By heuristic algorithms, we identify internal rotations in most cases automatically from the Hessian eigenvectors, and we also estimate the parameters of anharmonic partition functions (e.g., potential barrier, periodicity, and symmetry number) with thermodynamically sufficient precision. We demonstrate the validity of our schemes by comparison to pointwise calculated ab initio potential curves. © 2005 Wiley Periodicals, Inc. J Comput Chem 14: 1438,1451, 2005 [source]

New approaches for solving the block-to-train assignment problem

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 1 2008
Krishna C. Jha
Abstract Railroad planning involves solving two optimization problems: (i) the blocking problem, which determines what blocks to make and how to route traffic over these blocks; and (ii) the train schedule design problem, which determines train origins, destinations, and routes. Once the blocking plan and train schedule have been obtained, the next step is to determine which trains should carry which blocks. This problem, known as the block-to-train assignment problem, is considered in this paper. We provide two formulations for this problem: an arc-based formulation and a path-based formulation. The latter is generally smaller than the former, and it can better handle practical constraints. We also propose exact and heuristic algorithms based on the path-based formulation. Our exact algorithm solves an integer programming formulation with CPLEX using both a priori generation and dynamic generation of paths. Our heuristic algorithms include a Lagrangian relaxation-based method as well as a greedy construction method. We present computational results of our algorithms using the data provided by a major US railroad. We show that we can obtain an optimal solution of the block-to-train assignment problem within a few minutes of computational time, and can obtain heuristic solutions with 1,2% deviations from the optimal solutions within a few seconds. © 2007 Wiley Periodicals, Inc. NETWORKS, 2008 [source]

Analysis of block matrix preconditioners for elliptic optimal control problems

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2007
T. P. Mathew
Abstract In this paper, we describe and analyse several block matrix iterative algorithms for solving a saddle point linear system arising from the discretization of a linear-quadratic elliptic control problem with Neumann boundary conditions. To ensure that the problem is well posed, a regularization term with a parameter , is included. The first algorithm reduces the saddle point system to a symmetric positive definite Schur complement system for the control variable and employs conjugate gradient (CG) acceleration, however, double iteration is required (except in special cases). A preconditioner yielding a rate of convergence independent of the mesh size h is described for , , R2 or R3, and a preconditioner independent of h and , when , , R2. Next, two algorithms avoiding double iteration are described using an augmented Lagrangian formulation. One of these algorithms solves the augmented saddle point system employing MINRES acceleration, while the other solves a symmetric positive definite reformulation of the augmented saddle point system employing CG acceleration. For both algorithms, a symmetric positive definite preconditioner is described yielding a rate of convergence independent of h. In addition to the above algorithms, two heuristic algorithms are described, one a projected CG algorithm, and the other an indefinite block matrix preconditioner employing GMRES acceleration. Rigorous convergence results, however, are not known for the heuristic algorithms. Copyright © 2007 John Wiley & Sons, Ltd. [source]

DOGSET: pre-designed primer sets for fine-scale mapping and DNA sequence interrogation in the dog

ANIMAL GENETICS, Issue 4 2009
A. K. Wong
Summary DOGSET is an online resource that provides access to primer sequences that have been computationally mined from the reference genome using heuristic algorithms. The electronic repository includes PCR primers corresponding to 32 135 markers for genetic mapping and 334 657 sequence-tagged gene elements for targeted re-sequencing and mutation discovery. A customized report that tailors primer design to wet bench protocols can be exported for a region of interest by specifying genome coordinates in a graphical user interface. [source]