Bound Algorithm (bound + algorithm)

Distribution by Scientific Domains
Mathematics and Statistics66%

Selected Abstracts

Optimizing the number of multigrid cycles in the full multigrid algorithm

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2-3 2010
A. Thekale
Abstract Multigrid (MG) methods are among the most efficient and widespread methods for solving large linear systems of equations that arise, for example, from the discretization of partial differential equations. In this paper we introduce a new approach for optimizing the computational cost of the full MG method to achieve a given accuracy by determining the number of MG cycles on each level. To achieve this, a very efficient and flexible Branch and Bound algorithm is developed. The implementation in the parallel finite element solver Hierarchical Hybrid Grids leads to a significant reduction in CPU time. Copyright © 2010 John Wiley & Sons, Ltd. [source]

Task Pool Teams: a hybrid programming environment for irregular algorithms on SMP clusters

CONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 12 2006
Judith Hippold
Abstract Clusters of symmetric multiprocessors (SMPs) are popular platforms for parallel programming since they provide large computational power for a reasonable price. For irregular application programs with dynamically changing computation and data access behavior, a flexible programming model is needed to achieve efficiency. In this paper we propose Task Pool Teams as a hybrid parallel programming environment to realize irregular algorithms on clusters of SMPs. Task Pool Teams combine task pools on single cluster nodes by an explicit message passing layer. They offer load balance together with multi-threaded, asynchronous communication. Appropriate communication protocols and task pool implementations are provided and accessible by an easy-to-use application programmer interface. As application examples we present a branch and bound algorithm and the hierarchical radiosity algorithm. Copyright © 2006 John Wiley & Sons, Ltd. [source]

A global optimization approach for generating efficient points for multiobjective concave fractional programs

JOURNAL OF MULTI CRITERIA DECISION ANALYSIS, Issue 1 2005
Harold P. Benson
Abstract In this article, we present a global optimization approach for generating efficient points for multiobjective concave fractional programming problems. The main work of the approach involves solving an instance of a concave multiplicative fractional program (W,). Problem (W,) is a global optimization problem for which no known algorithms are available. Therefore, to render the approach practical, we develop and validate a branch and bound algorithm for globally solving problem (W,). To illustrate the performance of the global optimization approach, we use it to generate efficient points for a sample multiobjective concave fractional program. Copyright © 2006 John Wiley & Sons, Ltd. [source]

A specially structured nonlinear integer resource allocation problem

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 7 2003
Kurt M. Bretthauer
Abstract We present an algorithm for solving a specially structured nonlinear integer resource allocation problem. This problem was motivated by a capacity planning study done at a large Health Maintenance Organization in Texas. Specifically, we focus on a class of nonlinear resource allocation problems that involve the minimization of a convex function over one general convex constraint, a set of block diagonal convex constraints, and bounds on the integer variables. The continuous variable problem is also considered. The continuous problem is solved by taking advantage of the structure of the Karush-Kuhn-Tucker (KKT) conditions. This method for solving the continuous problem is then incorporated in a branch and bound algorithm to solve the integer problem. Various reoptimization results, multiplier bounding results, and heuristics are used to improve the efficiency of the algorithms. We show how the algorithms can be extended to obtain a globally optimal solution to the nonconvex version of the problem. We further show that the methods can be applied to problems in production planning and financial optimization. Extensive computational testing of the algorithms is reported for a variety of applications on continuous problems with up to 1,000,000 variables and integer problems with up to 1000 variables. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 770,792, 2003. [source]

A branch and bound algorithm for computing optimal replacement policies in consecutive k -out-of- n -systems

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2002
James Flynn
Abstract This paper presents a branch and bound algorithm for computing optimal replacement policies in a discrete-time, infinite-horizon, dynamic programming model of a binary coherent system with n statistically independent components, and then specializes the algorithm to consecutive k -out-of- n systems. The objective is to minimize the long-run expected average undiscounted cost per period. (Costs arise when the system fails and when failed components are replaced.) An earlier paper established the optimality of following a critical component policy (CCP), i.e., a policy specified by a critical component set and the rule: Replace a component if and only if it is failed and in the critical component set. Computing an optimal CCP is a optimization problem with n binary variables and a nonlinear objective function. Our branch and bound algorithm for solving this problem has memory storage requirement O(n) for consecutive k -out-of- n systems. Extensive computational experiments on such systems involving over 350,000 test problems with n ranging from 10 to 150 find this algorithm to be effective when n , 40 or k is near n. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 288,302, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10017 [source]