Speeding Up Paulson’s Procedure for Large-Scale Problems Using Parallel Computing

The article describes some recently-proposed procedures that identify the best simulated system when common random numbers are used. The procedures are based on a Bayesian average-case analysis, rather than a worst-case indifference zone formulation. The procedures allow decision makers to focus on reducing either the expected opportunity cost loss associated with potentially selecting an inferior system, or the probability of incorrect selection. Numerical experiments indicate that the new procedures outperform two existing procedures with respect to several criteria for a well-known selection problem.

Use of Lagrange Interpolating Polynomials in RLT. Systems in Series. Parallel Configurations. Spanning trees. Recycling. Split Cuts. Retrial Queues. Horse Racing. MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique). Dual simplex. History of CP. Procurement Contracts. MRP. Just in Time. Push and Pull Production. MULTIVARIATE INPUT MODELING. Operational Research Society. The M/G/1 Queue. Drama Theory. Hyper-heuristics. Antithetic Variates. Music. Edgeworth market games. Operational Risk. Queueing Notation. Environmental impact. Why variance is not risk. Conjugate gradient methods. Birth-and-Death Processes. Surgery Planning and Scheduling. Large-scale linear models. Standby Systems. Billiards/Pool. AXIOMATIC MEASURES OF RISK AND RISK-VALUE MODELS. Age Replacement Policies. PASTA and Related Results. Collaborative Procurement. LP projection algorithms. R&D risk management. Bioterrorism. Vendor-Managed Inventory. Gomory Cuts. Travel demand modeling. System Availability. Infinite horizon problems. Trust. Bayesian Network Classifiers. Integer Programming Duality. Queueing Disciplines. Stakeholder participation. Models and Basic Properties. Parametric LP analysis. Operations Research and Golfing. Ice Hockey. Clustering. Finite-Population Models. Batch Arrivals and Service. Optimal Monitoring Strategies. Basic Polyhedral Theory. Operations Research and Art. Managing portfolios of risks. Measures of risk equity. Branch and Bound Algorithms. Analytics in Retail. Variational Inequalities. Cross-Entropy Method. TSP heuristics. Capacity allocation. Control Variates. Cover Inequalities. Direct Search Methods. NLP Software. Bilinear optimization. Discrete-Time Martingales. Branch and Price. Column generation. IP Preprocessing. Optimal Reliability Allocation. Simplex-based LP solvers. Instance Formats. Clique generalizations. Availability in Stochastic Models. Evolutionary Algorithms. Basic CP theory: Search. Multimethodology. Branch and Cut. Memetic Algorithms. Urban mass transit. Coherent Systems. Subgradient optimization. Klimov's Model. Credit risk assessment. Branch-width and Tangles. Stochastic Hazard Process. Deterministic Global Optimization. Multistage (stochastic) games. Basis Reduction Methods. ACCIDENT PRECURSORS AND WARNING SYSTEMS MANAGEMENT: A BAYESIAN APPROACH TO MATHEMATICAL MODELS. Genetic Algorithms. Newsvendor models. Parallel Systems. Opportunities in Tennis. Job-shop scheduling. Simplex method and complexity. Geometric programming. Evacuation Planning. The Performance? Allocation Games. Scenario Generation. Robustness Analysis. Dynamic auctions. Neuroeconomics and game theory. Common Random Numbers. Selective Support Vector Machines. Semi-Markov Processes. Risk Averse Models. Sampling Methods. Domination problems. Simulation of Rare Events. Introduction to Tabu Search. Basic Interdiction Models. Introductory Concepts. Remanufacturing. PAUSE procedure. Wardrop equilibria. Mass customization. Ellipsoidal algorithms. Benders decomposition. Dynamic vehicle routing. Warranty Modeling. Design for Network Resiliency. Passenger rail transportation. Vehicle Routing Problem. Supply Chain Outsourcing. Lovasz-Schriver Reformulation. Hazard Rate Function. Lot-sizing. Differential games. Regenerative Processes. Guided Local Search. Preferences for repeated gambles. Percolation Theory. Simulated Annealing. Scoring Rules. Mixing Sets. Cricket. Prospect Theory. Combining Forecasts. Graph search techniques. Quasi-Newton methods. Random search algorithms. Supply chain coordination. Service Outsourcing. Markov Renewal Processes. K-out-of-n Systems.

In this paper we benchmark the performance of the Cray T3D, IBM 9076 SP/1 and Intel Paragon XP/S parallel computers, using implementations of parallel algorithms for the computation of the vector outer-product A = uvT operation. The vector outer-product operation, although very simple in nature, requires the computation of a large number of floating-point operations and its parallelization induces a great level of communication between the processors. It is thus suited to measure the relative speed of the processor, memory subsystem and network capabilities of a parallel computer. It should not be considered a ‘toy problem’, since it arises in numerical methods in the context of the solution of systems of non-linear equations – still a difficult problem to solve. We present algorithms for both the explicit shared-memory and message-passing programming models together with theoretical computation models for those algorithms. Actual experiments were run on those computers, using Fortran 77 implementations of the algorithms. The results obtained with these experiments show that due to the high degree of communication between the processors one needs a parallel computer with fast communications and carefully implemented data exchange routines. The theoretical computation model allows prediction of the speed-up to be obtained for some problem size on a given number of processors. © 1997 John Wiley & Sons, Ltd.

This paper examines the cost/performance of simulating a hypothetical target parallel computer using a commercial host parallel computer. We address the question of whether parallel simulation is simply faster than sequential simulation, or if it is also more cost-effective. To answer this, we develop a performance model of the Wisconsin Wind Tunnel (WWT), a system that simulates cache-coherent shared-memory machines on a message-passing Thinking Machines CM-5. The performance model uses Kruskal and Weiss's fork-join model to account for the effect of event processing time variability on WWT's conservative fixed-window simulation algorithm. A generalization of Thiebaut and Stone's footprint model accurately predicts the effect of cache interference on the CM-5. The model is calibrated using parameters extracted from a fully-parallel simulation (p=N), and validated by measuring the speedup as the number of processors (p) ranges from one to the number of target nodes (N. Together with simple cost models, the performance model indicates that for target system sizes of 32 nodes and larger, parallel simulation is more cost-effective than sequential simulation. The key intuition behind this result is that large simulations require large memories, which dominate the cost of a uniprocessor; parallel computers allow multiple processors to simultaneously access this large memory.

In the ray tracing method, each pixel can be computed independently. Therefore, when the ray tracing algorithm is implemented on a parallel computer, a group of pixels is usually assigned to each element processor. The element processor must have all the environment data and object data for the rendering. When there are too many objects for local memory, a distorted image will be generated. In solving this problem, to date, the necessary data had to be transmitted. However, when the number of element processors is increased, efficient rendering cannot be expected because of communication overheads. This paper proposes a hybrid parallel ray tracing algorithm that combines pixel-parallel and object-parallel ray tracing. As this algorithm inherits the advantages of pixel-parallel ray tracing, high efficiency can be achieved even on a parallel computer using a large number of element processors.

In the field of parallel computing, load balancing of parallel simulations is considered as a fundamental problem. The primary goal is to evenly distribute computing load across multiple processors while minimizing processor-to-processor communication. A prevalent approach to solving the problem of balancing is based on a graph model. To balance the load between k processors, we partition the graph into k parts, each one is assigned to a processor. This problem is difficult to solve, but effective heuristics have been proposed, including those based on a multilevel approach, used by most graph partitioning tools. All partitioning methods are only relevant if the number of processors is fixed. It is essential to choose the right number of processors for a simulation to get good performance and more efficiency.In this paper, we test several graphs partitioning using the metis framework then we try to find the optimal number of processors, named in this paper p* to execute a simulation and the max speed up that we can reach using parallelization. We also investigate the intrinsic graph characteristics that affect these parameters.

BackgroundPreviously, drug-resistant tuberculosis (DR-TB) patients were treated with long, toxic, and relatively ineffective regimens. However, in recent years, there have been major improvements made. The 2020 World Health Organization DR-TB Treatment guidelines recommended the use of a 6-months all-oral BPaL (bedaquiline, pretomanid and linezolid) regimen under operational research (OR) conditions for selected DR-TB patients.MethodsThe processes, challenges, and interim results of introducing BPaL under OR conditions in 7 countries supported under the Korea International Cooperation Agency/TB Alliance-funded “Leveraging Innovation for Faster Treatment of Tuberculosis (LIFT-TB)” project are described here. The OR objectives were to explore the feasibility of introducing the BPaL regimen, and to estimate its effectiveness and safety in a select group of DR-TB patients.ResultsBetween November 2020 and the end of March 2023, a total of 574 patients had been enrolled. Interim treatment success stands at an encouraging 90.9% (280/308). Although adverse events of special interest (AESI) were common, they were manageable, and only 1 patient had to discontinue the complete BPaL treatment regimen. In addition, no unexpected adverse events (AE) were seen.ConclusionWith careful advocacy, frequent communication with partners, and following steps to strengthen essential aspects of the delivery system, the project’s experiences show that BPaL OR was feasible across different country settings. Project documents were constantly updated. The sharing of information, experiences, and interim results had a significant positive and motivating effect within and across countries. Interim OR results show excellent patient responses and are comparable to those seen under trial conditions. Although common, the observed AEs and AESIs were manageable, and no unexpected AEs were seen.

We discuss the implementation of a numerical algorithm for simulating incompressible fluid flows based on the finite difference method and designed for parallel computing platforms with distributed-memory, particularly for clusters of workstations. The solution algorithm for the Navier-Stokes equations utilizes an explicit scheme for pressure and an implicit scheme for velocities, i. e., the velocity field at a new time step can be computed once the corresponding pressure is known. The parallel implementation is based on domain decomposition, where the original calculation domain is decomposed into several blocks, each of which given to a separate processing node. All nodes then execute computations in parallel, each node on its associated subdomain. The parallel computations include initialization, coefficient generation, linear solution on the subdomain, and inter-node communication. The exchange of information across the subdomains, or processors, is achieved using the message passing interface standard, MPI. The use of MPI ensures portability across different computing platforms ranging from massively parallel machines to clusters of workstations. The execution time and speed-up are evaluated through comparing the performance of different numbers of processors. The results indicate that the parallel code can significantly improve prediction capability and efficiency for large-scale simulations.

In recent multicore architectures, parallel computing with vectorization emerges for mathematical calculations and image processing by exploiting Intel Advanced Vector Extensions (AVX). In parallel computing, the performance of modern processors depends on many factors, such as the amount of memory storage, the size of caches, the number of available processors, and the programming methodologies for efficiency. Besides that, a hundred vector intrinsics supported by AVX can perform various calculations on floating-point operations that can be optimized by applying AVX-256 or AVX-512 registers. In this paper, fast recursive matrix multiplication is proposed by using AVX and OpenMP combined with the software prefetching method on block-wise matrix-matrix multiplication on shared memory. The proposed version applied prefetching which can attempt to reduce memory latencies by prefetching memory pages in advance before they have been used. As a result, when the matrix multiplication applied prefetching method for the size of 8192×8192, the execution time was reduced about 22% and the performance was enhanced by about 17% than without applying prefetching while testing on Intel core i7 processor.

This paper presents a mathematical framework for a family of discrete-time discrete-frequency transforms in terms of matrix signal algebra. The matrix signal algebra is a mathematics environment composed of a signal space, a finite dimensional linear operators and special matrices where algebraic methods are used to generate these signal transforms as computational estimators. The matrix signal algebra contribute to analysis, design and implementation of parallel algorithms in multi-core proccesors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB r with the Parallel Computing Toolbox TM . We found that there is advantage to use multi-core processors and a parallel computing environment to minimize the high execution time. Also, speedup and efficiency increases when the number of logical processor and length of the signal increase. Moreover, a superlinear speedup is obtained in this ex perimental investigation.

This paper derives tradeoffs between three basic costs of a parallel algorithm: synchronization, data movement, and computational cost. These tradeoffs are lower bounds on the execution time of the algorithm which are independent of the number of processors, but dependent on the problem size. Therefore, they provide lower bounds on the parallel execution time of any algorithm computed by a system composed of any number of homogeneous components, each with associated computational, communication, and synchronization payloads. We employ a theoretical model counts the amount of work and data movement as a maximum of any execution path during the parallel computation. By considering this metric, rather than the total communication volume over the whole machine, we obtain new insights into the characteristics of parallel schedules for algorithms with non-trivial dependency structures. We also present reductions from BSP and LogP algorithms to our execution model, extending our lower bounds to these two models of parallel computation. We first develop our results for general dependency graphs and hypergraphs based on their expansion properties, then we apply the theorem to a number of specific algorithms in numerical linear algebra, namely triangular substitution, Gaussian elimination, and Krylov subspace methods. Our lower bound for LU factorization demonstrates the optimality of Tiskin's LU algorithm answering an open question posed in his paper, as well as of the 2.5D LU algorithm which has analogous costs. We treat the computations in a general manner by noting that the computations share a similar dependency hypergraph structure and analyzing the communication requirements of lattice hypergraph structures.

Purpose – A variety of meshless methods have been developed in the last 20 years with an intention to solve practical engineering problems, but are limited to small academic problems due to associated high computational cost as compared to the standard finite element methods (FEM). The purpose of this paper is to develop an efficient and accurate algorithms based on meshless methods for the solution of problems involving both material and geometrical nonlinearities. Design/methodology/approach – A parallel two-dimensional linear elastic computer code is presented for a maximum entropy basis functions based meshless method. The two-dimensional algorithm is subsequently extended to three-dimensional adaptive nonlinear and three-dimensional parallel nonlinear adaptively coupled finite element, meshless method cases. The Prandtl-Reuss constitutive model is used to model elasto-plasticity and total Lagrangian formulations are used to model finite deformation. Furthermore, Zienkiewicz and Zhu and Chung and Belytschko error estimation procedure are used in the FE and meshless regions of the problem domain, respectively. The message passing interface library and open-source software packages, METIS and MUltifrontal Massively Parallel Solver are used for the high performance computation. Findings – Numerical examples are given to demonstrate the correct implementation and performance of the parallel algorithms. The agreement between the numerical and analytical results in the case of linear elastic example is excellent. For the nonlinear problems load-displacement curve are compared with the reference FEM and found in a very good agreement. As compared to the FEM, no volumetric locking was observed in the case of meshless method. Furthermore, it is shown that increasing the number of processors up to a given number improve the performance of parallel algorithms in term of simulation time, speedup and efficiency. Originality/value – Problems involving both material and geometrical nonlinearities are of practical importance in many engineering applications, e.g. geomechanics, metal forming and biomechanics. A family of parallel algorithms has been developed in this paper for these problems using adaptively coupled finite element, meshless method (based on maximum entropy basis functions) for distributed memory computer architectures.

In this paper, the calculation method of electromagnetic scattering is analyzed using method of moment in MPI (Message-Passing Interface) parallel environment. Due to the characteristics of Gauss elimination method, the approach of the matrix filling and solving by looping over column is described, which can save data communicating time between processors. The vehicle's scattered fields is calculated by the method using different numbers of processors. The results show that parallel computation can reduce computing time and memory requirements of each processor to the original's 1/process_num (processors number).

Due to the TFT LCD (Thin-Film-Transistor Liquid-Crystal-Display) manifestation into many related products, this industry has been growing rapidly along with increasing demand. To satisfy the demand, most companies have increased their production capacity and capability by increasing their number of factories in different places and causing complexity in this industry. This research develops a production and distribution planning model for the multi-stage and multi-site supply chain in the TFT LCD industry. Genetic algorithm proposed in this research to solve the problem. Maximizing capacity utilization and total profit in the supply chain are become the major performance indicator in this model. Regarding the high computational effort of genetic algorithm, then parallel computation performed. Genetic algorithm conducted in multi-processor computation using OpenMP for time efficiency. To compare the computational time, the genetic algorithm conducted in five different number of processors; 1, 2, 4, 8, and 16, to know how many processors are needed to get the optimal computational time. The result is the genetic algorithm using 4 processors has the optimal expected net profit compare to the others. The result shows that a larger number of processors doesn’t mean the computation time will become automatically faster.

The TOPAZ opacity code explicitly includes configuration term structure in the calculation of bound-bound radiative transitions. This approach involves myriad spectral lines and requires the large computational capabilities of parallel processing computers. It is important, however, to make use of these resources efficiently. For example, an increase in the number of processors should yield a comparable reduction in computational time. This proportional 'speedup' indicates that very large problems can be addressed with massively parallel computers. Opacity codes can readily take advantage of parallel architecture since many intermediate calculations are independent. On the other hand, since the different tasks entail significantly disparate computational effort, load-balancing issues emerge so that parallel efficiency does not occur naturally. Several schemes to distribute the labor among processors are discussed.