Parallel, iterative solution of sparse linear systems: Models and architectures

A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. A data transfer model predicting both the probability that data must be transferred between two tasks and the amount of data to be transferred is presented. This model is used to derive an execution time model for predicting parallel execution time and an optimal number of tasks given the dimension and sparsity of the coefficient matrix and the costs of computation, synchronization, and communication. The suitability of different parallel architectures for solving randomly sparse linear systems is discussed. Based on the complexity of task scheduling, one parallel architecture, based on a broadcast bus, is presented and analyzed

A model of asynchronous iterative algorithms for solving large, sparse, linear systems

Solving large, sparse, linear systems of equations is one of the fundamental problems in large scale scientific and engineering computation. A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. This model is then analyzed to determine the expected intertask data transfer and task computational complexity as functions of the number of tasks. Based on the analysis, recommendations for task partitioning are made. These recommendations are a function of the sparseness of the linear system, its structure (i.e., randomly sparse or banded), and dimension

A Diagnostic Assessment Of Evolutionary Multiobjective Optimization For Water Resources Systems

This study contributes a rigorous diagnostic assessment of state-of-the-art multiobjective evolutionary algorithms (MOEAs) and highlights key advances that the water resources field can exploit to better discover the critical tradeoffs constraining our systems. This study provides the most comprehensive diagnostic assessment of MOEAs for water resources to date, exploiting more than 100,000 MOEA runs and trillions of design evaluations. The diagnostic assessment measures the effectiveness, efficiency, reliability, and controllability of ten benchmark MOEAs for a representative suite of water resources applications addressing rainfall-runoff calibration, long-term groundwater monitoring (LTM), and risk-based water supply portfolio planning. The suite of problems encompasses a range of challenging problem properties including (1) many-objective formulations with 4 or more objectives, (2) multi-modality (or false optima), (3) nonlinearity, (4) discreteness, (5) severe constraints, (6) stochastic objectives, and (7) non-separability (also called epistasis). The applications are representative of the dominant problem classes that have shaped the history of MOEAs in water resources and that will be dominant foci in the future. Recommendations are provided for which modern MOEAs should serve as tools and benchmarks in the future water resources literature

Visual Analytics Clarify The Scalability And Effectiveness Of Massively Parallel Many-Objective Optimization: A Groundwater Monitoring Design Example

In this study, we contribute a comprehensive assessment of massively parallel multiobjective evolutionary algorithm (MOEA)-based search using a highly challenging optimization—assimilation application. The application focuses on a four objective groundwater monitoring application in which parallel scalability is tested across compute core counts ranging from 64 to a maximum of 8192. Our many-objective visual analytics framework clarifies how to assess and attain highly effective search on large scale high-performance computing systems. Moreover, our results also refute the common assumption that adding objectives in many-objective evolutionary optimization will always increase the computational difficulty of a problem. Our results agree with prior theoretical analysis demonstrating several instances where the overall four objective groundwater monitoring problem formulation is actually easier to solve than lower dimensional formulations composed of subsets of the original formulation’s objectives. Although a groundwater application is used to demonstrate our parallelization, the visual analytics and metrics utilized to characterize the parallel scalability of MOEA-based search are broadly applicable in water resources and beyond

Stencils and problem partitionings: Their influence on the performance of multiple processor systems

Given a discretization stencil, partitioning the problem domain is an important first step for the efficient solution of partial differential equations on multiple processor systems. Partitions are derived that minimize interprocessor communication when the number of processors is known a priori and each domain partition is assigned to a different processor. This partitioning technique uses the stencil structure to select appropriate partition shapes. For square problem domains, it is shown that non-standard partitions (e.g., hexagons) are frequently preferable to the standard square partitions for a variety of commonly used stencils. This investigation is concluded with a formalization of the relationship between partition shape, stencil structure, and architecture, allowing selection of optimal partitions for a variety of parallel systems

Improving the Protection of Aquatic Ecosystems by Dynamically Constraining Reservoir Operation Via Direct Policy Conditioning

Water management problems generally involve conflicting and non-commensurable objectives. Assuming a centralized perspective at the system-level, the set of Pareto-optimal alternatives represents the ideal solution of most of the problems. Yet, in typical real-world applications, only a few primary objectives are explicitly considered, taking precedence over all other concerns. These remaining concerns are then internalized as static constraints within the problem's formulation. This approach yields to solutions that fail to explore the full set of objectives tradeoffs. In this paper, we propose a novel method, called direct policy conditioning (DPC), that combines direct policy search, multi-objective evolutionary algorithms, and input variable selection to design dynamic constraints that change according to the current system conditions. The method is demonstrated for the management problem of the Conowingo Dam, located within the Lower Susquehanna River, USA. The DPC method is used to identify environmental protection mechanisms and is contrasted with traditional static constraints de fining minimum environmental flow requirements. Results show that the DPC method identifies a set of dynamically constrained control policies that overcome the current alternatives based on the minimum environmental flow constraint, in terms of environmental protection but also of the primary objectives

The UK electronics manufacturing industry 1997-2003: a case study of the effect of globalization

Statistical data and information from industry interviews are used to build a picture of the implications of, and responses to, globalization in the key industry of electronics contract manufacturing in the UK. A comprehensive list of companies in the sector with associated employment and turnover data has been created from a variety of sources. Comparison of 2003 data with a 1997 dataset produces a unique longitudinal statistical picture of the industry over a period marked by the increasing influence of globalization. Total employment in the industry has decreased by 39 per cent from approximately 37 600 to 23 100 between 1997 and 2003. This breaks down into a decline in the printed circuit board (PCB) manufacturing subsector of 61 per cent, from 16 300 to around 6400, and a much smaller decline in the printed circuit board sub-contract assembly (PCBA) subsector of 22 per cent, from approximately 21400 to 16700. There has been a major shift in employment distribution away from large companies. Interview results indicate that the loss of large company capacity may have strategic implications for future technological capability. However, the UK is seen as a source of innovation and retention of strong engineering skills is key to bringing new products to the market