High-Performance Prototyping of Decomposition Methods in GAMS

2020 ◽  
Author(s):  
Timo Lohmann ◽  
Michael R. Bussieck ◽  
Lutz Westermann ◽  
Steffen Rebennack
Keyword(s):  
High Performance ◽  
Large Scale ◽  
Benders Decomposition ◽  
Application Programming Interface ◽  
Decomposition Methods ◽  
Planning Problem ◽  
Modeling Languages ◽  
Expansion Planning ◽  
Algebraic Modeling Languages ◽  
Algebraic Modeling Language

Prototyping algorithms in algebraic modeling languages has a long tradition. Despite the convenient prototyping platform that modeling languages offer, they are typically seen as rather inefficient with regard to repeatedly solving mathematical programming problems, a concept on which many algorithms are based. The most prominent examples of such algorithms are decomposition methods, such as the Benders decomposition, column generation, and the Dantzig–Wolfe decomposition. In this work, we discuss the underlying reasons for repeated solve deficiency with regard to speed in detail and provide an insider’s look into the algebraic modeling language GAMS. Further, we present recently added features in GAMS that mitigate some of the efficiency drawbacks inherent to the way modeling languages represent model data and ultimately solve a model. In particular, we demonstrate the grid-enabled gather-update-solve-scatter facility and the GAMS object-oriented application programming interface on a large-scale case study that involves a Benders decomposition–type algorithm for a power-expansion planning problem.

scholarly journals Benders decomposition with adaptive oracles for large scale optimization

2020 ◽  
Author(s):  
Nicolò Mazzi ◽  
Andreas Grothey ◽  
Ken McKinnon ◽  
Nagisa Sugishita
Keyword(s):  
Large Scale ◽  
Benders Decomposition ◽  
Optimization Problems ◽  
Cutting Plane ◽  
Computational Effort ◽  
Planning Problem ◽  
Illustrative Case ◽  
Investment Planning ◽  
Cutting Plane Algorithms ◽  
Inexact Information

AbstractThis paper proposes an algorithm to efficiently solve large optimization problems which exhibit a column bounded block-diagonal structure, where subproblems differ in right-hand side and cost coefficients. Similar problems are often tackled using cutting-plane algorithms, which allow for an iterative and decomposed solution of the problem. When solving subproblems is computationally expensive and the set of subproblems is large, cutting-plane algorithms may slow down severely. In this context we propose two novel adaptive oracles that yield inexact information, potentially much faster than solving the subproblem. The first adaptive oracle is used to generate inexact but valid cutting planes, and the second adaptive oracle gives a valid upper bound of the true optimal objective. These two oracles progressively “adapt” towards the true exact oracle if provided with an increasing number of exact solutions, stored throughout the iterations. These adaptive oracles are embedded within a Benders-type algorithm able to handle inexact information. We compare the Benders with adaptive oracles against a standard Benders algorithm on a stochastic investment planning problem. The proposed algorithm shows the capability to substantially reduce the computational effort to obtain an $$\epsilon $$ ϵ -optimal solution: an illustrative case is 31.9 times faster for a $$1.00\%$$ 1.00 % convergence tolerance and 15.4 times faster for a $$0.01\%$$ 0.01 % tolerance.

The Benders Dual Decomposition Method

2020 ◽  
Vol 68 (3) ◽  
pp. 878-895
Author(s):  
Ragheb Rahmaniani ◽  
Shabbir Ahmed ◽  
Teodor Gabriel Crainic ◽  
Michel Gendreau ◽  
Walter Rei
Keyword(s):  
Decomposition Method ◽  
High Performance ◽  
Large Scale ◽  
Benders Decomposition ◽  
Master Problem ◽  
Computational Results ◽  
Dual Decomposition ◽  
High Quality ◽  
Lagrangian Dual ◽  
Decomposition Strategies

Many methods that have been proposed to solve large-scale MILP problems rely on the use of decomposition strategies. These methods exploit either the primal or dual structures of the problems by applying the Benders decomposition or Lagrangian dual decomposition strategy, respectively. In “The Benders Dual Decomposition Method,” Rahmaniani, Ahmed, Crainic, Gendreau, and Rei propose a new and high-performance approach that combines the complementary advantages of both strategies. The authors show that this method (i) generates stronger feasibility and optimality cuts compared with the classical Benders method, (ii) can converge to the optimal integer solution at the root node of the Benders master problem, and (iii) is capable of generating high-quality incumbent solutions at the early iterations of the algorithm. The developed algorithm obtains encouraging computational results when used to solve various benchmark MILP problems.

Modeling and solving a large-scale generation expansion planning problem under uncertainty

2011 ◽  
Vol 2 (3-4) ◽  
pp. 209-242 ◽  
Author(s):  
Shan Jin ◽  
Sarah M. Ryan ◽  
Jean-Paul Watson ◽  
David L. Woodruff
Keyword(s):  
Large Scale ◽  
Planning Problem ◽  
Generation Expansion Planning ◽  
Expansion Planning ◽  
Generation Expansion

The Structure and Properties of MoSi2 Thin Film in Mos Process

1980 ◽  
Vol 38 ◽  
pp. 326-327
Author(s):  
C.K. Wu ◽  
P. Chang ◽  
N. Godinho
Keyword(s):  
Thin Film ◽  
Integrated Circuits ◽  
High Performance ◽  
Large Scale ◽  
Process Development ◽  
Structure And Properties ◽  
Metal Silicides ◽  
High Oxidation ◽  
Important Approach ◽  
High Oxidation Resistance

Recently, the use of refractory metal silicides as low resistivity, high temperature and high oxidation resistance gate materials in large scale integrated circuits (LSI) has become an important approach in advanced MOS process development (1). This research is a systematic study on the structure and properties of molybdenum silicide thin film and its applicability to high performance LSI fabrication.

RECOMMENDATIONS FOR THE CHOICE OF MILKING INSTALLATIONS IN LOOSE HOUSING SYSTEMS OF COWS

2020 ◽  
Author(s):  
В.В. ГОРДЕЕВ ◽  
В.Е. ХАЗАНОВ
Keyword(s):  
Dairy Cows ◽  
High Performance ◽  
Large Scale ◽  
Dairy Farms ◽  
Economic Indicators ◽  
Technical Level ◽  
Housing Systems ◽  
Working Shift ◽  
Technical And Economic Indicators

При выборе типа доильной установки и ее размера необходимо учитывать максимальное планируемое поголовье дойных коров и размер технологической группы, кратность и время одного доения, продолжительность рабочей смены дояров. Анализ технико-экономических показателей наиболее распространенных на сегодняшний день типов доильных установок одинакового технического уровня свидетельствует, что наилучшие удельные показатели имеет установка типа «Карусель» (1), а установка типа «Елочка» (2) требует более высоких затрат труда и средств. Установка «Параллель» (3) занимает промежуточное положение. Из анализа пропускной способности и количества необходимых операторов: установка 2 рекомендована для ферм с поголовьем дойного стада до 600 голов, 3 — не более 1200 дойных коров, 1 — более 1200 дойных коров. «Карусель» — наиболее рациональный, высокопроизводительный, легко автоматизируемый и, следовательно, перспективный способ доения в залах, особенно для крупных молочных ферм. The choice of the proper type and size of milking installations needs to take into account the maximum planned number of dairy cows, the size of a technological group, the number of milkings per day, and the duration of one milking and the operator's working shift. The analysis of technical and economic indicators of currently most common types of milking machines of the same technical level revealed that the Carousel installation had the best specific indicators while the Herringbone installation featured higher labour inputs and cash costs. The Parallel installation was found somewhere in between. In terms of the throughput and the required number of operators Herringbone is recommended for farms with up to 600 dairy cows, Parallel — below 1200 dairy cows, Carousel — above 1200 dairy cows. Carousel was found the most practical, high-performance, easily automated and, therefore, promising milking system for milking parlours, especially on the large-scale dairy farms.

scholarly journals Statistical and machine learning models for optimizing energy in parallel applications

2019 ◽  
Vol 33 (6) ◽  
pp. 1079-1097 ◽  
Author(s):  
Mark Endrei ◽  
Chao Jin ◽  
Minh Ngoc Dinh ◽  
David Abramson ◽  
Heidi Poxon ◽  
...  
Keyword(s):  
Machine Learning ◽  
Energy Efficiency ◽  
High Performance ◽  
Large Scale ◽  
Energy Use ◽  
Parallel Applications ◽  
Learning Models ◽  
Trade Off ◽  
Time Required ◽  
Machine Learning Models

Rising power costs and constraints are driving a growing focus on the energy efficiency of high performance computing systems. The unique characteristics of a particular system and workload and their effect on performance and energy efficiency are typically difficult for application users to assess and to control. Settings for optimum performance and energy efficiency can also diverge, so we need to identify trade-off options that guide a suitable balance between energy use and performance. We present statistical and machine learning models that only require a small number of runs to make accurate Pareto-optimal trade-off predictions using parameters that users can control. We study model training and validation using several parallel kernels and more complex workloads, including Algebraic Multigrid (AMG), Large-scale Atomic Molecular Massively Parallel Simulator, and Livermore Unstructured Lagrangian Explicit Shock Hydrodynamics. We demonstrate that we can train the models using as few as 12 runs, with prediction error of less than 10%. Our AMG results identify trade-off options that provide up to 45% improvement in energy efficiency for around 10% performance loss. We reduce the sample measurement time required for AMG by 90%, from 13 h to 74 min.

scholarly journals Automated Cytogenetic Biodosimetry at Population-Scale

Radiation ◽  
2021 ◽  
Vol 1 (2) ◽  
pp. 79-94
Author(s):  
Peter K. Rogan ◽  
Eliseos J. Mucaki ◽  
Ben C. Shirley ◽  
Yanxin Li ◽  
Ruth C. Wilkins ◽  
...  
Keyword(s):  
High Performance ◽  
Large Scale ◽  
Dicentric Chromosome ◽  
Automated Assignment ◽  
Simulated Population ◽  
Dose Estimation ◽  
Processing Times ◽  
Multiple Processors ◽  
Exposure Levels ◽  
Population Scale

The dicentric chromosome (DC) assay accurately quantifies exposure to radiation; however, manual and semi-automated assignment of DCs has limited its use for a potential large-scale radiation incident. The Automated Dicentric Chromosome Identifier and Dose Estimator (ADCI) software automates unattended DC detection and determines radiation exposures, fulfilling IAEA criteria for triage biodosimetry. This study evaluates the throughput of high-performance ADCI (ADCI-HT) to stratify exposures of populations in 15 simulated population scale radiation exposures. ADCI-HT streamlines dose estimation using a supercomputer by optimal hierarchical scheduling of DC detection for varying numbers of samples and metaphase cell images in parallel on multiple processors. We evaluated processing times and accuracy of estimated exposures across census-defined populations. Image processing of 1744 samples on 16,384 CPUs required 1 h 11 min 23 s and radiation dose estimation based on DC frequencies required 32 sec. Processing of 40,000 samples at 10 exposures from five laboratories required 25 h and met IAEA criteria (dose estimates were within 0.5 Gy; median = 0.07). Geostatistically interpolated radiation exposure contours of simulated nuclear incidents were defined by samples exposed to clinically relevant exposure levels (1 and 2 Gy). Analysis of all exposed individuals with ADCI-HT required 0.6–7.4 days, depending on the population density of the simulation.

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