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.

Latest Advances on Benders Decomposition

2018 ◽  
pp. 5411-5421 ◽  
Author(s):  
Antonios Fragkogios ◽  
Georgios K. D. Saharidis
Keyword(s):  
Mathematical Programming ◽  
Operations Research ◽  
Decomposition Method ◽  
Large Scale ◽  
Benders Decomposition ◽  
Information Science ◽  
Solution Process ◽  
Cpu Time ◽  
Mathematical Problems ◽  
Modern Economic

Operations Research and Mathematical Programming together with Information Science and Technology are tools used to solve various problems in the modern economic environment. This chapter addresses the Benders Decomposition method, which is used for the solution of problems of Operations Research. This method, applied to certain large-scale mathematical problems, can make their solution feasible (if they cannot be solved with another procedure) or can accelerate the solution process in terms of CPU time. The authors provide a thorough presentation of how the decomposition of a problem is made and the Benders algorithm is applied for its solution. Main purpose of this chapter is to analyze the recent studies that address the method's weaknesses and accelerate its application for the faster solution of mathematical problems. A large number of papers is presented and the contribution of each one of them to the improvement of the method is described.

scholarly journals Stabilized Benders Methods for Large-Scale Combinatorial Optimization, with Application to Data Privacy

2020 ◽  
Vol 66 (7) ◽  
pp. 3051-3068 ◽  
Author(s):  
Daniel Baena ◽  
Jordi Castro ◽  
Antonio Frangioni
Keyword(s):  
Data Privacy ◽  
Large Scale ◽  
Benders Decomposition ◽  
Mixed Integer ◽  
Master Problem ◽  
Continuous Variables ◽  
Typical Structure ◽  
Disclosure Control ◽  
Current State ◽  
Statistical Disclosure

The cell-suppression problem (CSP) is a very large mixed-integer linear problem arising in statistical disclosure control. However, CSP has the typical structure that allows application of the Benders decomposition, which is known to suffer from oscillation and slow convergence, compounded with the fact that the master problem is combinatorial. To overcome this drawback, we present a stabilized Benders decomposition whose master is restricted to a neighborhood of successful candidates by local-branching constraints, which are dynamically adjusted, and even dropped, during the iterations. Our experiments with synthetic and real-world instances with up to 24,000 binary variables, 181 million (M) continuous variables, and 367M constraints show that our approach is competitive with both the current state-of-the-art code for CSP and the Benders implementation in CPLEX 12.7. In some instances, stabilized Benders provided a very good solution in less than 1 minute, whereas the other approaches found no feasible solution in 1 hour. This paper was accepted by Yinyu Ye, optimization.

scholarly journals Leri: a web-server for identifying protein functional networks from evolutionary couplings

2020 ◽  
Author(s):  
Ngaam J. Cheung ◽  
Arun T. John Peter ◽  
Benoit Kornmann
Keyword(s):  
Amino Acids ◽  
Amino Acid ◽  
Protein Function ◽  
Structure Prediction ◽  
High Performance ◽  
Web Server ◽  
Functional Networks ◽  
Computational Results ◽  
High Quality ◽  
Recent Developments

ABSTRACTInformation on the co-evolution of amino acid pairs in a protein can be used for endeavors such as protein engineering, mutation design, and structure prediction. Here we report a method that captures significant determinants of proteins using estimated co-evolution information to identify networks of residues, termed “residue communities”, relevant to protein function. By taking advantage of recent developments in high-performance and parallel computing, we constructed a web-server, Leri, that identifies relevant residue communities to allow researchers to investigate how a protein evolves and folds for function(s). All the data of the computational results including high-quality images can be downloaded and presented for publication. This web-server, written in C++, is sufficiently rapid to enable the studies on proteins of up to 400 amino acids.

Anbar: Collection and analysis of a large scale Urdu language Twitter corpus

2021 ◽  
pp. 1-12
Author(s):  
Bilal Tahir ◽  
Muhammad Amir Mehmood
Keyword(s):  
Computational Linguistics ◽  
High Performance ◽  
Large Scale ◽  
Temporal Frequency ◽  
Quality Data ◽  
User Characteristics ◽  
Vocabulary Size ◽  
High Quality ◽  
Social Analytics ◽  
One Year

 The confluence of high performance computing algorithms and large scale high-quality data has led to the availability of cutting edge tools in computational linguistics. However, these state-of-the-art tools are available only for the major languages of the world. The preparation of large scale high-quality corpora for low resource language such as Urdu is a challenging task as it requires huge computational and human resources. In this paper, we build and analyze a large scale Urdu language Twitter corpus Anbar. For this purpose, we collect 106.9 million Urdu tweets posted by 1.69 million users during one year (September 2018-August 2019). Our corpus consists of tweets with a rich vocabulary of 3.8 million unique tokens along with 58K hashtags and 62K URLs. Moreover, it contains 75.9 million (71.0%) retweets and 847K geotagged tweets. Furthermore, we examine Anbar using a variety of metrics like temporal frequency of tweets, vocabulary size, geo-location, user characteristics, and entities distribution. To the best of our knowledge, this is the largest repository of Urdu language tweets for the NLP research community which can be used for Natural Language Understanding (NLU), social analytics, and fake news detection.

Latest Advances on Benders Decomposition

2019 ◽  
pp. 1065-1077
Author(s):  
Antonios Fragkogios ◽  
Georgios K. D. Saharidis
Keyword(s):  
Mathematical Programming ◽  
Operations Research ◽  
Decomposition Method ◽  
Large Scale ◽  
Benders Decomposition ◽  
Information Science ◽  
Solution Process ◽  
Cpu Time ◽  
Mathematical Problems ◽  
Modern Economic

Operations research and mathematical programming together with information science and technology are tools used to solve various problems in the modern economic environment. This chapter addresses the Benders decomposition method, which is used for the solution of problems of operations research. This method, applied to certain large-scale mathematical problems, can make their solution feasible (if they cannot be solved with another procedure) or can accelerate the solution process in terms of CPU time. The authors provide a thorough presentation of how the decomposition of a problem is made and the Benders algorithm is applied for its solution. The main purpose of this chapter is to analyze the recent studies that address the method's weaknesses and accelerate its application for the faster solution of mathematical problems. A large number of papers is presented and the contribution of each one of them to the improvement of the method is described.

III-V CMOS technologies on Si platform

2011 ◽  
Vol 1336 ◽  
Author(s):  
M. Takenaka ◽  
S. Takagi
Keyword(s):  
Integrated Circuits ◽  
High Performance ◽  
Large Scale ◽  
Film Formation ◽  
High Electron ◽  
High Quality ◽  
Electron Effective Mass ◽  
Monolithically Integrated ◽  
Si Substrates ◽  
Future Technology

ABSTRACTThe heterogeneous integration of III-V semiconductors with the Si platform is expected to provide high performance CMOS logic for future technology nodes because of high electron mobility and low electron effective mass in III-V semiconductors. However, there are many technology issues to be addressed for integrating III-V MOSFETs on the Si platform as follow; high-quality MOS interface formation, low resistivity source/drain formation, and high-quality III-V film formation on Si substrates. In this paper, we present several possible solutions for the above critical issues of III-V MOSFETs on the Si platform. In addition, we present the III-V CMOS photonics platform on which III-V MOSFETs and III-V photonics can be monolithically integrated for ultra-large scale electric-optic integrated circuits.

scholarly journals Parallel Multiphysics Simulation of Package Systems Using an Efficient Domain Decomposition Method

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 158
Author(s):  
Weijie Wang ◽  
Yannan Liu ◽  
Zhenguo Zhao ◽  
Haijing Zhou
Keyword(s):  
Domain Decomposition ◽  
Antenna Arrays ◽  
Electromagnetic Interference ◽  
Decomposition Method ◽  
High Performance ◽  
Large Scale ◽  
Electromagnetic Compatibility ◽  
Domain Decomposition Method ◽  
Computation Time ◽  
Multiphysics Simulations

With the continuing downscaling in feature sizes, the thermal impact on material properties and geometrical deformations can no longer be ignored in the analysis of the electromagnetic compatibility or electromagnetic interference of package systems, including System-in-Package and antenna arrays. We present a high-performance numerical simulation program that is intended to perform large-scale multiphysics simulations using the finite element method. An efficient domain decomposition method was developed to accelerate the multiphysics loops of electromagnetic–thermal stress simulations by considering the fact that the electromagnetic field perturbations caused by geometrical deformation are small and constrained in one or a few subdomains. The multi-level parallelism of the algorithm was also obtained based on an in-house developed parallel infrastructure. Numerical examples showed that our algorithm is able to enable simulation with multiple processors in parallel and, more importantly, achieve a significant reduction in computation time compared with traditional methods.

Direct large-scale synthesis of 3D hierarchical mesoporous NiO microspheres as high-performance anode materials for lithium ion batteries

Nanoscale ◽  
2014 ◽  
Vol 6 (6) ◽  
pp. 3268-3273 ◽  
Author(s):  
Zhongchao bai ◽  
Zhicheng Ju ◽  
Chunli Guo ◽  
Yitai Qian ◽  
Bin Tang ◽  
...  
Keyword(s):  
Thermal Decomposition ◽  
Lithium Ion Batteries ◽  
Anode Materials ◽  
Decomposition Method ◽  
High Performance ◽  
Large Scale ◽  
Lithium Ion ◽  
Superior Performance ◽  
Thermal Decomposition Method ◽  
Large Scale Synthesis

3D hierarchical mesoporous NiO microspheres were scalably synthesized by a thermal decomposition method; they exhibit superior performance as anode materials for LIBs.

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