Stochastic Decomposition for Two-Stage Stochastic Linear Programs with Random Cost Coefficients

2020 ◽  
Author(s):  
Harsha Gangammanavar ◽  
Yifan Liu ◽  
Suvrajeet Sen
Keyword(s):  
Large Scale ◽  
Computational Time ◽  
Stochastic Decomposition ◽  
Linear Programs ◽  
Sample Sizes ◽  
Practical Applications ◽  
Second Stage ◽  
Sample Average Approximations ◽  
Incremental Sampling ◽  
Stochastic Linear Programs

Stochastic decomposition (SD) has been a computationally effective approach to solve large-scale stochastic programming (SP) problems arising in practical applications. By using incremental sampling, this approach is designed to discover an appropriate sample size for a given SP instance, thus precluding the need for either scenario reduction or arbitrary sample sizes to create sample average approximations (SAA). When compared with the solutions obtained using the SAA procedure, SD provides solutions of similar quality in far less computational time using ordinarily available computational resources. However, previous versions of SD were not applicable to problems with randomness in second-stage cost coefficients. In this paper, we extend its capabilities by relaxing this assumption on cost coefficients in the second stage. In addition to the algorithmic enhancements necessary to achieve this, we also present the details of implementing these extensions, which preserve the computational edge of SD. Finally, we illustrate the computational results obtained from the latest implementation of SD on a variety of test instances generated for problems from the literature. We compare these results with those obtained from the regularized L-shaped method applied to the SAA function of these problems with different sample sizes.

scholarly journals A warm-start approach for large-scale stochastic linear programs

2009 ◽  
Vol 127 (2) ◽  
pp. 371-397 ◽  
Author(s):  
Marco Colombo ◽  
Jacek Gondzio ◽  
Andreas Grothey
Keyword(s):  
Large Scale ◽  
Linear Programs ◽  
Warm Start ◽  
Stochastic Linear Programs

Combustion Driven by Fragment-based Ab Initio Molecular Dynamics Simulation

2019 ◽  
Author(s):  
Liqun Cao ◽  
Jinzhe Zeng ◽  
Mingyuan Xu ◽  
Chih-Hao Chin ◽  
Tong Zhu ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Ab Initio ◽  
Large Scale ◽  
Methane Combustion ◽  
Combustion Method ◽  
Dynamics Simulation ◽  
Ab Initio Molecular Dynamics ◽  
Computational Time ◽  
Combustion Mechanism ◽  
Daily Lives

Combustion is a kind of important reaction that affects people's daily lives and the development of aerospace. Exploring the reaction mechanism contributes to the understanding of combustion and the more efficient use of fuels. Ab initio quantum mechanical (QM) calculation is precise but limited by its computational time for large-scale systems. In order to carry out reactive molecular dynamics (MD) simulation for combustion accurately and quickly, we develop the MFCC-combustion method in this study, which calculates the interaction between atoms using QM method at the level of MN15/6-31G(d). Each molecule in systems is treated as a fragment, and when the distance between any two atoms in different molecules is greater than 3.5 Å, a new fragment involved two molecules is produced in order to consider the two-body interaction. The deviations of MFCC-combustion from full system calculations are within a few kcal/mol, and the result clearly shows that the calculated energies of the different systems using MFCC-combustion are close to converging after the distance thresholds are larger than 3.5 Å for the two-body QM interactions. The methane combustion was studied with the MFCC-combustion method to explore the combustion mechanism of the methane-oxygen system.

Bullying, School Violence, and Climate in Evolving Contexts

2018 ◽  
Author(s):  
Ron Avi Astor ◽  
Rami Benbenisthty
Keyword(s):  
School Violence ◽  
School Safety ◽  
Media Coverage ◽  
Large Scale ◽  
Ecological Model ◽  
Empirical Studies ◽  
Practical Applications ◽  
Teacher Student ◽  
Area Of Interest ◽  
New Research

Since 2005, the bullying, school violence, and school safety literatures have expanded dramatically in content, disciplines, and empirical studies. However, with this massive expansion of research, there is also a surprising lack of theoretical and empirical direction to guide efforts on how to advance our basic science and practical applications of this growing scientific area of interest. Parallel to this surge in interest, cultural norms, media coverage, and policies to address school safety and bullying have evolved at a remarkably quick pace over the past 13 years. For example, behaviors and populations that just a decade ago were not included in the school violence, bullying, and school safety discourse are now accepted areas of inquiry. These include, for instance, cyberbullying, sexting, social media shaming, teacher–student and student–teacher bullying, sexual harassment and assault, homicide, and suicide. Populations in schools not previously explored, such as lesbian, gay, bisexual, transgender, and queer students and educators and military- and veteran-connected students, become the foci of new research, policies, and programs. As a result, all US states and most industrialized countries now have a complex quilt of new school safety and bullying legislation and policies. Large-scale research and intervention funding programs are often linked to these policies. This book suggests an empirically driven unifying model that brings together these previously distinct literatures. This book presents an ecological model of school violence, bullying, and safety in evolving contexts that integrates all we have learned in the 13 years, and suggests ways to move forward.

scholarly journals Two-stage multi-tasking transform framework for large-scale many-objective optimization problems

2021 ◽  
Author(s):  
Lu Chen ◽  
Handing Wang ◽  
Wenping Ma
Keyword(s):  
Large Scale ◽  
Original Problem ◽  
Optimization Problems ◽  
Reference Points ◽  
Optimization Strategy ◽  
Two Stage ◽  
Decision Space ◽  
Second Stage ◽  
Decision Variables ◽  
Objective Space

AbstractReal-world optimization applications in complex systems always contain multiple factors to be optimized, which can be formulated as multi-objective optimization problems. These problems have been solved by many evolutionary algorithms like MOEA/D, NSGA-III, and KnEA. However, when the numbers of decision variables and objectives increase, the computation costs of those mentioned algorithms will be unaffordable. To reduce such high computation cost on large-scale many-objective optimization problems, we proposed a two-stage framework. The first stage of the proposed algorithm combines with a multi-tasking optimization strategy and a bi-directional search strategy, where the original problem is reformulated as a multi-tasking optimization problem in the decision space to enhance the convergence. To improve the diversity, in the second stage, the proposed algorithm applies multi-tasking optimization to a number of sub-problems based on reference points in the objective space. In this paper, to show the effectiveness of the proposed algorithm, we test the algorithm on the DTLZ and LSMOP problems and compare it with existing algorithms, and it outperforms other compared algorithms in most cases and shows disadvantage on both convergence and diversity.

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