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Accelerating benders decomposition with heuristicmaster problem solutions

Alysson M. Costa, Jean-François Cordeau, Bernard Gendron, Gilbert Laporte
2012 Pesquisa Operacional  
In this paper, a general scheme for generating extra cuts during the execution of a Benders decomposition algorithm is presented.  ...  The most important aspect of the proposed ideas is their generality, which allows them to be used in virtually any Benders decomposition implementation.  ...  This algorithm can be used to generate further extra cuts and its pseudo-code is presented in Algorithm 3.  ... 
doi:10.1590/s0101-74382012005000005 fatcat:or3cqyorvnf4vfokvp3baa4oui

In-Out Separation and Column Generation Stabilization by Dual Price Smoothing [chapter]

Artur Pessoa, Ruslan Sadykov, Eduardo Uchoa, Francois Vanderbeck
2013 Lecture Notes in Computer Science  
Stabilization procedures for column generation can be viewed as cutting plane strategies in the dual.  ...  Exploiting the link between in-out separation strategies and dual price smoothing techniques for column generation, we derive a generic bound convergence property for algorithms using a smoothing feature  ...  Techniques in Column Generation The above column generation procedure, also known as Kelley's cutting plane algorithm for the dual master, yields a sequence of dual solution candidates {π t } t converging  ... 
doi:10.1007/978-3-642-38527-8_31 fatcat:k4kzdevnsfgk5dkvuyjubl52i4

A Data-Driven Column Generation Algorithm For Bin Packing Problem in Manufacturing Industry [article]

Jiahui Duan, Xialiang Tong, Fei Ni, Zhenan He, Lei Chen, Mingxuan Yuan
2022 arXiv   pre-print
Then, two novel strategies, the constraint handling and process acceleration strategies are applied to the classic column generation approach to solve this set cover problem.  ...  To further eliminate the iteration process of column generation algorithm and accelerate the optimization process, a Learning to Price approach called Modified Pointer Network is proposed, by which we  ...  Based on the Branch and Cut, [31] proposed a Reinforcement Learning approach for generating Gomary Cut to tight the search space.  ... 
arXiv:2202.12466v1 fatcat:raxqis4pqbae3fmdhj4n7groae

Improving benders decomposition using maximum feasible subsystem (MFS) cut generation strategy

Georgios K.D. Saharidis, Marianthi G. Ierapetritou
2010 Computers and Chemical Engineering  
This strategy is referred to as maximum feasible subsystem (MFS) cut generation strategy.  ...  A new multi-generation of cuts algorithm is presented in this paper to improve the efficiency of Benders decomposition approach for the cases that optimality cuts are difficult to be achieved within the  ...  Acknowledgements The authors would like to gratefully acknowledge financial support from the National Science Foundation under the NSF CTS 0625515 grant and also the USEPA-funded Environmental Bioinformatics  ... 
doi:10.1016/j.compchemeng.2009.10.002 fatcat:jfyfq54fgffspiezcbkmgzchty

Smooth and flexible dual optimal inequalities [article]

Naveed Haghani, Claudio Contardo, Julian Yarkony
2020 arXiv   pre-print
We address the problem of accelerating column generation (CG) for set-covering formulations via dual optimal inequalities (DOI).  ...  iterations and the oscillations of the dual variables commonly observed in column generation procedures.  ...  Concluding remarks In this document we introduced a new approach to accelerate the convergence of column generation when applied to set-covering-based formulations.  ... 
arXiv:2001.02267v1 fatcat:stzk5y4ln5hxvjyo4zvt5cmst4

Automation and Combination of Linear-Programming Based Stabilization Techniques in Column Generation

A. Pessoa, R. Sadykov, E. Uchoa, F. Vanderbeck
2018 INFORMS journal on computing  
Interpreting column generation as cutting plane strategies in the dual problem, we analyze the mechanisms on which stabilization relies.  ...  The convergence of a column generation algorithm can be improved in practice by using stabilization techniques.  ...  Stabilization Techniques in Column Generation Stabilization techniques are devised to accelerate the convergence of the column generation algorithm, by targeting its drawbacks as reviewed in [31] : -Dual  ... 
doi:10.1287/ijoc.2017.0784 fatcat:svu62x7iavegxmhjqm3t5nlgli

Full 3D simulations of BNL one-sided silicon 3D detectors and comparisons with other types of 3D detectors

Tanja Grönlund, Zheng Li, Gabriella Carini, Michael Li
2008 Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment  
Single-type column detectors are easier to process than dual-type column detectors, but have a more complicated, non-uniform electric field profile.  ...  The dual-type column detectors are the best in radiation hardness due to their low depletion voltages and short drift distances.  ...  Acknowledgement This research was supported by the US Department of Energy: Contract no. DE-AC02-98CH10886.  ... 
doi:10.1016/j.nima.2007.12.005 fatcat:gtmrw3egxrggtfo4csxnmsnxbq

An exact solution approach based on column generation and a partial-objective constraint to design a cellulosic biofuel supply chain

Heungjo An, Wilbert E. Wilhelm
2014 Computers and Chemical Engineering  
An embedded structure can be transformed to a generalized minimum cost flow problem, which is used as a sub-problem in a column generation approach, to solve the linear relaxation of the mixed-integer  ...  This study proposes a dynamic programming algorithm to solve the sub-problem in O(m) time, generating improving pathflows.  ...  Liang and Wilhelm (2010) generalized extra dual cuts, noting that inserting a polynomial number of extra dual cuts into RMP upon initialization restricts the dual space, potentially accelerating CG convergence  ... 
doi:10.1016/j.compchemeng.2014.07.011 fatcat:pygztdb6ibcbzg5uhqdlnamzgu

Routing Trains Through Railway Junctions: A New Set-Packing Approach

Richard Lusby, Jesper Larsen, David Ryan, Matthias Ehrgott
2011 Transportation Science  
To exploit the structure of the problem we present a solution procedure which entails solving the dual of this formulation through the dynamic addition of violated cuts (primal variables).  ...  A discussion of the variable (train path) generation phase, as well as an efficient pricing routine in which these variables are represented by tree structures is also included.  ...  Providing that they represent feasible paths through the junction, they are nothing more than extra columns in the model.  ... 
doi:10.1287/trsc.1100.0362 fatcat:svghgsnw3zg5jkeusdyiygplpm

Interior point stabilization for column generation

Louis-Martin Rousseau, Michel Gendreau, Dominique Feillet
2007 Operations Research Letters  
Interior point stabilization is an acceleration method for column generation algorithms.  ...  The method is applied to the case of the vehicle routing problem with time windows.  ...  Typically, the branching procedure starts when the root node has been solved and thus a sufficiently large number of columns (dual cuts) have been generated.  ... 
doi:10.1016/j.orl.2006.11.004 fatcat:c4fkzvikkra4fpbd5odbrbp5ay

Functionality-Based Processing-In-Memory Accelerator for Deep Convolutional Neural Networks

Min-Jae Kim, Jeong-Geun Kim, Su-Kyung Yoon, Shin-Dug Kim
2021 IEEE Access  
In this work, we propose a functionality-based PIM accelerator for DCNNs. We design several modules in addition to the conventional PIM system based on a hybrid memory cube (HMC).  ...  Third, we compose dual prefetchers that can deal with DCNN's memory access patterns, thereby reducing the system's overall latency.  ...  SHARED CACHE Owing to energy limitations of 3D memory, conventional PIM cores cannot be used as general-purpose cores; they are restricted to simple atomic cores.  ... 
doi:10.1109/access.2021.3122818 fatcat:eer2kddywje7fjugcud5uokulu

Dual Inequalities for Stabilized Column Generation Revisited

Timo Gschwind, Stefan Irnich
2016 INFORMS journal on computing  
Dual-optimal inequalities for stabilized column generation.  ...  We also suggest the dynamic addition of violated dual inequalities in a cutting-plane fashion and the use of dual inequalities that are not necessarily (deep) DOIs.  ...  The additional use of dynamically generated DI saves an extra 17% of the computation time. The pure dynamic generation even results in a slightly slower overall algorithm than the static version.  ... 
doi:10.1287/ijoc.2015.0670 fatcat:nm74jopbhbf6bcgrxcf75o5x2q

A New Combination of Lagrangean Relaxation, Dantzig-Wolfe Decomposition and Benders Decomposition Methods for Exact Solution of the Mixed Integer Programming Problems

Hadi Mohammadi, Esmaile Khorram
2019 Communications in Mathematics and Applications  
decomposition and Benders decomposition methods are used in order to reinforce bounds and to speed up convergence.  ...  The basic idea for this technique is the generation of suitable upper and lower bounds for the optimal value of the original problem at each iteration.  ...  Furthermore, they suggested, for the problems that feasibility cuts are considerably being generated more than the optimality cuts, an extra cut in order to restrict the value of the master problem [20  ... 
doi:10.26713/cma.v10i3.1116 fatcat:akrhvoo5rnbrhihhl5gs6hxhjm

Vehicle Fleet Sizing, Positioning and Routing Problem with Stochastic Customers [article]

David Corredor-Montenegro and Maria Jose Consuegra-Laino and Alfaima Lucía Solano-Blanco and Camilo Gómez
2021 arXiv   pre-print
By using acceleration techniques we obtain solutions within 1 to 6 hours, reasonable times considering the strategic nature of the decision.  ...  For the ex-post evaluation, we solve 75% of the instances in less than 3 minutes, meaning that the methodology used to solve the MDVRP is well suited for daily operation.  ...  Column generation Auxiliary problem (Route Generator) The purpose of this section is to present how given a depot k ∈ H and some dual vectors π and λ a route r ∈ R k (ω) with minimum reduced costc r is  ... 
arXiv:2109.08114v3 fatcat:euqd2hkcqjcdlpt4tdpa7pnxai

Communication-Constrained Expansion Planning for Resilient Distribution Systems [article]

Geunyeong Byeon and Pascal Van Hentenryck and Russell Bent and Harsha Nagarajan
2018 arXiv   pre-print
The paper proposes an exact branch-and-price algorithm for the ORDPDC which features a strong lower bound and a variety of acceleration schemes to address degeneracy.  ...  Distributed generation and remotely controlled switches have emerged as important technologies to improve the resiliency of distribution grids against extreme weather-related disturbances.  ...  As shown later on, this optimal cut is critical to link the two phases of the column generation, preventing many potential columns to be generated in the second phase. columns are more likely to enter  ... 
arXiv:1801.03520v1 fatcat:6wdixktecbgjdlcce2zfp2cbaq
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