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Reformulation and Decomposition of Integer Programs [chapter]

François Vanderbeck, Laurence A. Wolsey
2009 50 Years of Integer Programming 1958-2008  
In this survey we examine ways to reformulate integer and mixed integer programs.  ...  First we cover in detail reformulations based on decomposition, such as Lagrangean relaxation, Dantzig-Wolfe and the resulting column generation and branch-and-price algorithms.  ...  Polyhedra, Reformulation and Decomposition Introduction Given a problem that has been formulated as a linear integer program, we are interested in finding reformulations (alternative problem descriptions  ... 
doi:10.1007/978-3-540-68279-0_13 fatcat:ozxqnowzqzdvzjfmsc2vfswjca

Decomposition and reformulation of integer linear programming problems

Fabio Furini
2011 4OR  
Wolsey : Reformulation and Decomposition of Integer Programs 50 s of Integer Programming 1958-2008 From the Early s to the State-of-the- Art, Springer, Berlin Heidelberg, 2010, 431–502 [42] F  ...  v vi KeywordsAbstract This thesis deals with an investigation of Decomposition and Reformulation to solve Integer Linear Programming Problems.  ... 
doi:10.1007/s10288-011-0178-4 fatcat:cp6c7sxqg5gudftye4ek5bedo4

A projection-based reformulation and decomposition algorithm for global optimization of a class of mixed integer bilevel linear programs

Dajun Yue, Jiyao Gao, Bo Zeng, Fengqi You
2018 Journal of Global Optimization  
We propose an extended variant of the reformulation and decomposition algorithm for solving a special class of mixed-integer bilevel linear programs (MIBLPs) where continuous and integer variables are  ...  By using the reformulation and decomposition scheme, an MIBLP is first converted into its equivalent single-level formulation, then computed by a column-and-constraint generation based decomposition algorithm  ...  [26] proposed a cut-generation algorithm and row-andcolumn generation framework. Zeng and An [22] proposed a reformulation and decomposition algorithm.  ... 
doi:10.1007/s10898-018-0679-1 fatcat:da5xs3mdtba7ritjijrczb4gyq

Mixed Integer Reformulations of Integer Programs and the Affine TU-dimension of a Matrix [article]

Jörg Bader, Robert Hildebrand, Robert Weismantel, Rico Zenklusen
2017 arXiv   pre-print
We study the reformulation of integer linear programs by means of a mixed integer linear program with fewer integer variables.  ...  We exhibit examples that demonstrate how integer programs can be reformulated using far fewer integer variables.  ...  Their detailed comments and suggestions on an earlier version of the manuscript led to enhancements on the general structure of our paper, as well as greatly improved the paper in many ways.  ... 
arXiv:1508.02940v3 fatcat:6w3po2gaujet3fmvzljjrmkope

Automatic Decomposition and Branch-and-Price—A Status Report [chapter]

Marco E. Lübbecke
2012 Lecture Notes in Computer Science  
We provide an overview of our recent efforts to automatize Dantzig-Wolfe reformulation and column generation/branch-and-price for structured, large-scale integer programs.  ...  A focus is on detecting structures in integer programs which are amenable to a Dantzig-Wolfe reformulation. We give computational results and discuss future research topics.  ...  for integer programs."  ... 
doi:10.1007/978-3-642-30850-5_1 fatcat:3znnxk33yjb3vdsi4jfqoxuddm

Page 3486 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
Summary: “Dantzig-Wolfe decomposition as applied to an inte- ger program is a specific form of problem reformulation that aims at providing a tighter linear programming relaxation bound.  ...  In this paper, we propose to base the Dantzig-Wolfe decomposition of an integer program on the discretization of the integer poly- hedron associated with a subsystem of constraints (as opposed to its convexification  ... 

Linear Reformulations of Integer Quadratic Programs [chapter]

Alain Billionnet, Sourour Elloumi, Amélie Lambert
2008 Communications in Computer and Information Science  
Our new approach, BIL (Binary Integer Linearization), consists in reformulating (QP ) into a particular quadratic integer program where each quadratic term is the product of an integer variable by a 0-  ...  However, this method, that we denote BBL (Binary Binary Linearization), leads to a quadratic program with a large number of variables and constraints.  ...  Concluding remarks In this paper, we have presented several linear reformulations of linearly constrained quadratic integer programs.  ... 
doi:10.1007/978-3-540-87477-5_5 fatcat:fgbk6xrotrfo5a67umukaxmhla

Page 1000 of The Journal of the Operational Research Society Vol. 57, Issue 8 [page]

2006 The Journal of the Operational Research Society  
Summary and future work This work presents a methodology based on Schur’s decomposition and SOS type 2 variables, to approximate bilinear problems in mathematical programming by mixed integer linear programs  ...  Model Building in Mathematical Programming. John Wiley and Sons Inc.: New York. Wilson JM (1990). Generating cuts in integer programming with families of special ordered sets.  ... 

Computational management science special issue on "Robust Optimization and Applications"

Erick Delage, Dan Iancu
2016 Computational Management Science  
solution schemes for solving static robust optimization problems: schemes based on reformulation using duality theory and schemes based on decomposition techniques and constraint generation.  ...  This question becomes especially relevant when binary decision variables are involved, since it allows employing mixed integer linear programming solvers instead of their second-order conic programming  ...  The authors show that a conservative approximation of the robust problem can be reformulated as a mixed integer linear programming problem, which can be solved using commercially available software.  ... 
doi:10.1007/s10287-016-0252-7 fatcat:4shdqg6srzgt7jezbiqwawjxgq

Approach to large distribution network optimisation using modern implementation of benders decomposition

Nathan D'Addio, Anula Abeygunawardana, Michael Forbes, Gerard Ledwich, Mehdi Shafiei
2017 CIRED - Open Access Proceedings Journal  
However, there is a major void in the literature surrounding applications of modern problem decomposition and reformulation techniques from operations research to solve EDNEPPs.  ...  Recently, many new problem reformulation and decomposition techniques have been reported to cope with large-scale optimisation problems.  ...  Recently, in operation research lecture, new problem reformulation and decomposition techniques have been proposed to deal with challenging integer-programming problems.  ... 
doi:10.1049/oap-cired.2017.0727 fatcat:xf5gofzuqbcsrc6cpyskmhqlw4

A Lagrange Relaxation Based Approach to Solve a Discrete-Continous Bi-Level Model

Zaida E. Alarcón-Bernal, Ricardo Aceves-García
2019 Open Journal of Optimization  
For the application of the method, the two-level problem is reformulated using the Karush-Kuhn-Tucker conditions.  ...  These problems are considered as the generalization of the Stackelberg problem [1] for non-cooperative games. The bilevel programming problem can be formulated as:  ...  Acknowledgements We thank the National Council of Science and Technology (CONACYT) of Mexico for the grant and the National Autonomous University of Mexico for the resources provided for the development  ... 
doi:10.4236/ojop.2019.83009 fatcat:5blyhmwqtne6xpjlbq6vmkvd2q

Hybrid Quantum Benders' Decomposition For Mixed-integer Linear Programming [article]

Zhongqi Zhao, Lei Fan, Zhu Han
2021 arXiv   pre-print
The Benders' decomposition algorithm is a technique in mathematical programming for complex mixed-integer linear programming (MILP) problems with a particular block structure.  ...  The strategy of Benders' decomposition can be described as a strategy of divide and conquer.  ...  MILP AND BENDERS' DECOMPOSITION BASICS A. Mixed-integer Linear Programming MILP has been widely adopted optimization problems that include but are not limited to communication and networks.  ... 
arXiv:2112.07109v2 fatcat:p63gen4wmnau5dvwsstahqssrm

A number theoretic reformulation and decomposition method for integer programming

Laurence A. Wolsey
1974 Discrete Mathematics  
Integer prcgramsning problems. and especially knapsack and finite abelian group problems, can be exactly replar.ed by equivalent problems of "smaller" size.  ...  This reformulation theoretically provides a new m :thod of solution for such problems, but the main advantages lie in reducing coeffitient magnierlldes and in removing selected constraints, while a disadvantage  ...  Conclusions V~Aous reformulations of integer programming problems have been suggested in recent years, and to date it is not clear which merit further investigation.  ... 
doi:10.1016/0012-365x(74)90046-6 fatcat:abdc2viukbg7ljoqss5b4vlk3q

Mixed integer optimal compensation: Decompositions and mean-field approximations

D. Bauso, Quanyan Zhu, T. Basar
2012 2012 American Control Conference (ACC)  
This last reformulation step mirrors a standard procedure in mixed integer programming.  ...  Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon.  ...  Mixed integer linear program and exact solution.  ... 
doi:10.1109/acc.2012.6315277 fatcat:reqx3hhwf5fn7cbnu3wxbe5t2y

Comparison of Exact Algorithms for Rectilinear Distance Single-Source Capacitated Multi-Facility Weber Problems

2010 Journal of Computer Science  
The first algorithm, decomposition algorithm, uses explicit branching on the allocation variables and then solve for location variable corresponding to each branch as the original Mixed Integer Programming  ...  The problem is considered as a p-median problem and the original formulation is transformed to a binary integer programming problem.  ...  The classical exact algorithm for Eq. 3 which is an integer programming problem is a branch-and-bound algorithm.  ... 
doi:10.3844/jcssp.2010.112.116 fatcat:4cmmheqkmjgd7pg2dsb3xpwmx4
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