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Reformulation and Decomposition of Integer Programs
[chapter]
2009
50 Years of Integer Programming 1958-2008
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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
2011
4OR
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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
2018
Journal of Global Optimization
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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]
2017
arXiv
pre-print
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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]
2012
Lecture Notes in Computer Science
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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
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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]
2008
Communications in Computer and Information Science
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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
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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"
2016
Computational Management Science
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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
2017
CIRED - Open Access Proceedings Journal
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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
2019
Open Journal of Optimization
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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]
2021
arXiv
pre-print
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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
1974
Discrete Mathematics
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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
2012
2012 American Control Conference (ACC)
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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
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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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