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Symmetry in Integer Linear Programming [chapter]

François Margot
<span title="2009-11-06">2009</span> <i title="Springer Berlin Heidelberg"> 50 Years of Integer Programming 1958-2008 </i> &nbsp;
An integer linear program (ILP) is symmetric if its variables can be permuted without changing the structure of the problem.  ...  This paper reviews techniques developed to take advantage of the symmetry in an ILP during its solution.  ...  As pointed out in Section 3, automatic symmetry detection is a difficult problem in itself.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-68279-0_17">doi:10.1007/978-3-540-68279-0_17</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vzpul5elmfdo3dt4dbflnbxx5u">fatcat:vzpul5elmfdo3dt4dbflnbxx5u</a> </span>
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Symmetries in Linear and Integer Programs [article]

R. Bödi, K. Herr
<span title="2009-08-23">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint.  ...  We show that for any linear program there exists an optimal solution in the fixed point set of its symmetry group.  ...  In general, a linear program and the associated integer program need not have the same symmetries. The following two examples illustrate this fact.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0908.3329v1">arXiv:0908.3329v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zjnks62qj5fwvppsyqxvadkywa">fatcat:zjnks62qj5fwvppsyqxvadkywa</a> </span>
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A Multiobjective Integer Linear Programming Model for the Cross-Track Line Planning Problem in the Chinese High-Speed Railway Network

Han, Nie, Fu, Gong, Wang
<span title="2019-05-15">2019</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nzoj5rayr5hutlurimhzyjlory" style="color: black;">Symmetry</a> </i> &nbsp;
In this study, we developed a multiobjective integer programming model to produce a balanced cross-track line plan by combining individual-track high-speed trains (ITHSTs) into CTHSTs, which is a discrete  ...  Thus, the main challenge in cross-track line planning is looking for a symmetry point between passenger transportation and disadvantages of running CTHSTs, which are two conflicting aspects.  ...  linear programming model.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/sym11050670">doi:10.3390/sym11050670</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3b4eeellknasnj7xr77zjiec2u">fatcat:3b4eeellknasnj7xr77zjiec2u</a> </span>
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Exploiting Symmetries in Polyhedral Computations [article]

Achill Schürmann
<span title="2014-06-20">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this note we give a short overview on symmetry exploiting techniques in three different branches of polyhedral computations: The representation conversion problem, integer linear programming and lattice  ...  Exploiting symmetries in integer programming is much more difficult than in linear programming.  ...  Integer linear programming is widely used in practical applications.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1406.5281v1">arXiv:1406.5281v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u2j5mvibv5dk5gvcy4wrks7vxu">fatcat:u2j5mvibv5dk5gvcy4wrks7vxu</a> </span>
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Symmetries in Integer Programs [article]

R. Bödi, K. Herr
<span title="2009-08-23">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint.  ...  We investigate the structure of integer solutions of integer programs and show that any integer program on n variables having an alternating group A_n as a group of symmetries can be solved in linear time  ...  Introduction This paper continues to investigate symmetries of linear and integer programs which we have started in [3] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0908.3331v1">arXiv:0908.3331v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3foesqqp2bb2xnxtur27mr5xmy">fatcat:3foesqqp2bb2xnxtur27mr5xmy</a> </span>
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Mini-Workshop: Exploiting Symmetry in Optimization

Volker Kaibel, Leo Liberti, Achill Schürmann, Renata Sotirov
<span title="">2010</span> <i title="European Mathematical Publishing House"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/mnv35em3uvgxdkcbx2cvykhugu" style="color: black;">Oberwolfach Reports</a> </i> &nbsp;
In recent years, several groups of researchers have independently worked on algorithmic approaches to exploit such symmetries in a variety of contexts.  ...  The workshop brought together researchers working on symmetry aspects in different areas of optimization.  ...  Symmetries in linear and integer linear programming Katrin Herr (joint work with Richard Bödi, Michael Joswig) We investigate the potential of symmetry in the context of linear and integer linear programming  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4171/owr/2010/38">doi:10.4171/owr/2010/38</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/n2zcqzooonex7d3kcknkfsxpxa">fatcat:n2zcqzooonex7d3kcknkfsxpxa</a> </span>
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Exploiting symmetry in integer convex optimization using core points

Katrin Herr, Thomas Rehn, Achill Schürmann
<span title="">2013</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/z7xgofryqjgkxjlwzlky45v4li" style="color: black;">Operations Research Letters</a> </i> &nbsp;
For symmetric integer linear programs we describe two algorithms based on this decomposition.  ...  We consider convex programming problems with integrality constraints that are invariant under a linear symmetry group.  ...  In convex, and particularly in linear programming the size of a problem formulation can be decreased if the problem formulation is invariant under a linear symmetry group.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.orl.2013.02.007">doi:10.1016/j.orl.2013.02.007</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mqkn42ziejgvngren66ull7lsy">fatcat:mqkn42ziejgvngren66ull7lsy</a> </span>
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Algorithms for highly symmetric linear and integer programs

Richard Bödi, Katrin Herr, Michael Joswig
<span title="2011-09-25">2011</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/o653fqsowvcyrhw6p4gdmpdkwm" style="color: black;">Mathematical programming</a> </i> &nbsp;
This paper deals with exploiting symmetry for solving linear and integer programming problems.  ...  Combining this approach with knowledge of the geometry of feasible integer solutions yields an algorithm for solving highly symmetric integer linear programs which only takes time which is linear in the  ...  As in the proof of Proposition 6 one can show that this linear transformation is a symmetry of the integer linear program.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10107-011-0487-6">doi:10.1007/s10107-011-0487-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wnaimntpx5c5fkhupw4dg33jda">fatcat:wnaimntpx5c5fkhupw4dg33jda</a> </span>
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Mixed integer programming

Jon Lee, Adam N. Letchford
<span title="">2007</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/s6sw62lf6zcxrghfhvjqhycu5y" style="color: black;">Discrete Optimization</a> </i> &nbsp;
Editorial Mixed integer programming The IMA Special Workshop on Mixed-Integer Programming was held in Minneapolis on July [25][26][27][28][29] 2005, at the Institute for Mathematics and its Applications  ...  We believe that these papers give an excellent 'snapshot' of the state-of-the-art in integer and mixed-integer programming, reflecting well the current trends in the field.  ...  Margot, in his paper, generalizes his group-theoretic techniques for combating symmetry in 0/1 linear programs to general integer linear programs. • Another recent development is the discovery of powerful  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.disopt.2006.10.005">doi:10.1016/j.disopt.2006.10.005</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yofa7pyiivaqfborh55fcqmy3m">fatcat:yofa7pyiivaqfborh55fcqmy3m</a> </span>
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Observing half and integer polarization vortices at band degeneracies [article]

Ang Chen, Wenzhe Liu, Yiwen Zhang, Bo Wang, Fang Guan, Xiaohan Liu, Lei Shi, Ling Lu, Jian Zi
<span title="2017-12-26">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Far-field polarization vortices were recently found on singlet bands in the momentum-space of two-dimensional photonic lattices, also known as the dark states and bound states in continuum.  ...  Half-charged vortices were generated from the Dirac points of π Berry phase and integer-charged vortices were generated from a quadratic degeneracy.  ...  Integer vortices could appear near the quadratic degeneracy while half vortices near the linear degeneracy.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1712.09296v1">arXiv:1712.09296v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6biwysur7jh4hmycok2yfo3gra">fatcat:6biwysur7jh4hmycok2yfo3gra</a> </span>
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Exploiting symmetry in computing polyhedral bounds on network coding rate regions

Jayant Apte, John Maclaren Walsh
<span title="">2015</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/mmetagdrurffnlsefei5xftbse" style="color: black;">2015 International Symposium on Network Coding (NetCod)</a> </i> &nbsp;
Herr, Symmetries in linear and integer programs, 2009.  ...  Herr, Symmetries in linear and integer programs, 2009. arXiv:0908.3329 [math.CO] / 39 / 39 Convex Hull method (CHM) Basic ideas behind CHM 4 Symmetry Exploiting CHM (symCHM) Symmetry Exploitation  ...  Restricted Symmetries A subgroup of combinatorial symmetry group:  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/netcod.2015.7176793">doi:10.1109/netcod.2015.7176793</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/netcod/ApteW15.html">dblp:conf/netcod/ApteW15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mwwya54dz5czrjfsbnzve6lsxm">fatcat:mwwya54dz5czrjfsbnzve6lsxm</a> </span>
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Global pose estimation using non-tree models

Hao Jiang, David R. Martin
<span title="">2008</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ilwxppn4d5hizekyd3ndvy2mii" style="color: black;">2008 IEEE Conference on Computer Vision and Pattern Recognition</a> </i> &nbsp;
The optimization may be expressed as an integer linear program and solved using a novel twostage relaxation scheme.  ...  exclusion constraints arising from inter-part occlusion and symmetry conditions.  ...  Optimizing the body part configuration embedded in the graph is formulated as an integer linear program and solved with a two-stage search scheme.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cvpr.2008.4587457">doi:10.1109/cvpr.2008.4587457</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cvpr/JiangM08.html">dblp:conf/cvpr/JiangM08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/itdivkcszbdhlg3u7ntvp7tssu">fatcat:itdivkcszbdhlg3u7ntvp7tssu</a> </span>
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Page 1172 of Mathematical Reviews Vol. 46, Issue 4 [page]

<span title="">1973</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Ju. 6825 On the question of the construction of supplementary restrictions in the Gomory integer linear programming method. (Russian) Ekonom. i Mat. Metody 8 (1972), 430-431.  ...  Glover, Fred 6829 | Cut search methods in integer programming. ' Math.  ... 
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Preface

A. Ridha Mahjoub, Giovanni Rinaldi, Gerhard Woeginger
<span title="2015-02-17">2015</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/o653fqsowvcyrhw6p4gdmpdkwm" style="color: black;">Mathematical programming</a> </i> &nbsp;
edition of ISCO was the second of a series of biennial conferences on combinatorial optimization with its first venue held in Hammamet, Tunisia in March 2010.  ...  Detailed information about ISCO 2012 is available in http://isco12.cs.aueb.gr/.  ...  In this paper the authors propose a modified orbital branching technique to exploit special structures in a problem's symmetry group.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10107-015-0869-2">doi:10.1007/s10107-015-0869-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/epqoua7uqbcupmakq7kurfegbm">fatcat:epqoua7uqbcupmakq7kurfegbm</a> </span>
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Symmetry in Mathematical Programming [chapter]

Leo Liberti
<span title="2011-11-15">2011</span> <i title="Springer New York"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/krxfiqil7zgqrho7rf74zzqvpm" style="color: black;">IMA Volumes in Mathematics and its Applications</a> </i> &nbsp;
We review symmetry-based analyses and methods for Linear Programming, Integer Linear Programming, Mixed-Integer Linear Programming and Semidefinite Programming.  ...  Symmetry is mainly exploited in mathematical programming in order to reduce the computation times of enumerative algorithms.  ...  Symmetry in Mixed-Integer Linear Programming.  ... 
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