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Mixed-Integer Cuts from Cyclic Groups

2006
*
Mathematical programming
*

Saturni,

doi:10.1007/s10107-006-0726-4
fatcat:tzs5nrq5u5fuxbetirdlh6jbju
*Mixed*-*Integer**Cuts**from**Cyclic**Groups*... of the following master*cyclic**group*polyhedron: T (k, r) = conv{t ∈ Z k−1 + : k−1 i=1 (i/k) · t i ≡ r/k (mod 1)} (4) where k ≥ 2 (*group*order) and r ∈ {1, · · · , k − 1} are given*integers*• The space ...##
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Mixed-Integer Cuts from Cyclic Groups
[chapter]

2005
*
Lecture Notes in Computer Science
*

of the following master

doi:10.1007/11496915_1
fatcat:ghakmopjfbf3faiwuxdj6zyba4
*cyclic**group*polyhedron: T (k, r) = conv{t ∈ Z k−1 + : k−1 i=1 (i/k) · t i ≡ r/k (mod 1)} (4) where k ≥ 2 (*group*order) and r ∈ {1, · · · , k − 1} are given*integers*• The space ... separation problem is embedded into the original ILP model • Letchford and Lodi (2002) and Cornuejols, Li and Vandenbussche (2003) address specific subfamilies of*cyclic*-*group**cuts*• To our knowledge ...##
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On a generalization of the master cyclic group polyhedron

2008
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Mathematical programming
*

Finally, we study the

doi:10.1007/s10107-008-0252-7
fatcat:t65ksqnjr5hxxatqd2y4nz6nwq
*mixed*-*integer*extension of the MEP and present an interpolation theorem that produces valid inequalities for general*Mixed**Integer*Programming Problems using facets of the MEP. ... We study the Master Equality Polyhedron (MEP) which generalizes the Master*Cyclic**Group*Polyhedron and the Master Knapsack Polyhedron. ... The Gomory*mixed*-*integer**cut*(also known as the*mixed*-*integer*rounding (MIR) inequality) can be derived*from*a facet of P (n, r) [10] . ...##
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Cyclic group and knapsack facets

2003
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Mathematical programming
*

Any

doi:10.1007/s10107-003-0390-x
fatcat:jxwdb56vqvfzxetu3a2b72kjhe
*integer*program may be relaxed to a*group*problem. ... We define the master*cyclic**group*problem and several master knapsack problems, show the relationship between the problems, and give several classes of facet-defining inequalities for each problem, as ... For example, for n ≤ 7, every*cyclic**group*facet, except one, is either a*mixed**integer**cut*itself or comes*from*one or more mappings of a*mixed**integer**cut*. ...##
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On the strength of Gomory mixed-integer cuts as group cuts

2007
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Mathematical programming
*

Further, it is well-known that GMI

doi:10.1007/s10107-007-0179-4
fatcat:x7grbjlyuzgztordwoimo2m6ki
*cuts*can be derived*from*facets of Gomory's master*cyclic**group*polyhedron and its*mixed*-*integer*extension studied by Gomory and Johnson. ... Gomory*mixed*-*integer*(GMI)*cuts*generated*from*optimal simplex tableaus are known to be useful in solving*mixed*-*integer*programs. ... GMI*cuts*for*mixed*-*integer*programs can similarly be derived*from*the*mixed*-*integer*extension of the master*cyclic**group*polyhedron; see Gomory and Johnson [18] . ...##
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Page 4241 of Mathematical Reviews Vol. , Issue 2004e
[page]

2004
*
Mathematical Reviews
*

The paper describes a theory that allows one to automatically derive many

*cutting*planes for*integer*or*mixed**integer*programs*from*rows of a tableau belonging to a basic feasible solution of the LP relaxation ...*From*any facet of the master polyhedron one can derive a valid inequality in the non-basic variables cf the original (*mixed*)*integer*program that*cuts*off the present basic feasible solution. ...##
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Valid inequalities based on simple mixed-integer sets

2005
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Mathematical programming
*

Facets of this polyhedron give strong valid inequalities for general

doi:10.1007/s10107-005-0599-y
fatcat:4rtsqasdafhqbi7vqq3smgbc7i
*mixed*-*integer*sets, such as the well-known Gomory*mixed*-*integer**cut*. ... These inequalities also define facets of the master*cyclic**group*polyhedron of Gomory. ... The well-known Gomory*mixed*-*integer**cut*(GMIC) can be derived*from*a facet of P (n, r) [10] . ...##
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Valid Inequalities Based on Simple Mixed-Integer Sets
[chapter]

2004
*
Lecture Notes in Computer Science
*

Facets of this polyhedron give strong valid inequalities for general

doi:10.1007/978-3-540-25960-2_3
fatcat:oedi6x36prbhpaps6reyo77ifa
*mixed*-*integer*sets, such as the well-known Gomory*mixed*-*integer**cut*. ... These inequalities also define facets of the master*cyclic**group*polyhedron of Gomory. ... The well-known Gomory*mixed*-*integer**cut*(GMIC) can be derived*from*a facet of P (n, r) [10] . ...##
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Profit-based FMS dynamic part type selection over time for mid-term production planning

1992
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European Journal of Operational Research
*

At the upper level, a large-scale linear programming Master Problem is solved, the columns of which are generated by solving a nonlinear,

doi:10.1016/0377-2217(92)90054-d
fatcat:b4zkubuouvbqvjst3swb6si4qa
*mixed*-*integer*, profit-based part type selection subproblem that ... Each*cyclic*schedule allows a subset of parts of different types to be released periodically in appropriate production ratios. ... Acknowledgments Kathy Stecke would like to acknowledge a Summer Grant*from*the Graduate School of Business at The University of Michigan and Eugeniusz Toczytowski acknowledges a Grant*from*the Polish Science ...##
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Throughput-Optimal Sequences for Cyclically Operated Plants

2008
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Discrete event dynamic systems
*

The resulting scheduling problem is solved by deriving a

doi:10.1007/s10626-008-0038-3
fatcat:kzf7ux236jhfzkbmduz44wtm74
*mixed**integer*optimization problem*from*a discrete event model. ... In*cyclic*operation, a large number of entities is processed in an identical time scheme. ... Acknowledgement The authors gratefully acknowledge funding by "Deutsche Forschungsgemeinschaft (DFG)" via the DFG-Forschergruppe 468 "Methods*from*Discrete Mathematics for the Synthesis and Control of ...##
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Page 1636 of Mathematical Reviews Vol. , Issue 88c
[page]

1988
*
Mathematical Reviews
*

The

*mixed**integer**cyclic**group*problem is then considered and a dual problem given. ... A generalized method of marks for a problem of*integer*linear programming. Soviet J. Comput. Systems Sci. 24 (1986), no. 5, 90-97 (1987); translated*from*Izv. Akad. Nauk SSSR Tekhn. ...##
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New inequalities for finite and infinite group problems from approximate lifting

2008
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Naval Research Logistics
*

*mixed*-

*integer*programming problems. ... These new inequalities not only illustrate the diversity of strong inequalities for the finite and infinite

*group*problems, but also provide a large variety of new

*cutting*planes for solving

*integer*and ... These inequalities can then be used as

*cutting*planes for general

*integer*and

*mixed*-

*integer*programs. We call these

*cutting*planes

*group*

*cuts*. ...

##
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Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes
[article]

2016
*
arXiv
*
pre-print

We address this difficulty using a

arXiv:1609.02063v1
fatcat:apocqj6p5berpopi6jigpc3eym
*mixed*-*integer*programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. ... In this paper, we present a new, optimization-based method to exhibit*cyclic*behavior in non-reversible stochastic processes. ...*Mixed*-*Integer*Programming for Cycle Detection in Non-reversible Markov Processes * Introduction Simulation data stemming*from*chemical or biological processes typically lead to a huge amount of data ...##
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Mixed-Integer Programming for Cycle Detection in Nonreversible Markov Processes

2018
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Multiscale Modeling & simulation
*

We address this difficulty using a

doi:10.1137/16m1091162
fatcat:iajn7ysnwfe3xmqarqjiledbda
*mixed*-*integer*programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. ... In this paper, we present a new, optimization-based method to exhibit*cyclic*behavior in non-reversible stochastic processes. ...*Mixed*-*Integer*Programming A*mixed*-*integer*program (MIP) is an optimization problem that can be written in the form (P ) z M IP = min{c T x | Ax ≥ b, ≤ x ≤ u, x ∈ Z l × R n−l }, with objective function ...##
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Page 2420 of Mathematical Reviews Vol. , Issue 92e
[page]

1992
*
Mathematical Reviews
*

A completion of a

*cyclically*ordered*group*was constructed by the author and J. Jakubik by means of*cuts*; they proved that each*cyclically*ordered*group*has a unique completion [Czechoslovak Math. ... A*mixed*product decomposition of a di- rected*group*is an isomorphism*from*the*group*to such a*mixed*product, and the system of all*mixed*product decompositions, modulo a natural equivalence relation, ...
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