نتایج جستجو برای: optimal cuts

تعداد نتایج: 378067  

2013
Marco Molinaro Sanjeeb Dash Santanu Dey François Margot R. Ravi

Cutting planes for a mixed-integer program are linear inequalities which are satisfied by all feasible solutions of the latter. These are fundamental objects in mixed-integer programming that are critical for solving large-scale problems in practice. One of the main challenge in employing them is that there are limitless possibilities for generating cutting planes; the selection of the stronges...

Journal: :Electric Power Systems Research 2021

In this paper, we present decomposition techniques for solving large-scale instances of the security-constrained optimal power flow (SCOPF) problem with primary response. Specifically, under each contingency state, require that nodal demands are met and synchronized units generating below their limits follow a linear model The resulting formulation is mixed-integer program since response introd...

2011
Björn Lellmann Dirk Pattinson

Motivated by the fact that nearly all conditional logics are axiomatised by so-called shallow axioms (axioms with modal nesting depth ≤ 1) we investigate sequent calculi and cut elimination for modal logics of this type. We first provide a generic translation of shallow axioms to (one-sided, unlabelled) sequent rules. The resulting system is complete if we admit pseudo-analytic cut, i.e. cuts o...

Journal: :Annals OR 2012
Edmund K. Burke Jakub Marecek Andrew J. Parkes Hana Rudová

This paper describes a branch-and-cut procedure for an extension of the bounded colouring problem, generally known as curriculum-based university course timetabling. In particular, we focus on Udine Course Timetabling [di Gaspero and Schaerf, J. Math. Model. Algorithms 5:1], which has been used in Track 3 of the 2007 International Timetabling Competition. First, we present an alternative intege...

2001
Neeraj Mittal Vijay K. Garg

We generalize the notion of slice introduced in our earlier paper [6]. A slice of a distributed computation with respect to a global predicate is the smallest computation that contains all consistent cuts of the original computation that satisfy the predicate. We prove that slice exists for all global predicates. We also establish that it is, in general, NP-complete to compute the slice. An opt...

2004
A. V. Balakrishnan

Abs t r ac t . J . F . Benders devised a clever approach for exploiting the structure of mathematical programming problems with complicating variables (variables which, when temporarily fixed, render the remaining optimization problem considerably more tractable). For the class of problems specifically considered by Benders, fixing the values of the complicating variables reduces the given prob...

Journal: :Math. Program. 2008
Gérard Cornuéjols

This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these...

2012
David Bergman John N. Hooker J. N. Hooker

We explore the idea of obtaining valid inequalities from a finite-domain formulation of a problem, rather than a 0-1 formulation. A finite-domain model represents discrete choices with variables that have several possible values, as is frequently done in constraint programming. We apply the idea to graph coloring and identify facet-defining cuts that, when converted to cuts in a 0-1 model of th...

2010
Franz Wesselmann

Gomory mixed-integer cuts are an important ingredient in state-ofthe-art software for solving mixed-integer linear programs. In particular, much attention has been paid to the strengthening of these cuts. In this paper, we give an overview of existing approaches for improving the performance of Gomory mixed-integer cuts. More precisely, we consider k-cuts, combined Gomory mixed-integer cuts, re...

2012
David Bergman John N. Hooker

We explore the idea of obtaining valid inequalities for a 0-1 model from a constraint programming formulation of the problem. In particular, we formulate a graph coloring problem as a system of alldifferent constraints. By analyzing the polyhedral structure of alldiff systems, we obtain facet-defining inequalities that can be mapped to valid cuts in the classical 0-1 model of the problem. We fo...

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