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Branch-and-cut and Branch-and-Cut-and-Price Algorithms for Solving Vehicle Routing Problems [PDF]

, 2011
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Geometry of branch cuts

ACM Communications in Computer Algebra, 2011
The word ‘Simplification’ is often used in Computer Algebra. However, the task is not simple even with the aids of modern Computer Algebra Systems (CASs). Not only ones face questions such as ‘is expression f simpler than expression g?’, but many well-known formulae are not true on some points, lines or regions due to the fact that the elementary ...
Nalina Phisanbut, Russell J. Bradford, James H. Davenport   +2 more
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Branch-and-Cut

2010
This chapter focuses on the approach for solving the LOP to optimality which can currently be seen as the most successful one. It is a branch-and-bound algorithm, where the upper bounds are computed using linear programming relax- ations.
Rafael Martí, Gerhard Reinelt
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Branch cuts in the phase function

Applied Optics, 1992
It is shown that, when the scalar field associated with the propagation of a distorted wave function has nulls in its intensity pattern, the phase function that goes with that scalar field has branch points at the location of these nulls and that there are unavoidable 2pi discontinuities across the associated branch cuts in the phase function.
D L, Fried, J L, Vaughn
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Branch and cut algorithms

1996
Abstract As is frequently the case for MIP, instead of attempting to optimize (1.3) directly over P, it may be advantageous to divide that region into a finite number of smaller regions and optimize the objective function over each smaller region individually.
Abilio Lucena, John E Beasley
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Branch cuts in computer algebra

Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '94, 1994
Most computer algebra systems provide little assistance in working with expressions involving functions with complex branch cuts. Worse, by their ignorance of the existence of branch cuts, algebra systems sometimes simplify complex expressions incorrectly.
Adam Dingle, Richard J. Fateman
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Cutting planes for branch‐and‐price algorithms

Networks, 2011
AbstractThis article presents a general framework for formulating cutting planes in the context of column generation for integer programs. Valid inequalities can be derived using the variables of an equivalent compact formulation (i.e., the subproblem variables) or the master problem variables.
Desaulniers, Guy, Desrosiers, Jacques, Spoorendonk, Simon   +2 more
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Branch-cut algorithm for optical phase unwrapping

Optics Letters, 2015
In this Letter, a proposal addressing the problem of two-dimensional phase unwrapping based on the theory of residues is presented. Here, wrapped phase maps with shifted phase jumps are used to balance residue charges. With this approach, we seek to minimize processing time and residue connection, which is essential in the development of branch-cut ...
J C, de Souza, M E, Oliveira, P A M, dos Santos   +2 more
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