Logical Reduction Methods in Zero-One Programming—Minimal Preferred Variables

Guignard, Monique; Spielberg, Kurt

doi:10.1287/opre.29.1.49

Cited by 76 publications

(28 citation statements)

References 16 publications

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“…This behavior is usually denoted double contracting [66,67,150] to contrast it with the behavior of branching on y (only up-branching fixes other variables), which is denoted single contracting. The fact that double contracting incremental formulations result in solves with fewer branch-and-bound nodes was confirmed computationally in [155,157].…”

Section: Incremental Formulationsmentioning

confidence: 99%

Mixed Integer Linear Programming Formulation Techniques

Vielma¹

2015

SIAM Rev.

258

143

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1. Introduction. Throughout more than 50 years of existence, mixed integer linear programming (MIP) theory and practice have been significantly developed, and it is now an indispensable tool in business and engineering [68,94,104]. Two reasons for the success of MIP are linear programming (LP) based solvers and the modeling flexibility of MIP. We now have several extremely effective state-of-the-art solvers [82,69, 52,171] that incorporate many advanced techniques [1,2,25,23,92,112,24] and, since its early stages, MIP has been used to model a wide range of applications [44,45].While in many cases constructing valid MIP formulations is relatively straightforward, some care should be taken in this construction as certain formulation attributes can significantly reduce the effectiveness of LP-based solvers. Fortunately, constructing formulations that behave well with state-of-the-art solvers can usually be achieved by following simple guidelines described in standard textbooks. However, more advanced techniques can often perform significantly better than textbook formulations and are sometimes a necessity. The main objective of this survey is to summarize the state of the art of such formulation techniques for a wide range of problems. To keep the length of this survey under control, we concentrate on formulations for sets of a mixed integer nature that require both integer constrained and continuous variables. We hence purposefully place less emphasis on some related areas such as combinatorial optimization, quadratic and polynomial 0/1 optimization, and polyhedral approximations of convex sets. These topics are certainly areas of important and active research, so we cover them succinctly in section 12.

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Section: Incremental Formulationsmentioning

confidence: 99%

Mixed Integer Linear Programming Formulation Techniques

Vielma¹

2015

SIAM Rev.

258

143

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“…In this regard, it is sometimes advantageous to use a model with a larger number of integer variables, a larger number of constraints, or both. Discussions of alternative formulation approaches are given in Guignard and Spielberg (1981) and Williams (1985), and a description of approaches to automatic reformulation or preprocessing is given in Anderson and Anderson (1995), Atamturk and Savelsbergh (2000), Brearley et al (1975), Hoffman and Padberg (1991), Roy and Wolsey (1987), and Savelsbergh (1994).…”

Section: Automatic Reformulationmentioning

confidence: 99%

Identity Matrix

2013

Encyclopedia of Operations Research and Management Science

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“…We will briefly discuss a number of these techniques here and mention how they can be controlled in modern IP solvers. We refer the reader to [3,28,31,53] for detailed explanation of preprocessing techniques.…”

Section: Preprocessingmentioning

confidence: 99%

Integer-Programming Software Systems

2005

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Abstract. Recent developments in integer-programming software systems have tremendously improved our ability to solve large-scale instances. We review the major algorithmic components of state-of-the-art solvers and discuss the options available to users to adjust the behavior of these solvers when default settings do not achieve the desired performance level. Furthermore, we highlight advances towards integrated modeling and solution environments. We conclude with a discussion of model characteristics and substructures that pose challenges for integer-programming software systems and a perspective on features we may expect to see in these systems in the near future.

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Logical Reduction Methods in Zero-One Programming—Minimal Preferred Variables

Cited by 76 publications

References 16 publications

Mixed Integer Linear Programming Formulation Techniques

Mixed Integer Linear Programming Formulation Techniques

Identity Matrix

Integer-Programming Software Systems

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