Solving 0-1 Integer Programming Problems Arising from Large Scale Planning Models

Johnson, Ellis L.; Kostreva, Michael M.; Suhl, Uwe H.

doi:10.1287/opre.33.4.803

Cited by 100 publications

(39 citation statements)

References 15 publications

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“…A survey of general ideas for preprocessing is given in Savelsbergh (1994). Other references include Guignard and Spielberg (1981), Johnson et al (1981), Dietrich and Escudero (1990) and Hoffman and Padberg (1991).…”

Section: Lifting Using Multiple Constraintsmentioning

confidence: 99%

Linear-Programming-Based Lifting and Its Application to Primal Cutting-Plane Algorithms

Dey

Richard

2009

INFORMS Journal on Computing

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We propose an approximate lifting procedure for general integer programs. This lifting procedure uses information from multiple constraints of the problem formulation and can be used to strengthen formulations and cuts for mixed integer programs. In particular we demonstrate how it can be applied to improve Gomory's fractional cut which is central to Glover's primal cutting plane algorithm. We show that the resulting algorithm is finitely convergent. We also present numerical results that illustrate the computational benefits of the proposed lifting procedure.

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Section: Lifting Using Multiple Constraintsmentioning

confidence: 99%

Linear-Programming-Based Lifting and Its Application to Primal Cutting-Plane Algorithms

Dey

Richard

2009

INFORMS Journal on Computing

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“…[8,10,13,14]). Preprocessing attempts to improve the initial formulation by using several automatic techniques such as infeasibility and redundancy detection, variable fixing and constraint reformulation (see [3,8,9,12,14] among many others). It is well known that preprocessing techniques can considerably reduce the time required to solve large-scale integer programming problems.…”

Section: Introductionmentioning

confidence: 99%

“…In 1985, Johnson, Kostreva and Suhl introduced a more advanced procedure that makes use of information from families of pairwise disjoint packings (see [8,9]) and, in 1996, Escudero, Garín and Pérez improved this procedure allowing overlapping among certain pairs of packings (see [5,12]). This is a theoretical paper whose contribution is twofold.…”

Section: Introductionmentioning

confidence: 99%

Detecting constraint redundancy in 0-1 linear programming problems

Muñoz

2001

RMTA

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ResumenEn este trabajo se presenta un procedimiento de obtención de cotas superiores para una función lineal a partir de ciertas familias de empaquetamientos, cubrimientos y conjuntos ordenados especiales. Asimismo, se presenta un nuevo método de detección de restricciones redundantes en problemas de programación lineal 0-1 basado en dichas cotas que permite considerar conjuntamente varias restricciones. Además, se muestra una situación de redundancia que es detectada por este método, pero no por los métodos tradicionales, los cuales consideran las restricciones individualmente. Palabras clave:Restricciones redundantes, empaquetamientos, cubrimientos, conjuntos ordenados especiales, familias admisibles AbstractIn this paper we present a procedure for obtaining upper bounds on a linear function by means of certain families of packings, coverings and special ordered sets. We also present a new method for detecting redundant constraints in 0-1 linear programming problems based on these bounds that allows consideration of several constraints jointly. Furthermore, we show a redundancy situation which is detected by this new method, but not by the traditional methods, which consider the constraints individually.

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“…In [18], coping with natural drainage networks, it is showed that fractal and multifractal properties evolve from arbitrary initial conditions by minimizing the local and global rates of energy expenditure in the system. [30] However, in the general case, the branch and bound technique [19,20,21,22] is usually considered. The basic concept underlying this technique is to divide and conquer.…”

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confidence: 99%

Agent preferences and the topology of networks

Cajueiro¹

2005

Phys. Rev. E

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In this paper, a new framework to study weighed networks is introduced. The idea behind this methodology is to consider that each node of the network is an agent that desires to satisfy his/her preferences in an economic sense. Moreover, the formation of a link between two agents depends on the benefits and costs associated to this link. Therefore, an edge between two given nodes will only arise if the tradeoff between satisfaction and cost for building it is jointly positive. Using a computational framework, I intend to show that depending on the agents combination of benefits and costs, some very well known networks can naturally arise.PACS numbers: During recent years, one of the main issues of the statistical physics literature has been the study of dynamic systems such as airports, wireless links, financial institutions, web pages and other communication networks and social networks that may be described by complex weblike structures [24].On one hand, several models such as small world networks [1,2] and free scale networks [3] have been introduced to specially accommodate the particularities of these structures that could not be modeled by the seminal well known random graphs [4]. One should notice that although most attempts have been devoted to the study of unweighed undirected networks as the ones presented in [1,3], recently some researchers have also introduced models to deal with undirected weighted networks [5] and also directed digraphs [6].On the other hand, several measures have been presented aiming at characterizing the properties of these networked systems, for instance, characteristic path length [7] [11]. The main advantage of using these measures to analyze these complex structures is the ability to compare different systems with each other and also to develop a unified theory to approach these systems. This paper focuses particularly on undirected weighted graphs. It proposes another way based on economic and decision theory to cope with these systems. I suppose that each node of the network is an agent [25] that has his/her own preferences and is "starving" to maximize them. Since all agents in the network will interact in order to maximize their preferences, an edge between two given nodes will only arise if the tradeoff between satisfaction and cost for building it is jointly positive. It is assumed that this happens when the benefit brought to an agent is greater than his own cost and the cost left by the other agent (that sometimes is zero). Therefore, if the benefits brought to the agents by the edge are positive enough to compensate the cost of construction, then the edge will exist. This makes sense if one considers that a connection between agents always brings some kind of benefits, but the connection sometimes does not exist in a given network because of the high costs involved.This tradeoff just presented above is very related to the formalism developed by [8,9] since the authors also seek a tradeoff between satisfaction (measured in a very specific way as efficiency of commun...

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Solving 0-1 Integer Programming Problems Arising from Large Scale Planning Models

Cited by 100 publications

References 15 publications

Linear-Programming-Based Lifting and Its Application to Primal Cutting-Plane Algorithms

Linear-Programming-Based Lifting and Its Application to Primal Cutting-Plane Algorithms

Detecting constraint redundancy in 0-1 linear programming problems

Agent preferences and the topology of networks

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