Model Building in Linear and Integer Programming

Williams, H. Paul

doi:10.1007/978-3-642-82450-0_2

Cited by 218 publications

(450 citation statements)

References 29 publications

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“…Because by definition only two adjacent variables can have nonzero values, setting the sum of the SOS variables equal to one provides interpolation along these points. Williams [36] provides a comprehensive explanation of the basic formulation possibilities: Nemhauser and Wolsey [37] describe potential solution algorithms; and Jeroslow [38] goes into more detail with respect to mixed integer formulations. Formulating the cost curve of technological learning using an SOS-2 formulation includes the following steps:…”

Section: C1mentioning

confidence: 99%

Endogenized technological learning in an energy systems model

Messner

1997

Journal of Evolutionary Economics

210

117

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Section: C1mentioning

confidence: 99%

Endogenized technological learning in an energy systems model

Messner

1997

Journal of Evolutionary Economics

210

117

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“…This type of model contains logical variables, dynamics that include continuous and binary variables, and constraints. The general form of MLD models (Williams, 1993) in discrete time can be presented as follows: The auxiliary variables are introduced during the translation of propositional logic into linear inequalities (Figure 1). …”

Section: Mld Formalismmentioning

confidence: 99%

Modelling and predictive control of an inverted pendulum system by MLD approach: multivariable case

Saidi

Hammi

Douik

2017

IJMIC

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This paper deals with a class of hybrid systems that is presented by mixed logical dynamical (MLD) formalism. This approach is well-adapted to hybrid systems, particularly because of its ability not only to model systems involving continuous and discrete dynamics under constraints, but also to address several issues such as model predictive control (MPC) of this class of systems. This approach will be illustrated by the multivariable modelling of the inverted pendulum system. Therefore, the resultant system is well-posed for MPC strategy. Simulations were effected using the HYSDEL compiler to illustrate the efficiency of this formalism.

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“…A standard way of linearizing these constraints (e.g., [35]) is to introduce a parameter, denote by M , and reformulate (13) by the following linear inequalities. The parameter M is chosen to be large enough such that the inequality has no effect if z ij = 0.…”

Section: The Pricing Problemmentioning

confidence: 99%

Joint routing and scheduling optimization in arbitrary ad hoc networks: Comparison of cooperative and hop-by-hop forwarding

Capone

Gualandi

Yuan³

2011

Ad Hoc Networks

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Cooperation schemes form a key aspect of infrastructure-less wireless networks that allow nodes that cannot directly communicate to exchange information through the help of intermediate nodes. The most widely adopted approach is based on hop-by-hop forwarding at the network layer along a path to destination. Cooperative relaying brings cooperation to the physical layer in order to fully exploit wireless resources. The concept exploits channel diversity by using multiple radio units to transmit the same message. The underlying fundamentals of cooperative relaying have been quite well-studied from a transmission efficiency point of view, in particular with a single pair of source and destination. Results of its performance gain in a multi-hop networking context with multiple sources and destinations are, however, less available. In this paper, we provide an optimization approach to assess the performance gain of cooperative relaying vis-a-vis conventional multi-hop forwarding under arbitrary network topology. The approach joint optimizes packet routing and transmission scheduling, and generalizes classical optimization schemes for non-cooperative networks. We provide numerical results demonstrating that the gain of cooperative relaying in networking scenarios is in general rather small and decreases when network connectivity and the number of traffic flows increase, due to interference and resource reuse limitations. In addition to quantifying the performance gain, our approach leads to a new framework for optimizing routing and scheduling in cooperative networks under a generalized Spacial Time Division Multiple Access (STDMA) scheme.Original Publication: Antonio Capone, Stefano Gualandi and Di Yuan, Joint routing and scheduling optimization in arbitrary ad hoc networks: Comparison of cooperative and hop-by-hop forwarding, 2011, Ad hoc networks, (9), 7, 1256-1269. http://dx.doi.org/10.1016/j.adhoc.2011.02.002 Copyright: Elsevier Science B. V., Amsterdam http://www.elsevier.com

show abstract

Model Building in Linear and Integer Programming

Cited by 218 publications

References 29 publications

Endogenized technological learning in an energy systems model

Endogenized technological learning in an energy systems model

Modelling and predictive control of an inverted pendulum system by MLD approach: multivariable case

Joint routing and scheduling optimization in arbitrary ad hoc networks: Comparison of cooperative and hop-by-hop forwarding

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