Problem of finding an ordering of the nodes of a graph on a straight line, and assigning, to each edge, a location in any of the two halfplanes induced by that line, such that the number of crossings between edges is minimum.
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MREM, Discrete Recurrent Network for Optimization
Enrique Mérida-Casermeiro (University of Málaga, Spain), Domingo López-Rodríguez (University of Málaga, Spain), and Juan M. Ortiz-de-Lazcano-Lobato (University of Málaga, Spain)
Copyright: © 2009
|Pages: 9
DOI: 10.4018/978-1-59904-849-9.ch163
Abstract
Since McCulloch and Pitts’ seminal work (McCulloch & Pitts, 1943), several models of discrete neural networks have been proposed, many of them presenting the ability of assigning a discrete value (other than unipolar or bipolar) to the output of a single neuron. These models have focused on a wide variety of applications. One of the most important models was developed by J. Hopfield in (Hopfield, 1982), which has been successfully applied in fields such as pattern and image recognition and reconstruction (Sun et al., 1995), design of analogdigital circuits (Tank & Hopfield, 1986), and, above all, in combinatorial optimization (Hopfield & Tank, 1985) (Takefuji, 1992) (Takefuji & Wang, 1996), among others. The purpose of this work is to review some applications of multivalued neural models to combinatorial optimization problems, focusing specifically on the neural model MREM, since it includes many of the multivalued models in the specialized literature.