An analogue approach to the travelling salesman problem using an elastic net method

By Richard Durbin, David J. Willshaw. 1987

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Citations in the corpus

Neural Combinatorial Optimization with Reinforcement Learning (2016, methodology): “Perhaps most pr minent is the invention of Elastic Nets as a means to solve TSP (Durbin, 1987), and the applic tion of Self Organizing Map to TSP (Fort, 1988; Angeniol et al., 1988; Kohonen, 1990).”
Using Generative Models for Handwritten Digit Recognition (1996, methodology): “The (cid:12)tting technique resembles the elastic net algorithm of Durbin and Willshaw [39] except that our elastic energy function is much more complex and we are also (cid:12)tting an a(cid:14)ne transformation.”
Deterministic annealing for clustering, compression, classification, regression, and related optimization problems (1998, methodology): “As an example, when applied to the famous " traveling salesman " problem, such DA derivation becomes identical to the " elastic net " method [26], [27].”
GTM: The Generative Topographic Mapping (1998, methodology): “The elastic net algorithm of Durbin and Willshaw (1987) can be viewed as a gaussian mixture density model, tted by penalized maximum likelihood.”
Dynamic self-organising map (2011, methodology): “…i } of p non biased observations is available, the distortion error may be empirically estimated by Neural maps deﬁne a special type of vector quantiﬁers whose most common approaches are the Self-Organising Map (SOM) [3], Elastic Net (EN) [21], Neural Gas (NG) [4] and Growing Neural Gas (GNG) [22].”
The Concave-Convex Procedure (CCCP) (2001, background): “The elastic net (Durbin and Willshaw 1987) attempts to solve the Travelling Salesman Problem (TSP) by finding the shortest tour through a set of cities at positions {~xi}.”
A study of the application of Kohonen-type neural networks to the Travelling Salesman Problem (1991, result): “Other authors working on the same geometric premises ( Durbin and Willshaw 1987; Hueter 1988; Angenioli 1988) have also obtained excellent results, though the algorithms used are different from our own.”
Kernel Methods and Machine Learning (2014, methodology): “The elastic net learning model, proposed by Durbin and Willshaw [57], is closely related to the active contour model presented by Kass, Witkin, and Terzopoulos [121].”
Continuous latent variable models for dimensionality reduction and sequential data reconstruction (2001, background): “The elastic net algorithm (Durbin and Willshaw, 1987) generates good solutions in much less time by stretching a circular tour formed by M knots elastically linked in succession to fit the cities (the topographic arrangement of the elastic net can be extended to any dimension); that is, it is an alg”