Convergence of the synaptic weights for the elastic net method, and its application

Rahman Ghamasaee, Jeffrey B. Goldberg

Research output: Contribution to journalConference article

Abstract

Solution procedures for the traveling salesman problem (TSP), i.e. the problem of finding the minimum Hamiltonian circuit in a network of cities, can be divided into two categories: exact methods and approximate (or heuristic) methods. Since TSP is an NP hard problem, good heuristic approaches are of interest. The neural networks heuristic solutions of TSP was initiated by Hopfield and Tank. One such heuristic called the elastic net method is illustrated by the following, an imaginary rubber band is placed at the centroid of the distribution of n cities. Then some finite number (m greater than n) of points (nodes) on this rubber band changes their positions according to the dynamics of the method. Eventually they describe a tour around the cities. We express the dynamics and stability of the elastic net algorithm. We show that if a unique node is converging to a city, then the synaptic strength between them approaches one. Then we generalize to the case where more than one node converges to a city. Furthermore, a typical application that could make use of the elastic net method (e.g. multi-target tracking) will be pointed out for later studies. In order to verify the proof of the concept and the associated theorems, computer simulations were conducted for a reasonable number of cities.

Original languageEnglish (US)
Pages (from-to)145-153
Number of pages9
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume3069
DOIs
StatePublished - Dec 1 1997
EventAutomatic Target Recognition VII - Orlando, FL, United States
Duration: Apr 22 1997Apr 22 1997

Keywords

  • Convergence
  • Elastic net
  • MTT
  • Neural networks
  • TSP

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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