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

Nature volume 326, pages 689–691 (1987)Cite this article

Abstract

The travelling salesman problem1 is a classical problem in the field of combinatorial optimization, concerned with efficient methods for maximizing or minimizing a function of many independent variables. Given the positions of N cities, which in the simplest case lie in the plane, what is the shortest closed tour in which each city can be visited once? We describe how a parallel analogue algorithm, derived from a formal model2–3 for the establishment of topographically ordered projections in the brain4–10, can be applied to the travelling salesman problem1,11,12. Using an iterative procedure, a circular closed path is gradually elongated non-uniformly until it eventually passes sufficiently near to all the cities to define a tour. This produces shorter tour lengths than another recent parallel analogue algorithm13, scales well with the size of the problem, and is naturally extendable to a large class of optimization problems involving topographic mappings between geometrical structures14.

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Authors and Affiliations

  1. MRC Laboratory of Molecular Biology, Hills Road, Cambridge, CB2 2QH

    Richard Durbin

  2. King's College Research Centre, Cambridge, CB2 1ST, UK

    Richard Durbin

  3. Department of Zoology, University of Edinburgh, West Mains Road, Edinburgh, EH9 3JT, UK

    David Willshaw

Authors
  1. Richard Durbin
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  2. David Willshaw
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Durbin, R., Willshaw, D. An analogue approach to the travelling salesman problem using an elastic net method. Nature 326, 689–691 (1987). https://doi.org/10.1038/326689a0

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