Journal ArticleDOI
An analogue approach to the travelling salesman problem using an elastic net method
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This work describes how a parallel analogue algorithm, derived from a formal model for the establishment of topographically ordered projections in the brain, can be applied to the travelling salesman problem, and produces shorter tour lengths than another recent parallel analogue algorithms.Abstract:
The travelling salesman problem 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 model for the establishment of topographically ordered projections in the brain, can be applied to the travelling salesman problem. 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 algorithm, scales well with the size of the problem, and is naturally extendable to a large class of optimization problems involving topographic mappings between geometrical structures.read more
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A global geometric framework for nonlinear dimensionality reduction.
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Ant colony system: a cooperative learning approach to the traveling salesman problem
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References
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Journal ArticleDOI
Optimization by Simulated Annealing
TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
Book
Self Organization And Associative Memory
TL;DR: The purpose and nature of Biological Memory, as well as some of the aspects of Memory Aspects, are explained.
Journal ArticleDOI
An Effective Heuristic Algorithm for the Traveling-Salesman Problem
S. Lin,Brian W. Kernighan +1 more
TL;DR: This paper discusses a highly effective heuristic procedure for generating optimum and near-optimum solutions for the symmetric traveling-salesman problem based on a general approach to heuristics that is believed to have wide applicability in combinatorial optimization problems.