Limitations of neural networks for solving traveling salesman problems

Feedback neural networks enjoy considerable popularity as a means of approximately solving combinatorial optimization problems. It is now well established how to map problems onto networks so that invalid solutions are never found. It is not as clear how the networks' solutions compare in terms...

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Bibliographic Details
Published in:IEEE transactions on neural networks Vol. 6; no. 1; pp. 280 - 282
Main Authors: Gee, A.H., Prager, R.W.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.01.1995
Institute of Electrical and Electronics Engineers
Subjects:
Annealing
Applied sciences
Artificial intelligence
Computer science; control theory; systems
Connectionism. Neural networks
Councils
Eigenvalues and eigenfunctions
Equations
Exact sciences and technology
Lyapunov method
Neural network hardware
Neural networks
Neurofeedback
Prototypes
Traveling salesman problems
Feedback
Combinatorial problem
Eigenvector
Network analysis
Optimal solution
Travelling salesman problem
Problem solving
Neural network
Optimization
ISSN:1045-9227
Online Access:Get full text
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Summary:Feedback neural networks enjoy considerable popularity as a means of approximately solving combinatorial optimization problems. It is now well established how to map problems onto networks so that invalid solutions are never found. It is not as clear how the networks' solutions compare in terms of quality with those obtained using other optimization techniques; such issues are addressed in this paper. A linearized analysis of annealed network dynamics allows a prototypical network solution to be identified in a pertinent eigenvector basis. It is possible to predict the likely quality of this solution by examining optimal solutions in the same basis. Applying this methodology to traveling salesman problems, it appears that neural networks are well suited to the solution of Euclidean but not random problems; this is confirmed by extensive experiments. The failure of a network to adequately solve even 10-city problems is highly significant.< >
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ISSN:1045-9227
DOI:10.1109/72.363424