Solving the traveling salesman problem using a recurrent neural network

A new algorithm (NWTA algorithm) for solving the traveling salesman problem (TSP) is proposed. The algorithm is based on the use of the Hopfield recurrent neural network, the “Winner takes all” (WTA) method for the cycle formation, and the 2-opt optimization method. A special feature of the algorith...

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Bibliographic Details
Published in:Numerical analysis and applications Vol. 8; no. 3; pp. 275 - 283
Main Author: Tarkov, M. S.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.07.2015
Subjects:
Mathematics
Mathematics and Statistics
Numerical Analysis
CUDA technology
LKH algorithm
traveling salesman problem
recurrent neural Hopfield network
2-opt
ISSN:1995-4239, 1995-4247
Online Access:Get full text
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Summary:A new algorithm (NWTA algorithm) for solving the traveling salesman problem (TSP) is proposed. The algorithm is based on the use of the Hopfield recurrent neural network, the “Winner takes all” (WTA) method for the cycle formation, and the 2-opt optimization method. A special feature of the algorithm proposed is in the use of the method of partial (prefix) sums to accelerate the solution of the system of the Hopfield network equations. For attaining additional acceleration, the parallelization of the algorithm proposed is performed on GPU with the CUDA technology. Several examples from the TSPLIB library with the number of cities from 51 to 2,392 show that the algorithm finds approximate solutions of the TSP (a relative increase in the length of the route with respect to the optimum is 0.03 ÷ 0.14). With a large number of cities (130 and more), the NWTA algorithm running duration on the CPU is 4 ÷ 24 times shorter than the duration of the heuristic LKH algorithm giving optimal solutions for all TSPLIB examples.
ISSN:1995-4239
1995-4247
DOI:10.1134/S1995423915030088