scholarly journals A Self-Organizing Neural Network for the Traveling Salesman Problem That Is Competitive with Simulated Annealing

1996 ◽  
Vol 8 (2) ◽  
pp. 416-424 ◽  
Author(s):  
Marco Budinich
Keyword(s):  
Neural Network ◽  
Simulated Annealing ◽  
Unsupervised Learning ◽  
Traveling Salesman Problem ◽  
Approximate Solutions ◽  
Elastic Net ◽  
Traveling Salesman ◽  
The Traveling Salesman Problem ◽  
Better Than ◽  
Self Organizing

Unsupervised learning applied to an unstructured neural network can give approximate solutions to the traveling salesman problem. For 50 cities in the plane this algorithm performs like the elastic net of Durbin and Willshaw (1987) and it improves when increasing the number of cities to get better than simulated annealing for problems with more than 500 cities. In all the tests this algorithm requires a fraction of the time taken by simulated annealing.

TRAINING SIMULTANEOUS RECURRENT NEURAL NETWORK WITH RESILIENT PROPAGATION FOR STATIC OPTIMIZATION

2002 ◽  
Vol 12 (03n04) ◽  
pp. 203-218 ◽  
Author(s):  
GURSEL SERPEN ◽  
JOEL CORRA
Keyword(s):  
Neural Network ◽  
Traveling Salesman Problem ◽  
Recurrent Neural Network ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Training Algorithm ◽  
Comparable Amount ◽  
Static Optimization ◽  
The Traveling Salesman Problem

This paper proposes a non-recurrent training algorithm, resilient propagation, for the Simultaneous Recurrent Neural network operating in relaxation-mode for computing high quality solutions of static optimization problems. Implementation details related to adaptation of the recurrent neural network weights through the non-recurrent training algorithm, resilient backpropagation, are formulated throughan algebraic approach. Performance of the proposed neuro-optimizer on a well-known static combinatorial optimization problem, the Traveling Salesman Problem, is evaluated on the basis of computational complexity measures and, subsequently, compared to performance of the Simultaneous Recurrent Neural network trained with the standard backpropagation, and recurrent backpropagation for the same static optimization problem. Simulation results indicate that the Simultaneous Recurrent Neural network trained with the resilient backpropagation algorithm is able to locate superior quality solutions through comparable amount of computational effort for the Traveling Salesman Problem.

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