A Gradient Ascent Learning Algorithm for Elastic Nets

Zheng TANG  Jia Hai WANG  Qi Ping CAO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A   No.4   pp.940-945
Publication Date: 2003/04/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Neural Networks and Bioengineering
elastic net,  traveling salesman problem,  gradient ascent learning,  optimization problems,  

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This paper proposes a gradient ascent learning algorithm for the elastic net approach to the Traveling Salesman Problem (TSP). The learning model has two phases: an elastic net phase, and a gradient ascent phase. The elastic net phase is equivalent to gradient descent of an energy function, and leads to a local minimum of energy that represents a good solution to the problem. Once the elastic net gets stuck in local minima, the gradient ascent phase attempts to fill up the valley by modifying parameters in a gradient ascent direction of the energy function. Thus, these two phases are iterated until the elastic net gets out of local minima. We test the algorithm on many randomly generated travel salesman problems up to 100 cities. For all problems, the systems are shown to be capable of escaping from the elastic net local minima and generating shorter tour than the original elastic net.