Attractor Basin Analysis of the Hopfield Model: The Generalized quadratic knapsack problem.



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Garcia, L. and Talavan, P. M. and Yáñez, Javier (2017) Attractor Basin Analysis of the Hopfield Model: The Generalized quadratic knapsack problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science, 1 (10305). Springer Verlag, pp. 420-431. ISBN 978-331959152-0

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The Continuous Hopfield Neural Network (CHN) is a neural network which can be used to solve some optimization problems. The weights of the network are selected based upon a set of parameters which are deduced by mapping the optimization problem to its associated CHN. When the optimization problem is the Traveling Salesman Problem, for instance, this mapping process leaves one free parameter; as this parameter decreases, better solutions are obtained. For the general case, a Generalized Quadratic Knapsack Problem (GQKP), there are some free parameters which can be related to the saddle point of the CHN. Whereas in simple instances of the GQKP, this result guarantees that the global optimum is always obtained, in more complex instances, this is far more complicated. However, it is shown how in the surroundings of the saddle point the attractor basins for the best solutions grow as the free parameter decreases, making saddle point neighbors excellent starting point candidates for the CHN. Some technical results and some computational experiences validate this behavior.

Item Type:Book Section
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14th International Work-Conference on Artificial Neural Networks, IWANN 2017; Cadiz; Spain; 14 June 2017 through 16 June 2017; Code 192889

Uncontrolled Keywords:Artificial neural networks; Optimization; Machine Learning; Hopfield network
Subjects:Sciences > Mathematics > Applied statistics
ID Code:43807
Deposited On:11 Jul 2017 08:12
Last Modified:31 Oct 2017 11:37

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