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A solution to combinatorial optimization problems using an accelerated hopfield neural network
Author(s) -
Oohori Takahumi,
Yamamoto Hiroaki,
Setsu Nenso,
Watanabe Kazuhisa
Publication year - 1995
Publication title -
electrical engineering in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.136
H-Index - 28
eISSN - 1520-6416
pISSN - 0424-7760
DOI - 10.1002/eej.4391150307
Subject(s) - maxima and minima , hopfield network , acceleration , artificial neural network , mathematical optimization , convergence (economics) , sigmoid function , hypercube , computer science , function (biology) , mathematics , algorithm , artificial intelligence , mathematical analysis , physics , classical mechanics , evolutionary biology , parallel computing , economics , biology , economic growth
Hopfield has shown that the combinatorial optimization problem can be solved on an artificial neural network system by minimizing the quadratic energy function. One of the difficulties in applying the network to actual problems is that the network converges to local minimum solutions very slowly because the sigmoid function is used for an input‐output function of the neuron. To overcome this difficulty, this paper proposes an accelerated Hopfield neural network which can control the speed of convergence near the local minima by an acceleration parameter. Computational results for the combinatorial problems with two and twenty‐five variables show that: (1) the proposed model converges to the local minima more quickly than the conventional model; (2) that the acceleration of convergence makes the attraction region of each local minimum change and worsens the accuracy of the solution; and (3) that if an initial point is selected around the center of the unit hypercube, the proposed network converges to a local minimum very quickly with high accuracy, and these good properties remain unchanged by the acceleration parameter.