Design of the inverse function delayed neural network for solving combinatorial optimization problems

Authors:
Yoshihiro Hayakawa;Koji Nakajima
Affiliations:
Department of Information Systems, Sendai National College of Technology, Sendai, Japan;Laboratory for Brainware, Laboratory for Nanoelectronics and Spintronics Research Institute of Electrical Communication, Tohoku University, Sendai, Japan
Venue:
IEEE Transactions on Neural Networks
Year:
2010

Citing 6
Cited 0

Basins of attraction in a perceptron-like neural network

Complex Systems
Correct reaction neural network

Neural Networks
Chaotic simulated annealing by a neural network model with transient chaos

Neural Networks
Retrieval Property of Associative Memory Based on Inverse Function Delayed Neural Networks

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Temporal Sequences of Patterns with an Inverse Function Delayed Neural Network

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Avoidance of the Permanent Oscillating State in the Inverse Function Delayed Neural Network

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Quantified Score

Hi-index	0.00

Visualization

Abstract

We have already proposed the inverse function delayed (ID) model as a novel neuron model. The ID model has a negative resistance similar to Bonhoeffer-van der Pol (BVP) model and the network has an energy function similar to Hopfield model. The neural network having an energy can converge on a solution of the combinatorial optimization problem and the computation is in parallel and hence fast. However, the existence of local minima is a serious problem. The negative resistance of the ID model can make the network state free from such local minima by selective destabilization. Hence, we expect that it has a potential to overcome the local minimum problems. In computer simulations, we have already shown that the ID network can be free from local minima and that it converges on the optimal solutions. However, the theoretical analysis has not been presented yet. In this paper, we redefine three types of constraints for the particular problems, then we analytically estimate the appropriate network parameters giving the global minimum states only. Moreover, we demonstrate the validity of estimated network parameters by computer simulations.