### Abstract

Many researchers have attempted to solve the combinatorial optimization problems, that are NP-hard or NP-complete problems, by using neural networks. Though the method used in a neural network has some advantages, the local minimum problem is not solved yet. It has been shown that the Inverse Function Delayed (ID) model, which is a neuron model with a negative resistance on its dynamics and can destabilize an intended region, can be used as the powerful tool to avoid the local minima. In our previous paper, we have shown that the ID network can separate local minimum states from global minimum states in case that the energy function of the embed problem is zero. It can achieve 100% success rate in the N-Queen problem with the certain parameter region. However, for a wider parameter region, the ID network cannot reach a global minimum state while all of local minimum states are unstable. In this paper, we show that the ID network falls into a particular permanent oscillating state in this situation. Several neurons in the network keep spiking in the particular permanent oscillating state, and hence the state transition never proceed for global minima. However, we can also clarify that the oscillating state is controlled by the parameter α which affects the negative resistance region and the hysteresis property of the ID model. In consequence, there is a parameter region where combinatorial optimization problems are solved at the 100% success rate.

Original language | English |
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Pages (from-to) | 2101-2107 |

Number of pages | 7 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E90-A |

Issue number | 10 |

DOIs | |

Publication status | Published - 2007 Oct |

### Keywords

- Combinatorial optimization problem
- Inverse function delayed model
- N-Queen problem
- Negative resistance
- Neural network

### ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics

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## Cite this

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*,

*E90-A*(10), 2101-2107. https://doi.org/10.1093/ietfec/e90-a.10.2101