### Abstract

The Hopfield neural network is attracting attention as a high‐speed solver for optimization and other problems. However, it contains a problem in that the network may not arrive at the globally optimal solution but stops at a locally optimal solution unless the initial state is selected appropriately. In other words, the selection of the initial state is important in solving a problem using the Hopfield neural network. This paper considers the real number partition problem, the problem of finding the k largest elements from a given set of real numbers, given integer k. A network to solve this problem is constructed. It is shown that the network arrives at the globally optimal solution if the initial state satisfies a certain condition. Its basin also is examined. As an application example of the network, the sorting problem is considered.

Original language | English |
---|---|

Pages (from-to) | 88-95 |

Number of pages | 8 |

Journal | Systems and Computers in Japan |

Volume | 22 |

Issue number | 10 |

DOIs | |

Publication status | Published - Jan 1 1991 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Hardware and Architecture
- Computational Theory and Mathematics

### Cite this

*Systems and Computers in Japan*,

*22*(10), 88-95. https://doi.org/10.1002/scj.4690221010

**Set partition of real numbers by hopfield neural network.** / Hisanaga, Yutaka; Yamashita, Masafumi; Ae, Tadashi.

Research output: Contribution to journal › Article

*Systems and Computers in Japan*, vol. 22, no. 10, pp. 88-95. https://doi.org/10.1002/scj.4690221010

}

TY - JOUR

T1 - Set partition of real numbers by hopfield neural network

AU - Hisanaga, Yutaka

AU - Yamashita, Masafumi

AU - Ae, Tadashi

PY - 1991/1/1

Y1 - 1991/1/1

N2 - The Hopfield neural network is attracting attention as a high‐speed solver for optimization and other problems. However, it contains a problem in that the network may not arrive at the globally optimal solution but stops at a locally optimal solution unless the initial state is selected appropriately. In other words, the selection of the initial state is important in solving a problem using the Hopfield neural network. This paper considers the real number partition problem, the problem of finding the k largest elements from a given set of real numbers, given integer k. A network to solve this problem is constructed. It is shown that the network arrives at the globally optimal solution if the initial state satisfies a certain condition. Its basin also is examined. As an application example of the network, the sorting problem is considered.

AB - The Hopfield neural network is attracting attention as a high‐speed solver for optimization and other problems. However, it contains a problem in that the network may not arrive at the globally optimal solution but stops at a locally optimal solution unless the initial state is selected appropriately. In other words, the selection of the initial state is important in solving a problem using the Hopfield neural network. This paper considers the real number partition problem, the problem of finding the k largest elements from a given set of real numbers, given integer k. A network to solve this problem is constructed. It is shown that the network arrives at the globally optimal solution if the initial state satisfies a certain condition. Its basin also is examined. As an application example of the network, the sorting problem is considered.

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U2 - 10.1002/scj.4690221010

DO - 10.1002/scj.4690221010

M3 - Article

AN - SCOPUS:0025814168

VL - 22

SP - 88

EP - 95

JO - Systems and Computers in Japan

JF - Systems and Computers in Japan

SN - 0882-1666

IS - 10

ER -