## Abstract

Analog Hopfield neural networks (HNNs) have so far been used to solve many kinds of optimization problems, in particular, combinatorial problems such as the TSP, which can be described by an objective function and some equality constraints. When we solve a minimization problem with equality constraints by using HNNs, however, the constraints are satisfied only approximately. In this paper we propose a circuit which rigorously realizes the equality constraints and whose energy function corresponds to the prescribed objective function. We use the SPICE program to solve circuit equations corresponding to the above circuits. The proposed method is applied to several kinds of optimization problems and the results are very satisfactory.

Original language | English |
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Pages (from-to) | 2325-2332 |

Number of pages | 8 |

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

Volume | E86-A |

Issue number | 9 |

Publication status | Published - Sep 2003 |

Externally published | Yes |

## Keywords

- Energy function
- Equality constraints
- HNNs
- Optimization problem
- SPICE program

## ASJC Scopus subject areas

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