### Abstract

An `Evolutionary Neural Network (ENN)' is presented for the max cut problem of an undirected graph G(V, E) in this paper. The goal of the NP-hard problem is to find a partition of V into two disjoint subsets such that the cut size be maximized. The cut size is the sum of weights on edges in E whose endpoints belong to different subsets. The ENN combines the evolutionary initialization scheme of the neural state into the energy minimization criteria of the binary neural network. The performance of ENN is evaluated through simulations in randomly weighted complete graphs and unweighted random graphs with up to 1000 vertices. The results show that the evolutionary initialization scheme drastically improves the solution quality. ENN can always find better solutions than the maximum neural network, the mean field annealing, the simulated annealing, and the greedy algorithm.

Original language | English |
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Title of host publication | IEEE International Conference on Neural Networks - Conference Proceedings |

Publisher | IEEE |

Pages | 1260-1265 |

Number of pages | 6 |

Volume | 2 |

Publication status | Published - 1997 |

Externally published | Yes |

Event | Proceedings of the 1997 IEEE International Conference on Neural Networks. Part 4 (of 4) - Houston, TX, USA Duration: Jun 9 1997 → Jun 12 1997 |

### Other

Other | Proceedings of the 1997 IEEE International Conference on Neural Networks. Part 4 (of 4) |
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City | Houston, TX, USA |

Period | 6/9/97 → 6/12/97 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Control and Systems Engineering
- Artificial Intelligence

### Cite this

*IEEE International Conference on Neural Networks - Conference Proceedings*(Vol. 2, pp. 1260-1265). IEEE.

**Evolutionary neural network algorithm for Max cut problems.** / Funabiki, Nobuo; Kitamichi, Junji; Nishikawa, Seishi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IEEE International Conference on Neural Networks - Conference Proceedings.*vol. 2, IEEE, pp. 1260-1265, Proceedings of the 1997 IEEE International Conference on Neural Networks. Part 4 (of 4), Houston, TX, USA, 6/9/97.

}

TY - GEN

T1 - Evolutionary neural network algorithm for Max cut problems

AU - Funabiki, Nobuo

AU - Kitamichi, Junji

AU - Nishikawa, Seishi

PY - 1997

Y1 - 1997

N2 - An `Evolutionary Neural Network (ENN)' is presented for the max cut problem of an undirected graph G(V, E) in this paper. The goal of the NP-hard problem is to find a partition of V into two disjoint subsets such that the cut size be maximized. The cut size is the sum of weights on edges in E whose endpoints belong to different subsets. The ENN combines the evolutionary initialization scheme of the neural state into the energy minimization criteria of the binary neural network. The performance of ENN is evaluated through simulations in randomly weighted complete graphs and unweighted random graphs with up to 1000 vertices. The results show that the evolutionary initialization scheme drastically improves the solution quality. ENN can always find better solutions than the maximum neural network, the mean field annealing, the simulated annealing, and the greedy algorithm.

AB - An `Evolutionary Neural Network (ENN)' is presented for the max cut problem of an undirected graph G(V, E) in this paper. The goal of the NP-hard problem is to find a partition of V into two disjoint subsets such that the cut size be maximized. The cut size is the sum of weights on edges in E whose endpoints belong to different subsets. The ENN combines the evolutionary initialization scheme of the neural state into the energy minimization criteria of the binary neural network. The performance of ENN is evaluated through simulations in randomly weighted complete graphs and unweighted random graphs with up to 1000 vertices. The results show that the evolutionary initialization scheme drastically improves the solution quality. ENN can always find better solutions than the maximum neural network, the mean field annealing, the simulated annealing, and the greedy algorithm.

UR - http://www.scopus.com/inward/record.url?scp=0030660005&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030660005&partnerID=8YFLogxK

M3 - Conference contribution

VL - 2

SP - 1260

EP - 1265

BT - IEEE International Conference on Neural Networks - Conference Proceedings

PB - IEEE

ER -