### Abstract

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

Place of Publication | Eindhoven |

Publisher | Technische Universiteit Eindhoven |

Publication status | Published - 1989 |

Externally published | Yes |

### Publication series

Name | Memorandum COSOR |
---|

### Fingerprint

### Cite this

*A note on the convergence of a synchronously parallel Boltzmann machine for the Knapsack problem*. (Memorandum COSOR). Eindhoven: Technische Universiteit Eindhoven.

}

*A note on the convergence of a synchronously parallel Boltzmann machine for the Knapsack problem*. Memorandum COSOR, Technische Universiteit Eindhoven, Eindhoven.

**A note on the convergence of a synchronously parallel Boltzmann machine for the Knapsack problem.** / Zwietering, P.J.; Aarts, E.H.L.

Research output: Book/Report › Book › Scientific

TY - BOOK

T1 - A note on the convergence of a synchronously parallel Boltzmann machine for the Knapsack problem

AU - Zwietering, P.J.

AU - Aarts, E.H.L.

PY - 1989

Y1 - 1989

N2 - This note elaborates on material that was presented earlier in the COSOR Memorandum 89-21, titled: Synchronously Parallel Boltzmann machines, a Mathematical Model. We discuss the main results obtained in a study of a mathematical model of synchronously parallel Boltzmann machines. We present supporting evidence for the conjecture that a synchronously parallel Boltzmann machine maximizes a consensus function that consists of a weighted sum of the regular consensus function and a pseudo consensus function. The weighting is determined by the fraction of units that can change their states simultaneously. The derived theoretical results are evaluated on the basis of a numerical study carried out for the knapsack problem. Keywords: Boltzmann machines, neural networks, synchronous parallelism, combinatorial optimization, simulated annealing.

AB - This note elaborates on material that was presented earlier in the COSOR Memorandum 89-21, titled: Synchronously Parallel Boltzmann machines, a Mathematical Model. We discuss the main results obtained in a study of a mathematical model of synchronously parallel Boltzmann machines. We present supporting evidence for the conjecture that a synchronously parallel Boltzmann machine maximizes a consensus function that consists of a weighted sum of the regular consensus function and a pseudo consensus function. The weighting is determined by the fraction of units that can change their states simultaneously. The derived theoretical results are evaluated on the basis of a numerical study carried out for the knapsack problem. Keywords: Boltzmann machines, neural networks, synchronous parallelism, combinatorial optimization, simulated annealing.

M3 - Book

T3 - Memorandum COSOR

BT - A note on the convergence of a synchronously parallel Boltzmann machine for the Knapsack problem

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -