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

P.J. Zwietering, E.H.L. Aarts

Research output: Book/ReportBookScientific

Abstract

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.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Publication statusPublished - 1989
Externally publishedYes

Publication series

NameMemorandum COSOR

Fingerprint

Boltzmann Machine
Knapsack Problem
Mathematical Model
Combinatorial Optimization
Weighted Sums
Simulated Annealing
Parallelism
Weighting
Numerical Study
Maximise
Neural Networks
Unit

Cite this

Zwietering, P. J., & Aarts, E. H. L. (1989). A note on the convergence of a synchronously parallel Boltzmann machine for the Knapsack problem. (Memorandum COSOR). Eindhoven: Technische Universiteit Eindhoven.
Zwietering, P.J. ; Aarts, E.H.L. / A note on the convergence of a synchronously parallel Boltzmann machine for the Knapsack problem. Eindhoven : Technische Universiteit Eindhoven, 1989. (Memorandum COSOR).
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Zwietering, PJ & Aarts, EHL 1989, 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.

Eindhoven : Technische Universiteit Eindhoven, 1989. (Memorandum COSOR).

Research output: Book/ReportBookScientific

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AU - Aarts, E.H.L.

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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.

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Zwietering PJ, Aarts EHL. A note on the convergence of a synchronously parallel Boltzmann machine for the Knapsack problem. Eindhoven: Technische Universiteit Eindhoven, 1989. (Memorandum COSOR).