Fast combinatorial optimization with parallel digital computers

Author

Kakeya, Hideki ; Okabe, Yoichi

Author_Institution

Commun. Res. Lab., Minist. of Posts & Telecommun., Tokyo, Japan

Volume

11

Issue

6

fYear

2000

fDate

11/1/2000 12:00:00 AM

Firstpage

1323

Lastpage

1331

Abstract

This paper presents an algorithm which realizes fast search for the solutions of combinatorial optimization problems with parallel digital computers. With the standard weight matrices designed for combinatorial optimization, many iterations are required before convergence to a quasioptimal solution even when many digital processors can be used in parallel. By removing the components of the eigenvectors with eminent negative eigenvalues of the weight matrix, the proposed algorithm avoids oscillation and realizes energy reduction under synchronous discrete dynamics, which enables parallel digital computers to obtain quasi-optimal solutions with much less time than the conventional algorithm.

Keywords

Hopfield neural nets; combinatorial mathematics; computational complexity; eigenvalues and eigenfunctions; matrix algebra; optimisation; parallel processing; eigenvectors; eminent negative eigenvalues; energy reduction; fast combinatorial optimization; fast search; oscillation avoidance; parallel digital computers; quasi-optimal solutions; synchronous discrete dynamics; weight matrix; Concurrent computing; Costs; Design optimization; Eigenvalues and eigenfunctions; Geometry; Neurons; Optimization methods; Partitioning algorithms; State-space methods; Traveling salesman problems;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/72.883436

Filename

883436