Results 1 
3 of
3
Convergence Properties of the Softassign Quadratic Assignment Algorithm
 Neural Computation
, 1999
"... The softassign quadratic assignment algoithm is a discrete time, continuous state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching and graph partitioning in thousands of simulations, there was no associated stud ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
(Show Context)
The softassign quadratic assignment algoithm is a discrete time, continuous state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching and graph partitioning in thousands of simulations, there was no associated study of its convergence properties. Here, we construct discrete time Lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction which can be used to show convergence to a fixed point. The combination of good convergence properties and experimental success make the softassign algorithm the technique of choice for neural QAP optimization. 1 Introduction Discrete time optimizing neural networks are a well honed topic in neural computation. Beginning with the discrete state Hopfield model (Hopfield, 1982), considerable effort has been spent in analyzing the convergence properties of discrete time networks, especially along the dimensions of continuous versu...
The MIT Press
"... Published one article at a time in L ATEX source form on the Internet. Pagination ..."
Abstract
 Add to MetaCart
(Show Context)
Published one article at a time in L ATEX source form on the Internet. Pagination
Oscillations in Discrete and Continuous Hopfield Networks
"... This chapter is neatly partitioned into two parts: one dealing with oscillations in discrete Hopfield networks and the other with oscillations in continuous Hopfield networks. The single theme spanning both parts is that of the Hopfield model and its energy function. The first part deals with analyz ..."
Abstract
 Add to MetaCart
This chapter is neatly partitioned into two parts: one dealing with oscillations in discrete Hopfield networks and the other with oscillations in continuous Hopfield networks. The single theme spanning both parts is that of the Hopfield model and its energy function. The first part deals with analyzing oscillations in the discrete Hopfield network with symmetric weights, and speculating on possible uses of such behavior. By imposing certain restrictions on the weights, an exact characterization of the oscillatory behavior is obtained. Possible uses of this characterization are examined. The second part deals with injecting chaotic or periodic oscillations into continuous Hopfield networks, for the purposes of solving optimization problems. When the continuous Hopfield model is used to solve an optimization problem, the results are often mediocre because of the convergent nature of its dynamical algorithm. To circumvent this limitation, we develop mechanisms for injecting controllable c...