A self-organising neural network with intermittent switching dynamics for combinatorial optimisation

Authors:
Terence Kwok;Kate A. Smith
Affiliations:
School of Business Systems, Faculty of Information Technology, Monash University, Clayton, Victoria 3168, Australia;School of Business Systems, Faculty of Information Technology, Monash University, Clayton, Victoria 3168, Australia
Venue:
Design and application of hybrid intelligent systems
Year:
2003

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Abstract

A previously proposed self-organising neural network with weight normalisation (SONN-WN) is found to exhibit a new kind of global optimisation dynamics that connects multiple solutions of an NP-hard combinatorial optimisation problem (COP). The N-Queen problem with N = 8 and 10 is used as an example to demonstrate the intermittent switching dynamics of the SONN-WN, which describes the network states switching amongst all the global minima of the cost landscape in an intermittent manner. All 92 solutions of the 8-Queens problem and 724 solutions of the 10-Queens problem are obtained by this approach. Experimental results show that the phenomenon arises when the normalisation function (also called softmax function) is operating near its bifurcation temperature, together with a non-zero neighbourhood size for the Kohonen-type updating scheme.