Title: Efficiency of applying Hopfield neural networks with simulated annealing and genetic algorithms for solving m-partite graph problem

Authors: X.G. Ming, K.L. Mak

Addresses: Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong. Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong

Abstract: An m-partite graph is defined as a graph that consists of m nodes each of which contains a set of elements, and the arcs connecting elements from different nodes. Each element in this graph comprises its specific attributes such as cost and resources. The weighted values of arcs represent the dissimilarities of resources between elements from different nodes. The m-partite graph problem is defined as selecting exactly one representative from a set of elements for each node in such a way that the sum of both the costs of the selected elements and their dissimilarities is minimised. In order to solve such a problem, Hopfield neural networks based approach is adopted in this paper. The Liapunov function (energy function) of Hopfield neural networks specially designed for solving m-partite graph problem is constructed. In order to prohibit Hopfield neural networks from becoming trapped in their local minima, simulated annealing and genetic algorithms are thus utilised and combined with Hopfield neural networks to get globally optimal solution to m-partite graph problem. The result of the approaches developed in this paper shows the definitive promise for leading to the optimal solution to the m-partite graph problem compared with that of other currently available algorithms.

Keywords: m-partite graph problem; simulated annealing; genetic algorithms; process plan selection; manufacturing operation set selection.

DOI: 10.1504/IJCAT.1999.000217

International Journal of Computer Applications in Technology, 1999 Vol.12 No.6, pp.339-348

Published online: 13 Jul 2003 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article