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

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 minimized. In order to solve such a problem, a Hopfield neural networks based approach is adopted in this paper. The Liapunov function (energy function) of Hopfield neural networks specially designed for solving the m-partite graph problem is constructed. In order to prohibit Hopfield neural networks from being trapped in their local minima, Simulated Annealing and Genetic Algorithms are utilized and combined with Hopfield neural networks to get a globally optimal solution to the m-partite graph problem. The result of the approaches developed in this paper shows the definitive promise of an optimal solution to the m-partite graph problem compared with that of other currently available algorithms.