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

A m-partite graph is defined as a graph that consists of m nodes each of wh ich contains a set of elements, and the arcs connecting elements from diffe rent nodes. Each element in this graph comprises its specific attributes su ch as cost and resources. The weighted values of arcs represent the dissimi larities 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 s olve such a problem, Hopfield neural networks based approach is adopted in this paper. The Liapunov function (energy function) of Hopfield neural netw orks specially designed for solving m-partite graph problem is constructed. In order to prohibit Hopfield neural networks from becoming trapped in the ir local minima, simulated annealing and genetic algorithms are thus utiliz ed and combined with Hopfield neural networks to get globally optimal solut ion to m-partite graph problem. The result of the approaches developed in t his paper shows the definitive promise for leading to the optimal solution to the m-partite graph problem compared with that of other currently availa ble algorithms.