Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
Introduction to the theory of neural computation
Introduction to the theory of neural computation
Neural network methods in combinatorial optimization
Computers and Operations Research - Special issue on neural networks and operations research
Mapping combinatorial optimization problems onto neural networks
Information Sciences—Intelligent Systems: An International Journal
Genetic Algorithms Plus Data Structures Equals Evolution Programs
Genetic Algorithms Plus Data Structures Equals Evolution Programs
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Neural Computation in Hopfield Networks and Boltzmann Machines
Neural Computation in Hopfield Networks and Boltzmann Machines
Artificial Neural Networks: An Introduction to Ann Theory and Practice
Artificial Neural Networks: An Introduction to Ann Theory and Practice
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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.