Parallel analog method for optimization by using neural networks

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Some deficiencies have been observed for the Hopfield networks, e.g.growth of its computational time with problem size, its often outputs of illegal solutions and no theoretical guarantee for its performance. The aim of this research is to give some solutions for these difficulties of the Hopfield method for solving combinatorial optimization problems. A method based on a mixed integer programming is first developed for speeding up of the algorithm. Next a Lagrangean method is proposed for obtaining only legal solutions. A theoretical guarantee is derived for this Lagrangean method for the maximum cut problem which is one of the most popular NP-hard combinatorial optimization problems. A novel deterministic annealing technique is devised for raising up the performance of the developed method for extremely hard problems. The devised new method is applied to many combinatorial optimization problems, e.g.assignment problems, placement problems, data clustering.topology preserving mappings and image restoration. Some numerical experiments have revealed a promising performance of the solution method developed in this research.