Automatic translation of constraints for solving optimization problems by neural networks

The author discusses an automatic method for the direct mapping of the constraints and the objectives related to 0-1 programming of formulated combinatorial optimization problems onto neural networks. The model is a massively interconnected network (a Hopfield network or a Boltzmann machine), and the right connection pattern and the associated appropriate connection strengths are generated. The author explains why constraints and objectives can be efficiently mapped onto such a network through weights. A proof that generated weights imply constraint satisfaction is presented. The author gives a set of general forms of met constraints and translates them into weights. It is shown that it is difficult to generate a network with weights that simultaneously satisfy all the constraints. A way to build such a network by using Π-E units is proposed