抄録
Combinatorial optimization by neural networks can be roughly classified into the following two approaches. One is the application of the Hopfield type neural networks with continuous state transitions to continuous versions of combinatorial problems. The other is a direct application of the neural networks with discrete state transitions to original problems. In this paper, our attention is paid to the latter approach in order to propose the fundamentals of a new mechanism in which the artificial neurons have more advanced operational elements.
Discrete state transition rules in usual neural networks are regarded as the operational realization of the comparison between two states whose firing parts have reverse states to each other whether the firing is asynchronous or linked. The proposed transition rule realizes the comparison between more than two states corresponding to every combination of firing neurons' states at once. Concretely, the transition generates the best state among 2N combinations of states as the outputs from the firing neurons, if the number of firing neurons is N. Such transition rules can be interpreted as a coopertive operation of plural neurons with a single input and a single output. From a different point of view, it can be a new basis to design a single advanced neuron with multi-inputs and multi-outputs which realizes the selection of a vertex with the best state in a unit hypercube composed of the single neuron's multi-dimensional state variables. This paper concentrates on a fundamental development of an advanced operation of a neuron, and limits to confirmation of its effectiveness by computer simulations for simple combinatorial problems.
