The ordering-oriented Hopfield network

The travelling salesman problem (TSP) is a well known problem which can be solved using Hopfield networks. The TSP solution with Hopfield networks is based on the uniqueness constraint. This is, each city must be visited once and only once while trying to minimize the travelling distance. But in real world applications, usually there are other equally important constraints needing to be considered. For example, an ordering constraint on how cities are to be visited. This paper proposes a modified Hopfield neural network architecture that can solve a new class of optimization problem, called “the picking stone problem (PSP)”. The PSP requires not only the uniqueness but also the ordering constraints. The neural network implementation to solve PSP tends to turn on neurons which satisfy the ordering constraint and this constraint is essential in solving the stereo correspondence problem in binocular vision and can be applied to many other pattern recognition problems. In this paper the authors define the PSP, formulate its computational complexity, propose the ordering-oriented neural network architecture, discuss the performance of the proposed network by the traditional random initialization method, and propose a new initialization method to improve the performance of the network