A dual neural network for solving entropy-maximising models

The entropy-maximixing model has been applied with varying degrees of success in the analysis and planning of origin-destination types of spatial interaction. Although theoretical underpinnings and solution methods have been developed over the years, there are still outstanding problems that need to be thoroughly investigated. From the practical point of view, solving this model directly and in real time has high theoretical and pragmatic value. In this paper we propose a neural network for solving the dual problem of this model in real time. The size of the proposed network is very small and its structure is very simple, so it can be implemented in hardware. From the theoretical perspective, we solve the seldom investigated issue of convergence to the optimal solution of the entropy-maximising model. We strictly prove that the proposed dual neural network is Lyapunov stable and that each of its trajectories can converge asymptotically to an exact solution of the dual problem. The validity and transient behaviour of the proposed neural network are demonstrated by numerical examples. It is also demonstrated that the proposed network approach renders for the first time a tight integration of an entropy-maximising model and a neural network, and offers a general representation and solution to a large variety of entropy-maximising models.