Solving the production transportation problem via a deterministic annealing neural network method

The production transportation problem is a famous NP-hard problem which is a challenge to be solved. This study develops a deterministic annealing neural network method based on Lagrange-barrier functions and two neural network models to solve the problem of this kind. According to the problem’s formulation, the Lagrange function will be applied to deal with the linear equality constraints. At the same time, the barrier function will be applied to make the solution arrive at the near-global or global optimal solution. For each of the two neural network models, an iterative procedure to optimize the proposed neural network will be developed and the descent direction is obtained. Then two Lyapunov functions corresponding to the two neural network models are proposed. On the basis of the Lyapunov functions, this deterministic annealing neural network method are shown to converge to the stable equilibrium state and be completely stable. Finally, preliminary numerical results on a number of test problems show that the developed method is promising and could be expanded to other similar issues in the real world.