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.

生产运输问题是著名的 NP-hard 问题，是一个需要解决的挑战。本研究开发了一种基于拉格朗日势垒函数和两个神经网络模型的确定性退火神经网络方法来解决此类问题。根据问题的表述，将应用拉格朗日函数来处理线性等式约束。同时，将应用屏障函数，使解达到近全局或全局最优解。对于两个神经网络模型中的每一个，将开发优化所提出的神经网络的迭代程序并获得下降方向。然后提出两个神经网络模型对应的两个李雅普诺夫函数。根据李雅普诺夫函数，这种确定性退火神经网络方法被证明收敛到稳定的平衡状态并完全稳定。最后，对一些测试问题的初步数值结果表明，所开发的方法很有前途，可以扩展到现实世界中的其他类似问题。