The mean field annealing approach is a new neural network model,which improves the simulated annealing approach greatly.In the paper,the via minimization problem in multi-layer routing with adjacent constraints is translated to a k-colorable problem which has more general meanings,and a mean field annealing algorithm for the k-colorable problem is proposed.On the basis of the segment-crossing graph model,the adjacent matrix and the crossing matrix are introduced.A permute matrix of binary variables is used to map the problem to the neural network,and then the energy function is presented.The object item,crossing constrained item and adjacency constrained item in the energy function,and the normalization of neurons prove that the effective result can be gotten.The experimental results show that it is an effective method.