A new approach to via minimization problem in VLSI chip design

Hopfield neural networks (HNN) and simulated annealing (SA) are two recent approaches to solving many combinatorial optimization problems. But, the disadvantages of HNN are that it can often converge at local minimum and the quality of solutions depends on the initial state because of sensitivity of parameterization. On the other hand, SA is designed to cope with the problem of convergence to a local minimum. SA, however, requires unacceptably large computing time. So, a new algorithm called mean field annealing (MFA) which can be interpreted as a generalization of HNN, is applied to optimization problems efficiently. In this paper, we propose a new approach based on MFA to solving of the minimization problem. Also we show that our approach can be applied to multi-layer as well as two-layer routing, and optimal solutions can be obtained by properly adjusting the parameter in the given energy function.