**1. Introduction**

The neuro-computing approaches based on Hopfield model were successfully applied to various combinatorial optimization problems such as the traveling salesman problem [1-3], scheduling problem [4], mapping problem [5], knapsack problem [6,7], communication routing problem [8], graph partitioning problem [2,9,10], graph layout problem [11], circuit partitioning problem [12,13].

MFA, as a neuro-computing technique, is applied for solving combinatorial optimization problems [1,2,4-8,10,13] , cell placement problem [14].

MFA combines the *annealing* notion of SA approach with the collective computation property of *Hopfield neural network*s to obtain optimal solution for np-hard problems.

We begin our study with the review of basic concepts of MFA techniques and describe the applied use of this technique to solve the problems in high speed Integrated Circuits (IC) design and in addition we applied a modified MFA algorithm to solve VLSI relocation problem [15].
