**Single Objective**

**Chapter 1** 

© 2012 Karimi and Verki, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 Karimi and Verki, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Mean Field Annealing Based Techniques** 

Gholam Reza Karimi and Ahmad Azizi Verki

Additional information is available at the end of the chapter

problems [1,2,4-8,10,13] , cell placement problem [14].

http://dx.doi.org/10.5772/52092

partitioning problem [12,13].

**1. Introduction** 

problem [15].

**1.1. Annealing** 

making it more stable.

it feels most comfortable, i.e., less stress.

**for Resolving VLSI Automatic Design Problems** 

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

MFA, as a neuro-computing technique, is applied for solving combinatorial optimization

MFA combines the *annealing* notion of SA approach with the collective computation

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

Annealing is a mechanical process in which material is slowly cooled allowing the molecules to arrange themselves in such a way that the material is less strained thereby

If materials such as glass or metal are cooled too quickly its constituent molecules will be under high stress lending it to failure (breaking) if further thermal or physical shocks are encountered. Slowing the cooling of the material allows each molecule to move into a place

property of *Hopfield neural network*s to obtain optimal solution for np-hard problems.
