**11. References**

Engrand, P. (1997). A multi-objective approach based on simulated annealing and its application to nuclear fuel management, *5th International Conference on Nuclear Engineering*, Nice, France, pp. 416-423.

<sup>\*</sup> Corresponding Author

Chu, C.L., Xue, X.Y., Zhu, J.C. & Yin, Z.D. (2006). In vivo study on biocompatibility and bonding strength of hydroxyapatite-20 vol%Ti composite with bone tissues in the rabbit. *Biomedical Materials and Engineering*, Vol.16, No. 3, pp. 203-213.

236 Simulated Annealing – Single and Multiple Objective Problems

This chapter presents some important findings for Functionally Graded Material (FGM) dental implant design in a power law configuration. This is vital for maintaining the overall health of the bone tissues. The research clearly suggests that, a better performance in bone turnover can be achieved by lowering the FGM dental implant material gradient. However, this will at the same time reduce the stiffness of implantation, consequently placing the

The problem may be solved by the multi-objective optimization method. The Pareto front was determined using the Suppapitnarm Multi-Objective Simulated Annealing (SMOSA) optimization procedure. The results obtained from the SMOSA confirm the results obtained by the Response Surface Methodology (RSM), in addition to offering further improvements. The SMOSA optimized the objective functions on a wider data range than RSM and offered better results with respect to the cortical density function (almost 33% more than RSM). SMOSA optimization in this case, gives more selection of material gradient (*m*) for designing FGM dental implant compared to RSM. The material gradient varies from 0.1 to 0.65 given

By considering the point that the scale in the FGM dental implant is in micro, the importance of accuracy in optimization of the FGM implant is understood. The design of FGM gradient parameter is expected to maximize the densities (cortical and cancellous) and minimize the displacement and plays a more important role in the design methodology. However, sacrifice may be made when the third criterion of displacement is introduced, which means that an optimal gradient *m* for bone remodeling may not be the best for stiffness. It is expected that the design methodology can produce more favorably patient specific implant, better improving the immediate and long-term restorative outcomes.

The authors would like to acknowledge for the Ministry of Higher Education of Malaysia and the University of Malaya, Kuala Lumpur, Malaysia for the financial support under

Engrand, P. (1997). A multi-objective approach based on simulated annealing and its application to nuclear fuel management, *5th International Conference on Nuclear* 

bone-implant interface at higher risk of damage during the early healing stage.

**10. Conclusions** 

by SMOSA.

**Author details** 

**Acknowledgement** 

**11. References** 

Corresponding Author

 \*

Ali Sadollah and Ardeshir Bahreininejad\*

UM.TNC2/IPPP/UPGP/628/6/ER013/2011A grant.

*Engineering*, Nice, France, pp. 416-423.

*Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia* 


Suman, B. & Kumar, P. (2006). A survey of simulated annealing as a tool for single and multi-objective optimization. *Journal of the Operational Research Society, Vol. 57, pp. 1143- 1160.*

**Chapter 12** 

© 2012 Sheng and Takahashi, 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 Sheng and Takahashi, 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.

**A Simulated Annealing Based Approach** 

The optimization techniques for integrated circuit (IC) layout design are important. Generally speaking, the basic process of modern hardware engineering includes designing, manufacturing and testing. IC layout is an inevitable stage of designing before manufacturing. There are many applications which are directly related with layout optimization in practice, such as floor plan for very-large-scale integration (VLSI) design, placement for printed circuit board (PCB) design, packing for logistics management, and so on. In this research, we mainly focus on the optimization for three layout problems, which are 2D packing, 3D packing and 2D placement. The 2D/3D packing is to position different modules into a fixed shape, normally rectangular one, with area or volume minimization. The placement can be regarded as the packing problem with interconnect optimization. Since a general placement problem is NP-hard, there are no practical exact algorithms so far to be sure to find optimal solutions. As an alternative to get the optima, heuristics [1-6] are

As product size keeps shrinking, product lifecycle keeps shortening and product complexity goes up, more electronic components will be integrated into a smaller IC chip or PCB with higher density and shorter time to market. At the same time, multi-objective optimization is common for IC/PCB layout in real product design, so another difficulty is the trade-off between conflicting objectives, such as low power and high performance. Pareto improvement for multiple objectives is one of the biggest challenges we have to face nowadays. The layout problem becomes much harder to find near-optimal or even acceptable solutions with high requirements. In order to improve the best cases and mitigate the worst cases of IC/PCB layout, it becomes increasingly critical and urgent to improve the

Simulated annealing based algorithm with a good representation for 2D/3D packing is one of the most popular ways to improve the quality of solution. On the one hand, many

**to Integrated Circuit Layout Design** 

typically used to find near optimal solutions within a given runtime.

quality of solution and reduce runtime.

Yiqiang Sheng and Atsushi Takahashi

http://dx.doi.org/10.5772/51126

**1. Introduction** 

Additional information is available at the end of the chapter


**Chapter 12** 
