A Survey on Various Genetic Approaches for Standard Cell Placement

Jobanpreet Kaur1, Maninder Kaur

2

1,2School of Mathematics and Computer Applications, Thapar University, India

1joban.preet.92@gmail.com; 2manindersohal@thapar.edu

Abstract

The Standard Cell Placement problem is to place the

modules on a fixed size chip such that certain constraints

are satisfied. Cell Placement being a major step in

physical design has been studied since many decades.

Many heuristic approaches have been developed to

optimize this NP Hard problem. One of the evolutionary

approaches is genetic algorithms that are well-suited for

solving selected combinatorial optimization problems.

This paper presents a survey on various genetic

approaches that have been applied to solve the standard

cell placement problem. The summary of the key features

and parameters for various approaches have been shown

in the tabulated form.

1. Introduction

Physical design of VLSI circuits is a process of

conversion of the specification of a circuit into the

geometric description of a layout [3]. The main stages of

physical design process include partitioning, placement

and routing [11]. Cell Placement has always been a very

crucial phase in the physical design process. It has been

widely studied by the researchers since decades and a lot

of techniques have been developed for optimization of

this problem. The cell placement problem is the

placement of cell modules (in a two-dimensional plane)

on a fixed size chip satisfying certain constraints. Various

approaches have been devised by the researchers to solve

this NP Hard problem. Some of the techniques were

described by the researchers in the work [6], [7], [8] and

[17].

Standard cells in a library have fixed shapes and terminal

locations. They are modules with identical height but

varied widths. The total chip area includes two parts: the

area required for the cell rows and the area required for

routing of wires. In general, given a circuit consisting of a

set of modules and a net list providing the

interconnections between these modules, the standard cell

placement problem is arranging a layout that indicates the

positions of the modules in parallel rows so that all the

nets are interconnected using wires and the total layout

area is minimized. The layout area could be minimized by

a)minimizing the wire lengths between the cells,

b)minimizing the width of the longest row and

c)minimizing the width of channel heights. [2]

One of the evolutionary approaches for solving cell

placement problem includes application of Genetic

Algorithms. Genetic Algorithms (GAs) were introduced

by Holland [1] in 1975 based on the Darwinian principle

of reproduction and survival of the fittest. GAs work on a

population of individuals called chromosomes that

represent a potential solution to a given problem. A

fitness function is used to evaluate each individual's

fitness value to measure the quality of a solution to the

problem. In each iteration of the algorithm, the algorithm

generates a population of individuals by applying genetic

operators such as selection, crossover, inversion and

mutation. A new generation then evolves from the

existing population with new solutions. Genetic

Algorithms are multi-point heuristics and are less likely to

get stuck in local optima than most other heuristic

techniques [5].

This paper is divided into three sections:

Section 1: Problem Description

Section 2: Description of various genetic approaches on

cell placement

Section 3: Conclusion

2. Problem Description

Given an electrical circuit consisting of modules, with

predefined input and output terminals, interconnected in a

predefined way, the Standard Cell Placement problem is

constructing a layout indicating the positions of the

modules, so that the estimated wire length and the layout

area are minimized and other given constraints are

satisfied. The inputs to the problem are module

description with sizes and terminal locations and the

netlist that describes the interconnections between the

cells. The output list contains a list of x- and y-

coordinates of the modules. [4]

Jobanpreet Kaur et al , Int.J.Computer Technology & Applications,Vol 4 (3),533-536

IJCTA | May-June 2013 Available online@www.ijcta.com

533

ISSN:2229-6093

Graph theory could be used to model VLSI physical

design problems including Standard Cell Placement [3]. A

circuit can be represented by a hypergraph G (V,E) where

the vertex set V = {v1,v2,…,vn} represent the set of cells

to be placed and the edge set E = {e1,e2,…,en} represent

the set of nets connecting the cells. Each edge ej is an

ordered pair of vertices with a non-negative weight wj

assigned to it. The placement problem is to assign all cells

of the circuit to the locations in the chip such that cells do

not overlap. Each cell i is assigned to a location (xi, yi) on

XY plane. Minimizing the wire-length is approximately

equivalent to minimizing the total chip area for the

standard cell layout [2],therefore, the total cost of a

placement layout, denoted f (x, y), can be estimated by

the sum of wire length over all nets [9].

( ) ∑ ( ) ( )

where (xi , yi) denotes the location of cell i; wij is a non-

negative weight of the edge connecting cell i and cell j.

The above formulation can be rewritten in matrix form as:

( )

Vectors x and y represent the coordinates of the N cells;

matrix C is the Hessian matrix; vectors dxT and dy

T and the

constant term t result from the contributions of the fixed

cells.

The solutions are evaluated based on the fitness value.

Each individual solution is evaluated to determine its

fitness value using a fitness function F:

∑

where HPWLi is the estimated wire-length of the net i

and n is the number of nets. HPWL is Half Perimeter

Wire Length method used to approximately estimate the

total wire length.

3. Description of Various Versions of

Genetic Algorithms on Standard Cell

Placement

3.1 Genetic Approaches

The work on standard cell placement using genetic

algorithms started in 1990. Shahookar et al in [2]

proposed a Genetic algorithm to solve the standard cell

placement problem. The proposed algorithm worked on a

set of solutions constituting a constant size population.

The authors implemented the algorithm by applying

various crossover operators namely PMX crossover,

cyclic crossover and order crossover. The experimental

results showed that cyclic crossover outer performed in

comparison to PMX and order crossover methods. The

authors also incorporated mutation and inversion operator

in the proposed algorithm.

In the paper [16], the proposed algorithm applies

transformations on the chromosomal representation of the

physical layout instead of directly applying the

transformations on physical layout. The work presented in

this paper incorporates a Selection method that selects the

cell having maximum area first and so on, and the

crossover operator applied on every cell with cells having

next higher, next lower and equal area. The algorithm

used a Random Point crossover.

3.2 Meta-Genetic Approach

In the year 1990, the genetic algorithm for cell placement

was further extended by the authors. Shahookar et al in

[10] extended their previous approach by incorporating

meta-genetic algorithm. The meta-genetic algorithm is

itself a genetic optimization process, which runs the

genetic algorithm to solve a placement problem, and

manipulates its parameters to optimize its fitness. The

proposed work used the genetic operators with different

rates and probabilities which led to the execution of GA

with different parameters giving more efficient results.

3.3 Hybrid Approaches

The authors in the [15] proposed an optimization of

hybrid and local search algorithms for standard cell

placement problem. The work focused on investigating in

detail the hybrid systems based on heuristic techniques

including hybrids of HNN (Hopfield Neural Network)

and GA (Genetic Algorithm) with SA (Simulated

Annealing) & GA based PRSA algorithms. The authors

first suggested HNN & GA hybrid system and then

extended to SA & GA hybrid systems that used either a

coupling mechanism or integrating the methods with their

key features to develop a new method, Parallel

Recombinative SA (PRSA) and proposed a solution

representation and development of cross-over and

neighborhood operators. Finally the authors proposed and

took up parallelization of PRSA.

The authors in the work [18] addressed the optimization

of cell placement phase in VLSI design process and

proposed a novel hybrid algorithm for performance and

Jobanpreet Kaur et al , Int.J.Computer Technology & Applications,Vol 4 (3),533-536

IJCTA | May-June 2013 Available online@www.ijcta.com

534

ISSN:2229-6093

low power driven VLSI standard cell placement. The

authors in the proposed work suggested the incorporation

of fuzzy logic in the design of aggregating function rather

than a single objective. Further the authors combined the

better searching features of Tabu Search and parallel

exploration capabilities of Genetic Algorithm to give an

efficient hybrid algorithm.

The authors in [12] proposed an approach that dealt with

different constraints and objectives in one optimization

step. The proposed algorithm used genetic algorithms

with tree-structured genotype representation. The authors

suggested hybrid algorithms for two constrained

placement problems namely Facility layout Generation

and VLSI Macro Cell Layout Generation. The suggested

work used genetic algorithm with non-standard genotype

representation for bottom up construction slicing tree for

individual that considered all constraints. The

experimental results showed better scalability than other

approaches.

The author in paper [14] proposed a hybrid cell placement

approach for low power VLSI standard cell placement

based on two evolutionary approaches namely Tabu

Search and Genetic Algorithm. The comparison between

the proposed technique with that of the GA was shown in

the work and the author concluded that the proposed

technique outperforms Genetic Algorithm in terms of

quality of final solution and CPU run time. The proposed

technique encodes the solution in the form of 2-D grid

unlike other approaches.

In the work [13], the authors proposed a memetic

algorithm for standard cell placement. The suggested

algorithm is a pure GA combined with tile-based local

search in three different ways i.e. before crossover, after

crossover and before and after crossover. As stated

experimentally, the authors concluded that the amount of

improvement of the quality of solution and decreased

CPU time is enhanced by integrating GA with local

search method.

3.4 Summary of Genetic Approaches

Table 1.1

Author Name Year Proposed Technique Key Features

K. Shahookar, P.

Mazumder

1990 Genetic Algorithm - Comparison of three crossover

operators i.e. Order crossover,

PMX and Cyclic

- Cyclic crossover operator used.

- Inversion operator used

K. Shahookar, P.

Mazumder

1990 Genetic Algorithm using

Meta-Genetic Parameter

Optimization

- Parameters of GA optimized

- Genetic operators used at different

rates in each execution of GA

Volker Schnecke,

Oliver Vornberger

1997 Hybrid Genetic Algorithm - GA with tree-structured

representation used

- Bottom up construction of slicing

tree for an individual used

- Crossover operator is Gene Pool

Recombination

- Three mutation operators used

Sadiq M. Sait,

Mahmood R.

Minhas

2002 Novel Hybrid Algorithm - Fuzzy logic incorporated in

aggregating function

- TS + GA

Mahmood R.

Minhas

2003 Evolutionary Cell

Placement Technique

- Tabu Search + Genetic Algorithm

- Solution encoding in form of 2D

grid

Shawki Areibi,

Zhen Yang

2004 Memetic Algorithm - Pure GA + Tile Based Local

Search

- Local search called after

crossover, before crossover and

both

Jobanpreet Kaur et al , Int.J.Computer Technology & Applications,Vol 4 (3),533-536

IJCTA | May-June 2013 Available online@www.ijcta.com

535

ISSN:2229-6093

Aaquil

Bunglowala, Dr.

B. M. Singhi, Dr.

Ajay Verma

2009 Hybrid and Local Search

Algorithms

- Hopfield Neural Network + GA

- SA + GA

- PRSA included crossover and

neighborhood operators

Rini Mahajan,

Amit Saxena,

Baljit Singh Khera

2010 Genetic Algorithm using

various genetic operators

- Selection Method: cell having

maximum area selected first

- Random point Crossover

4. Conclusion

The standard cell placement problem has been widely

studied by the researchers and various algorithms

have been developed. This paper presents a brief

survey on the evolutionary approaches applied on the

basic cell placement problem. The work discussed in

this survey paper focusses on specific constraints of

cell placement problem that does not include the

orientation of cell modules, time delay of circuits etc.

The various genetic approaches applied differs on the

selection method, crossover operators, hybrid

approaches thereby changing the performance of

algorithm. The table 1.1 shows a brief summary of

the approaches studied and their key features.

5. References

[1] J.H. Holland, Adaption in Natural and Artificial

Systems, University of Michigan Press, Ann Arbor,

Michigan, 1975.

[2] K. Shahookar and P. Mazumder, “Gasp: a genetic

algorithm for standard cell placement," In Proceedings of

the conference on European design automation, pp. 660-

664, IEEE Computer Society Press, 1990.

[3] Naveed A. Sherwani, Algorithms for VLSI Physical

Design Automation, Kluwer Academic Publishers, Intel

Corporation, Hillsboro, OR, USA, 1998.

[4] Mazumder, Pinaki, and Elizabeth M. Rudnick. Genetic

algorithms for VLSI design, layout & test automation.

Prentice Hall PTR, 1999.

[5] Golin R. Reeves and Jonathan E. Rowe, Genetic

algorithms : principles and perspectives : a guide to GA

theory, Kluwer Academic Publishers, School of

Mathematical and Information Sciences, Coventry

University, USA, 2003.

[6] Pan, Min, Natarajan Viswanathan, and Chris Chu. "An

efficient and effective detailed placement algorithm."

Computer-Aided Design, 2005. ICCAD-2005. IEEE/ACM

International Conference on. IEEE, 2005.

[7] Huang, Dennis J-H., and Andrew B. Kahng.

"Partitioning-based standard-cell global placement with an

exact objective." Proceedings of the 1997 international

symposium on Physical design. ACM, 1997.

[8] Hur, Sung Woo, and John Lillis. "Mongrel: hybrid

techniques for standard cell placement." Proceedings of the

2000 IEEE/ACM international conference on Computer-

aided design. IEEE Press, 2000.

[9] Zheng Yang, \Master's thesis, area/congestion-driven

placement for vlsi circuit layout," 2003.

[10] K. Shahookar and P. Mazumder, \A genetic approach

to standard cell placement using metagenetic parameter

optimization," IEEE Trans. On CAD , vol. 9, pp. 500-511,

May 1990.

[11] K. Shahookar and P. Mazumder, \VLSI Cell

Placement Techniques," ACM Computing Surveys, vol. 23,

No. 2, pp. 143-220, 1991.

[12] Schnecke, Volker, and Oliver Vornberger. "Hybrid

genetic algorithms for constrained placement problems."

Evolutionary Computation, IEEE Transactions on 1.4

(1997): 266-277.

[13] Areibi, Shawki, and Zhen Yang. "Effective memetic

algorithms for VLSI design= genetic algorithms+ local

search+ multi-level clustering." Evolutionary Computation

12.3 (2004): 327-353.

[14] Minhas, Mahmood R. "An evolutionary algorithm for

low power VLSI cell placement." Circuits and Systems,

2003 IEEE 46th Midwest Symposium on. Vol. 3. IEEE,

2003.

[15] Bunglowala, Aaquil, B. M. Singhi, and Ajay Verma.

"Optimization of Hybrid and Local Search Algorithms for

Standard Cell Placement in VLSI Design." Advances in

Recent Technologies in Communication and Computing,

2009. ARTCom'09. International Conference on. IEEE,

2009.

[16] Mahajan, Rini, Amit Saxena, and Baljit Singh Khehra.

"A genetic approach to standard cell placement using

various genetic operators." International Journal of

Computer Applications 1.9 (2010): 0975-8887.

[17] Kim, Myung-Chul, Dong-Jin Lee, and Igor L. Markov.

"SimPL: An effective placement algorithm." Computer-

Aided Design of Integrated Circuits and Systems, IEEE

Transactions on 31.1 (2012): 50-60.

[18] Sait, Sadiq M., and Mahmood R. Minhas. "GATS: A

Novel Hybrid Algorithm for Cell Placement in VLSI

Circuit Design." (2002).

Jobanpreet Kaur et al , Int.J.Computer Technology & Applications,Vol 4 (3),533-536

IJCTA | May-June 2013 Available online@www.ijcta.com

536

ISSN:2229-6093