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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
[email protected]; [email protected]
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
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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 [email protected]
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 [email protected]
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
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University, USA, 2003.
[6] Pan, Min, Natarajan Viswanathan, and Chris Chu. "An
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[8] Hur, Sung Woo, and John Lillis. "Mongrel: hybrid
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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,
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[11] K. Shahookar and P. Mazumder, \VLSI Cell
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[12] Schnecke, Volker, and Oliver Vornberger. "Hybrid
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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
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[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,
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[15] Bunglowala, Aaquil, B. M. Singhi, and Ajay Verma.
"Optimization of Hybrid and Local Search Algorithms for
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Recent Technologies in Communication and Computing,
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[16] Mahajan, Rini, Amit Saxena, and Baljit Singh Khehra.
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various genetic operators." International Journal of
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[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
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[18] Sait, Sadiq M., and Mahmood R. Minhas. "GATS: A
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Jobanpreet Kaur et al , Int.J.Computer Technology & Applications,Vol 4 (3),533-536
IJCTA | May-June 2013 Available [email protected]
536
ISSN:2229-6093