Evolutionary Algorithmical Approach for VLSI Physical Design- Placement Problem

ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 02, August 2011

Evolutionary Algorithmical Approach for VLSI
Physical Design- Placement Problem
Varatharajan .R 1, Perumal Sankar.S 2 , Lekha.R 3 , Kumaravel 4
1
Bharath University,Department of ECE,Chennai,India
E-mail :varathu21@!yahoo.com
2
Cape Institute of Technology,Department of ECE,Kanyakumari,India
E-mail:spsankar2004@yahoo.co.in
3
Bharath University,Department of ECE,Chennai,India
E-mail:lekhavathy@gmail.com
4
Bharath University,Department of CSC,Chennai,India
E-mail:drkumaravel@gmail.com

Abstract:-Physical layout automation is very important in problem considered here. The placement algorithms are
VLSI’s field. With the advancement of semiconductor classified into constructive and iterative improvement methods
technology, VLSI is coming to VDSM (Very Deep Sub [3]. The constructive algorithm starts with the empty set and
Micrometer), and the scale of the random logic IC circuits builds up the partition by adding one element at a time. These
goes towards million gates. Physical design is the process of
algorithms are faster but the quality of result is not good. An
determining the physical location of active devices and
interconnecting them inside the boundary of the VLSI iterative algorithm starts with initial placements and repeatedly
chip.The earliest and the most critical stage in VLSI layout modifies it. These algorithms give good result but takes long
design is the placement. The background is the rectangle time. The placement problems are the wire length [2] and area
packing problem: given a set of rectangular modules of of the die [3], routability, power minimization and delay [2].
arbitrary sizes, place them without overlap on a plane within Out of these above mentioned problems the area minimization
a rectangle of minimum area [1], [5]. The VLSI placement and the wire length minimization are the most critical part. For
problem is to place the object in the fixed area of die without the area and wire length optimization a modern placer needs
overlap and with some cost constrain such as the wire length to handle the large-scale design with millions of objects,
and area of the die. The wire length and the area optimization
heterogeneous objects with different sizes and various
is the major task in the physical design. We first
introduce about the major technique involved in the algorithm. constrained placement such as preplaced blocks and chip
density. The traditional approach in placement is to construct
Index Terms: Placement problems, Memetic algorithm, wire an initial solution by using constructive heuristic algorithms.
length minimization, area minimization. A final solution is then produced by using iterative
improvement techniques where a modification is usually
I .INTRODUCTION accepted if a reduction in cost occurs, otherwise it is rejected.
The solution generated by constructive algorithms may be
The task of the very large scale integration (VLSI) far from optimal. Thus an iterative improvement algorithm is
placement is to assign exact location to various circuit performed next to improve the solution and the computation
components within the chip area. It involves number of time of such algorithm is also large. For many combinatorial
objectives such as wire length, area of the die, timing and optimization problems, no effective algorithms capable of
power. Placement treats the shapes of all blocks as fixed, i.e., finding guaranteed optimum solutions in short time are
it only determines the location of each block on the chip. The available. Therefore, powerful heuristics have been developed
variables are the xy locations of the blocks; most blocks are that deliver the guarantee optimum solution, but have shown
standard cells. The y-locations of cells are restricted to to be highly effective in many test cases. A special class of
standard- cell rows. Placement instance sizes range in to the heuristics is investigated. The algorithms under consideration
tens of millions and will continue to increase. Placement is are called memetic algorithms, which are roughly speaking
usually divided into two steps: global placement and detailed hybrids of evolutionary algorithms and problem-specific
placement [1]. Global placement assigns blocks to certain search algorithms, such as greedy heuristics and local search.
sub regions of the chip with out determining the exact location Memetic algorithms (MAs) are evolutionary algorithms (EAs)
of each component within its sub region. As a result, the that apply the local search process to refine the individual
blocks may still overlap. Detailed placement starts from the MAs include a broad of metaheuristics [5] ,[4]. This method is
result of global placement, removes all overlap between based on the population of agents and proved to be of practical
blocks, and further optimizes the design. Placement objectives success in a variety of problem domains. We can be sure that
include the estimated total wire length needed to connect MAs constitute one of the most successful approaches for
blocks in nets, the maximum expected wiring congestion in combinatorial optimization in general and for the approximate
subsequent routing and the timing performances of the solution of NP optimization problems. The reminder of this
circuit. To solve such large scale mixed size VLSI placement paper is organized as follows: section 2 gives the memetic
problem many algorithms are used in VLSI. Among these algorithm flow, Section 3 involves the equation in the
algorithms memetic algorithm is used to solve the placement
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placement problem and Section 4 shows the experiment result Algorithms have been shown to be very effective in solving
for the problem considered. many hard combinatorial optimization problems. The
approach combines a hierarchical design technique, Genetic
II. MEMETIC ALGORITHMS Algorithms, constructive algorithms and advance local search
to solve the VLSI layout in various steps like partitioning
Memetic Algorithms are class of stochastic global search
and placement. The efficient optimization algorithm used to
heuristics in which Evolutionary Algorithm based approaches
solve hard problems usually employs a hybrid of at least two
are combined with problem-specific solvers. Later local search
techniques to find a near optimal solution to problem
heuristics techniques are implemented. This hybridisation is
considered. The main motivation for this hybridisation is to
to either accelerate or to discover good solution from the
increase the efficiency that is to get the good quality solution
population where the evolution alone would take long time
in specified time.
to discover or to reach the solution. Memetic Algorithms use
heuristic local searches either approximate method or exact
method to get the local refined solution from the population.
There are several reasons for hybridising evolutionary
algorithms with local searchers. Some of them are mentioned
below:
1. Complex problems are decomposed to different sub
problems could be better solved by different methods.
2. The hybridisation of evolutionary algorithm with local
search algorithm result in fine tuning or repairing the best
solution(s) produced by the evolutionary algorithm. The
powerful local searcher introduces diversity into the solution.
3. The sub problems are dealt by the various operators,
for example cross over and mutation or by the local searcher.
Thus the search process is done with in the search space
region.
4. In some cases the available exact or approximate
methods for the sub problems are included with the
evolutionary algorithm.
5. The heuristic or local search is used to repair the
solutions found by the evolutionary algorithm. The heuristic
or local search do the same in the Memetic algorithm. Such
heuristic are called Meteheuristic algorithm.
A. Memetic algorithm flow
Memetic algorithms try to simulate cultural evolution
rather than the biological one, as evolutionary algorithm do. Figure 1. Algorithm Template
They are a combination of population based global The above figure identifies the Memetic algorithm
optimization and heuristic local search. First individuals are template. The structure is the basic evolutionary algorithm
initialized randomly. Starting with each single individual, one structure and the black mark placed on the particular block is
local search is performed. After that, the individuals start to to mention that hybridisation takes place in that block. Each
interact either competitively (in selection form) or by of the black mark provides an opportunity for hybridisation.
cooperatively (in recombination form). These two steps are For example the initial population could be seed with
repeated until the stopping criterion is met. From this context solutions arising from sophisticated problem for specific
of above we can know that memetic algorithm acts as two heuristics. The cross over and mutation operator could be
level optimization algorithm, the top level algorithm is an enhanced with domain specific and representation specific
evolutionary algorithm otherwise a population based constrain as to provide better search ability to Evolutionary
algorithm and at the bottom levels a single individual Algorithm. More over local search could be applied to any or
optimizer like hill climbing or simulated annealing or some all of the intermediate set of solution, for example, offspring
other local search algorithm. set. The more problem specific knowledge is incorporated
B. Evolutionary Algorithms + Local Search = Memetic with in a Memetic algorithm the better it will perform. The
Algorithms most popular form of hybridisations is to apply one or more
phase of local search, based on some probability parameter,
Combining global and local search algorithm used for
to individual members of population in each generation.
many hybrid optimization approaches. Memetic algorithms
(MAs) are Evolutionary Algorithms (EAs) and along with C. Memetic Algorithm for Circuit Placement
that we apply some sort of local search algorithm to further The placement is nothing but arranging the circuit
improve the fitness of individual in the population. Memetic components in layout. In general-cell and standard-cell
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placement, we have to position the components of the circuit (iii) Before and after the crossover.
such that the layout area is minimized. The area measure
used here comprises the area taken up by the circuit III.PLACEMENT PROBLEM DESCRIPTION
components as well as the area needed for wiring the circuit
A. Area Estimation
components. The placement problem has the dual flavour of
a two dimensional packing problem and connection cost Given a set of module M1, M2,…..Mn and set of n
optimization problem. The packing problem is concerned interconnects N1,N2……Nn the objective of the placement is
with fitting a number of cells of different sizes and shapes to obtain the non overlapping package of all the modules
tightly into a rectangle. The connection cost optimization which achieves some optimization objective such as
aims at minimizing the amount of wire that is needed. The minimizing the area of package[3], the interconnection length
proposed Memetic Algorithm for circuit placement [4] [5] is as shown in the figure below:
based on the Genetic Algorithm . In each generation, a Tile-
based local search heuristic is performed on part of the
population to improve their fitness. The local search may be
introduced in genetic algorithm to offspring population, it
may be in cross over or else where. For the circuit placement
problem, the pure Genetic Algorithm is combined with Tile-
based local search in three different ways, referred to as
performing local search on part of the population: (i) before
the crossover (ii)after the crossover (iii) before and after the
crossover.[1].
1. Encode solution space for placement
2. Set population size, max-gen, generation=0;
Set crossover-rate, mutation-rate;
3. Generate the initial population
4. Evaluate the initial population
5. While (generation < max-gen) Figure 3.Six block placement
Apply genetic algorithm
Apply tile-based local search to population B. Horizontal Constrain:
End while If (-X,Y) =(. . . a. . .b. . .,a. . . b. . .) Block b is is at right side
6. Return the best solution in current population of the block a
Figure 2.Pseudocode for Memetic placement algorithm C. Vertical Constrain:
A Memetic algorithm for the circuit placement is purely If (X,Y) =(. . . a. . .b. . .,b .. . a. . .) Block b is at the below
based on the Genetic algorithm. From the above figure we can side of the block a Based on “left of’ constraint of (X, Y), a
under stand that the memetic algorithm for the circuit place- directed and vertex-weighted graph GH (V, E) (V: vertex set, E:
ment starts with the initial random population generation edge set), called the horizontal-constraint graph (HCG) is
before that we have to set the size of the population , maxi- constructed as follows:
mum number of generation, cross over rate, and mutation rate.
Next we apply the Genetic algorithm, the genetic algorithm
start with the selection process, the selection process is based Where bi correspond to the block
on the fitness function. The chromosome for the cross over is Sh is the source node representing the left boundary
selected using this fitness function . Cross over is the base th is the target node representing the right boundary
point for the next generation population. The cross over tech-
nique used in Genetic algorithm is one point cross over, two
point cross over, cut and splice cross over , uniform cross
over and half uniform cross over. After the cross over, the
mutation process is done to maintain the genetic diversity If existing, edge (bi,bi+1) edge (bi+1,bi+2) and edge (bi,bi+2)
from one generation to next generation. In this mutation the then (bi,bi+2) omitted
genetic sequence will be changed from its original by gener- 3) Vertex Weight equals the width of the block bi, but zero for
ating a random variable for each bit sequence. After the muta- Sh and th similarly the vertical constrain graph (VGH) as show
tion, accepting offspring is placed in the new population for in the below figure. Vertical constrain graph Gv(V,E) is
further iteration. The next step in memetic algorithm for cir- constructed using “above” constrain and the height of the
cuit placement is to apply the local search algorithm in be- each block. As for the example show in the above figure. The
tween this genetic algorithm. As mentioned before the local corresponding constrain graph Gh(V,E) and Gv(V,E) are as
search is applied in three ways as given below: show in the figures. Both Gh(V,E) and Gv(V,E) are vertex
(i) Before the crossover weighted acyclic graph so longest path algorithm can be
(ii) After the crossover applied to find the x and y co ordinates of each block.
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Cost wire = “l i
i€M
Where l is the wire length estimation for net i and M denotes
total number of nets in circuit.

IV. EXPERIMENTAL RESULT
The Memetic algorithm for VLSI cell placement problem
was tested on real life circuits chosen from a benchmark suite
that for design work shop in early 1990’s and it is often referring
to as MCNC benchmark. They were originally released and
maintained by North Carolina’s Microelectronics, computing
and networking centre and now it got changed to CAD
Benchmarking Laboratory (CBL). All results of our Memetic
algorithm presented in this section were obtained by
implementation of Memetic algorithm for placement. Here
first the initial population is generated and the fitness function
is evaluated. Based on that fitness selection of parents for
the cross over. After this process the normal mutation and
inversion operation takes place, in addition to this process
Figure 4. Example for vertical constrain graph (VGH) for each sub population, the local search is applied to refine
The coordinates of the block coordinate of the lower left the fitness of each individual to get the most optimal
corner of the block. solution.We are implementing our algorithm in c language as
(genetic algorithm + local search) , and the experiment is
executed on the Intel Pentium processor (3.1GHz, 512 RAM)
machine running windows xp . The memetic algorithm (genetic
algorithm + local search) is embedded in our algorithm the
block placement. The results obtained by implementing our
algorithm are shown in the table below:
TABLE 1.PERFORMANCE STATISTICS FOR MCNC B ENCHMARK CIRCUITS

V. CONCLUSIONS
Figure 5.Example for horizontal constrain graph
The hybrid approach for the combinatorial placement
D. Wire length estimation. problem is memetic algorithm, this memetic algorithm may
We are addressing the problem of VLSI standard Cell also be called as hybrid genetic algorithm, here the
placement with the objectives of minimizing wire length [2], hybridisation is done in genetic algorithm with some local
power consumption, and timing performance (delay), while search technique. First the memetic algorithm starts with the
considering the layout width as a constraint. genetic algorithm, finds the global minimum solution and to
E. Wire length measurement and Cost: further refine the individual and to get the local minimum we
introduce a local search. The main future of the approach
In VLSI placement the cells present in the module are introduced here, in comparison with other approaches, is the
connected by wire. The estimation of wire length [2] required manner in which block flexibility is treated. During the
for connection is calculated by the formula iteration several implementation such as wire length
Wire length = “wi,j ((xi – xj)2 + (yi - yj)2) calculation and area estimation are considered and some
I>j shape functions are introduced for the block. The common
Where hill climbers in genetic algorithm for combinatorial optimization
wi,j weight of the connection between cell x and y problem randomly explore the solutions neighbouring the
(xi – xj) distance in X direction candidate solution encoded in the current individual and
(yi - yj) distance in Y direction accept those with better fitness. In hybrid approaches, local
Inter connect wire length of each net in the circuit is estimate search techniques explore the solution space close to the
during Steiner tree and then total wire length is computed by sample points by applying specialized heuristics. When
adding the individual estimates
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including problem specific knowledge during creation of REFERENCES
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ACKNOWLEDGMENT Point-Addition-Based VLSI Placement” IEEE Transactionson
Computer Aided Design Of Integrated Circuits And Systems, Vol.24,
It is to note here that this topic-specific article for the No.8, August2005.
easy reference of VLSI Placement Problem, optionally being
used together with the all the problems in VLSI
PhysicalDesign. Author Varatharajan, I thank the management
of Bharath University, India to conduct his research in this
area and also he worked under the Guidance of Dr.Perumal
sankar and Dr.Kumaravel , the Eminent Professors in India.
He thank the guide for his moral support to continue the
research.

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Evolutionary Algorithmical Approach for VLSI Physical Design- Placement Problem

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Evolutionary Algorithmical Approach for VLSI Physical Design- Placement Problem