Floorplanning Based on Particle Swarm Optimization
Tsung-Ying Sun, Member, IEEE, Sheng-Ta Hsieh, Student Member, IEEE, Hsiang-Min Wang
and Cheng-Wei Lin
Department of Electrical Engineering
National Dong Hwa University
Hualien, Taiwan, R.O.C.
E-mail: sunty@mail.ndhu.edu.tw
Abstract
This paper presents a floorplanning method based on
particle swarm optimization (PSO). We adopted the
B*-tree floorplan structure to generate an initial stage
with overlap free for placement and utilized PSO to
find out the potential optimal placement solution.
Unlike other related research, our method can avoid
the solution from falling into the local minimal and has
ability of more efficiency and robustness for explored
solution space. Experiments employing MCNC and
GSRC benchmarks show that the performance of our
method for placement by the ability of exploring better
solutions. The proposed approach exhibited rapidly
convergence and led to more optimal solutions than
other related approach.
1. Introduction
Floorplanning has been an important stage in VLSI
design as a means to manage circuit complexity and
deep-submicron effects. Floorplanning in VLSI design
is to arrange the modules on a chip under the constraint
that no two modules are overlap while controlling the
area, wire length, and other performance indices to be
optimal. Today, automatic floorplanning is encouraged
by the growing adoption of embedded memories and
IP blocks in System on Chips (SoCs) deigns.
The physical placement of circuits in VLSI chips or
SoCs has been given sustained attention in the recent
years. Early research on the placement problem applied
force to reduce the overlap betweens cells [1]. [2-4]
shows the generation of overlap free placements, and
[5] compare various floorplan representations which
cooperate with simulated annealing (SA). Adopting a
floorplan representations could easily apply to different
applications and various requirements through modify
objective functions. The drawback of adopting SA is
that the system must be close to equilibrium
throughout the process, which demands a careful
adjustment of the annealing schedule parameters. [6-7]
shows the generated layouts with cell overlaps. While
allowing overlaps during the process of placement was
shown to obtain a better floorplanning solution, this
process could not guarantee the entire elimination of
overlaps.
[8] introduced an integer linear programming (ILP)
formula for finding the optimal module orientations in
macrocell placement. The proposed method handles
multi-terminal nets based on the Manhattan metric of
the minimum bounding box of the pin positions which
is more accurate than some earlier approaches which
can only adapt to two-terminal nets based on the
Euclidean metric for wire length estimation.
As opposed to these previously mentioned methods,
we adopt a non-slicing structure of representation B*tree with particle swarm optimization (PSO) algorithm
in this paper. PSO is a swarm intelligence method that
roughly models the social behavior of swarms. The
consequence of modeling this social behavior is that
the search process allows particles to stochastically
return toward previously successful regions in the
search space. It has proved to be efficient on many
problems in science and engineering. Our method can
reduce much of computational time, obtains rapid
convergence and better solutions. Furthermore, our
floorplanner can widely explore the solution space and
prevent the solution from falling into the local minimal
We divided this paper into five sections. Section II
describes the original PSO methodology. Section III
presents B*-tree representation and our proposed
methods for floorplanning. Section IV exhibits the
experiment results. Finally, the conclusion is in section
V.
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2. Particle swarm optimization
3. PSO for floorplanning
The PSO is a population based optimization
technique that was proposed by Kennedy and Eberhart
[9] in 1995, which the population is referred to as a
swarm. The particles express the ability of fast
convergence to local and/or global optimal position(s)
over a small number of generations.
A swarm in PSO consists of a number of particles.
Each particle represents a potential solution of the
optimization task. All of the particles iteratively
discover the probable solution. Each particle generates
a position according to the new velocity and the
previous positions of the cell, and is compared with the
best position which is generated by previous particles
in the cost function and keeps the best one; i.e., each
particle accelerates the directions not only the local
best solution but also the global best position. If a
particle discovers a new probable solution, other
particles will move closer to it so as to explore the
region more completely in the process [10].
Let s denote the swarm numbers. In general, there are
three attributes, current position xi, current velocity vi
and local best position yi, for particles in the search
space to present their features. Each particle in the
swarm is iteratively updated according to the
aforementioned attributes. Assuming that the function f
is to be minimized so that the dimension consists of n
particles and the new velocity of every particle is
updated by (1).
3.1. The B*-tree representation
vi , j (t + 1) = wvi , j (t ) + c1 r1,i, j (t )[ yi, j (t ) − xi , j (t )]
+ c2 r2,i, j (t )[ yˆ j (t ) − xi , j (t )]
In this paper, we adopted the B*-tree representation
to model a floorplan [4]. A B*-tree is an ordered binary
tree for modeling non-slicing floorplans. Figure 1
shows a packing of floorplan and its corresponding B*tree, where the tree nodes ni are directly mapping to the
placement blocks bi . The root of B*-tree which denotes
as n0 is corresponding to the block b0 on the bottom-left
corner of the placement. The construction of a B*-tree
is starting from the root, and then the first recursively
create the left subtree, finally is the right subtree. Let Ri
be the set of blocks located on the right-hand side and
adjacent to bi. The left child of the node ni corresponds
to the lowest, unvisited block in Ri. The right child of
ni represents the lowest block located above and with
its x-coordinate equal to that of bi and its y-coordinate
less than that of the top boundary of the module on the
left-hand side and adjacent to bi.
n0
b5
b7
n2
n1
b4
b2
b3
b0
b1
(1)
(a)
n3
b6
n5
n4
n7
n6
(b)
where vi , j is the velocity of the ith particle of the jth
swarm for all j ∈1... s , w is the inertia weight of
velocity, c1 and c2 denote the acceleration coefficients,
r1 and r2 are elements from two uniform random
sequences in the range (0, 1), and t is the number of
generations. The new position of the ith particle is
calculated as follows:
xi (t + 1) = xi (t ) + vi (t + 1)
Figure 1. A packing represented by B*-tree
Each nodes combination of B*-tree corresponds to
a floorplan. Therefore, the solution space consists of all
B*-trees with the given nodes (blocks). In order to find
a next better solution, the B*-tree is disturbed by
following operations to get another nodes combination:
(2)
The local best position of each particle could be
updated by (3), and the global best position ŷ was
found from all particles by (4).
if f (xi (t + 1)) ≥ f ( yi (t ))
⎧ yi (t ),
yi (t + 1) = ⎨
⎩ xi (t + 1), if f (xi (t + 1)) < f ( yi (t ))
yˆ (t + 1) = arg min f ( yi (t + 1)), 1 ≤ i ≤ n
(3)
(4)
yi
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1. Node movement
This operation will delete a node and insert it
into other place of the tree.
2. Nodes (blocks) swap
This operation will swap two blocks of the tree.
3. Block rotation
This operation just rotate blocks without change
the tree structure.
3.2. Handling Floorplanning Using Particle
Swarm Optimization
Create and initiate a B*-tree and an N-dimensional
PSO: P
Repeat:
Execute PSO to update P by (1) and (2)
Perturb the B*-tree
for each particle i ∈ [1... m]
if f ( xi ) < f ( yi ) or f ( xi ) is acceptable
At the beginning move, each particle move will
random pick up one operation that mentioned above,
after that, the particles movement will inherit the
pervious experience, i.e. past best solution and global
best solution to guide them to select a suitable
operation for finding a better solution. In the searching
space, each particle move will lead the solution toward
global best solution. Figure 2 illustrates the particle
movement behavior for getting a better solution.
then yi = xi
if f ( yi ) < f ( yˆ )
then yˆ = yi
endfor
Until Termination condition reached
Figure 3. Pseudo code
Circuit
: Particles
: Optimal solution
Figure 2. Particle movement behavior
Adopting more than one particle will explore more
potential better solutions and each particle would
provide its experience for other particles to prevent any
particle’s solution from trapping into local minimal
and jump out to find better solution. The amount of
particles would not influence the computation time
directly. Due to more amounts of particles will find
more solution in current generation and spend more
time on computation. Therefore, it would spend less
generation for getting an acceptable solution. On the
contrary, in case of adopting small quantity particles
will reverse the result. After a number of generations,
each module will get closer, i.e. the chip size is gets
smaller. The requirement of minimized chip area is
estimated by the objective function f. The amount of
particles in the swarm is defined as 1 ≤ i ≤ m . The xi
represents the particle’s current position in solution
space and the initial states of vi,j, yi and ŷ were set as
0. As soon as particles moved following (1) and (2),
the new local best position and the global best position
would be updated by (3) and (4) respectively. The
particle would keep moving to find a better solution
until it reached the goal or met the termination
condition [11][12]. The pseudo code of our method is
presented in Figure 3.
apte
xerox
hp
ami33
ami49
n_30
n_50
4. Experiments result
The experiments in this study employed GSRC and
MCNC benchmarks [13] for the proposed floorplanner
and compare with [4]. All the cells were set as hard IP
modules. The simulation programs were written in
MATLAB [14], and the results were obtained on a
Pentium 4 1.7 GHz with 512MB RAM. The PSO
experiments with w, c1 and c2 initializations were 1,
0.1 and 0.1, respectively. The particle number is set as
five. We ran the both floorplanner 10 times and
calculated their average outcomes of chip area and run
time.
The experiment results of both floorplanner are
shown in Table 1. Compare with [4], our method can
find a better placement solution in even less
computation time. Under the same tree structure, that is
to say, our method has more efficiency and solution
searching ability for floorplan. Although the SA in [4]
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TABLE 1 EXPERIMENTAL RESULTS
SA
with B*-tree
Our method
# of
[4]
modules
Time
Area
Time
Area
(mm2) (sec) (mm2) (sec)
9
47.30
58 46.92
23
10
20.47
69 19.55
6
11
9.57
213
9.22
87
33
1.36
1821
1.28
614
49
43.34
5762 41.01
3710
30
0.247
178 0.238
101
50
0.243
769 0.233
154
adopted three the same operations that mentioned
above, but it would randomly pick up the operation
(somewhat like a kind of trial and error strategy) but
not following the previous experience while trying to
find another better solution. This will result in the
floorplanner waste too much time on trapping the
solution into local minimal and harder to get a better
solution. Our method can overcome these drawbacks.
Thus, the acceptable solution can find out in shorter
computational time. The convergence curves of both
methods are shown in Figure 4. Relative to both
methods, our method possesses more robustness to
prevent the solution from falling into local minimal. It
would be beneficial to find a better solution in shorter
time. Figures 5-7 show three benchmark results of hard
modules packing for n50, ami33 and xerox.
Figure 6. Placement result in GSRC ami33
Figure 7. Placement result in GSRC xerox
Figure 4. Convergence curves
5. Conclusion
In this paper, we proposed a floorplanner based on
the PSO with B*-tree structure for placing blocks. PSO
exhibits the ability of searching the solution space
more efficiency than SA, Furthermore, PSO can save
more computation time for finding an acceptable
solution. The experiment results proved that the
proposed PSO method can lead to a more optimal and
reasonable solutions on the hard IP modules placement
problem.
6. Future works
Our future works will focus on finding ways to
apply to different representations for enhancing the
efficiency of the floorplanning, and dealing with soft
IP modules placement problem.
Figure 5. Placement result in MCNC n50
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[10] V. G. Gudise and G. K. Venayagamoorthy,
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[13] http://www.cse.ucsc.edu/research/surf/GSRC/progress.h
tml
[14] http://www.mathworks.com/
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