V o l k e r S c h n e c k e

connectionbuttsElectronics - Devices

Nov 26, 2013 (4 years and 7 months ago)


Pro cs st IEEEEE Int Conf on GAs in Engineering Systems Innovations and pplications A
GALESIA Sep Sheld U IEE Conf ublication P No pp

V olk hnec k e lvi er V b erger
Univ ersit y o f Osnabr uc k
Departmen t of MathComputer Science
D Osnabr uc k German y
f v olk er j er g inform atik unisnabruec ke
h ttprahmsnformatik unisnabruec kerakt engrakt
Abstract A genetic algorithm or f PHYSICAL VLSIESIGN
the ph ysical design of VLSI hips is
The d esignycle of VLSI hips consists of
presen ted The algorithm sim ultane
diren t consecutiv e steps from highev el
ously optimizes the placemen t of the
syn thesis unctional design to pro uction d
cells with the total routing During
ac k aging The physic al design is the
the placemen t he t detailed routing is
pro cess o f transforming a circuit description
done while the g lobal routes are opti
in to the h p ysical la y out hic w h escrib d es the
mized b y t he genetic algorithm This
p osition f o ells c and routes for the i n tercon
is just opp osed to the usual serial ap
nections b et w een hem t Figure s ho a
proac h where the computation of the
sc hematic represen tation o f a la y out The
detailed outing r is the last step in the
main concern in the h p ysical design of VLSI
la y outesi gn
c hips is to d a la y out with minim al area
further the total w irelength has t o b e ini m
mized F or some critical nets here t are ard h
limitatio ns for the maxim al wirelength
The physic al design of VLSI hips is a v ery
complex optimization problem whic h s i nor
mally olv s v arious subteps ecause B
there are man yin terdep e ndencies b et w
these subteps i t is r ecommendable to com
bine some of them Due to the complexit y
only heuristic approac e g enetic algo
rithms can b e used
The main problem when solving eal appli
cations with genetic algorithms is to d a
useful genot yp e nco e ding for a s ingle solu
tion Our approac h uses a binary tree with
additional information for eac h no de The
main adv an tage here is the straigh tforw ard
implem tation of the genetic op erators
Figure Ala y out of a c hip
In the follo wing t here is a detailed d escrip
tion giv en of the classical w a y of solving the
Due to ts i complexit y eh ph ysical design is
ph ysical design of VLSI hips After this
normally brok v arious subteps
our genetic algorithm is describ e d whic h
com bines most of the t ypical subteps A t First the circuit has to b e p artitione d
generate some up to macro cells
the end some st results are presen ted and
some plans for extensions re a giv en
In the orplanning phase the cells ha v e

to b e placed on the la y out surface
The w ork of this author is b eing supp orted
in the BMBFro ject YBRIDpplications of
After placemen tteh glob r outing has
P arallel Genetic Algorithms f or Com binatorial
Optimization to b e done In this step the lo ose


in en

lik hes
in ed
orn Sc erroutes for the in terconnections b et w
the single mo dules acro cells are de
In the detaile dr outing the exact routes
for the in terconnection w ires in the
c hannels b e t w een the m acro cells ha v e
to b e computed
The last s tep n i the ph ysical design is
the c omp action of the la y out where it
is compressed in all dimensions so that
the total rea a is reduced
This classical approac h of he t ph ysical de
sign is strongly serial with man yin terdep en
Figure The hap s eunction for a
dencies b et w een the subteps F or exam
macro cell with three ir d
ple during o o rplanning a nd global routing
t i mplemen tations
there m ust b e enough outing r space reserv ed
to complete the exact wiring i n he t detailed
routing phase Otherwise the placemen thas
to b e corrected and the global routing has describ e a branc h nd a b ound approac hfro
to b e computed again the o orplan sizing p roblem i e ding an
optimal com bination of all p ossible la y
In the follo wing there is a c loser lo ok at steps alternativ es for a ll mo dules fter a placemen t
to b ecause orplanning and outing r While their algorithm is able to d he t b est
are solv ed b y he t application describ ed in solution f or this problem t i s i v ery ime t
this pap er consuming esp ecially for real problem i n
stances Coho on et al implemen ted a
genetic algorithm for the hole w orplan
Flo orplanni ng
ning problem Their algorithm mak of
In the orplanning p hase he t macro ells c
estimates or f the required routing space o t
ha v e to b e p ositioned o n the la y out surface
ensure completion of the n i terconnections
in suc h a manner that no blo c ks o v erlap
Another m ore often used heuristic olution s
and that t here is enough space left to c om
metho d for placemen tis mSi ulated Anneal
plete the in terconnections The input for the
orplanning is a set of mo dules a l ist of ter
minals ins for in terconnections for eac h
mo dule and a n etlist whic h describ es the
terminals whic hha v e to b e connected A t The a im of the r outing phase is to d the
this stage go o d estimates for the area of the geometrical a l y outs for all nets In the o or
single macro cells are a v ailable but their ex planning hase p space on the la y out surface
act dimensions can still v ary in a wide range has b een pro vided to complete the i n tercon
Consider or f example a r egister e o m d ule nections This space c an b e describ ed s a
consisting of registers It can b e orga a c ollection of single r outing r e gions ac h
nized as a or arra y region has a xed capacit y i e a maxi
whic h ields y four implemen tations with dif m um n um b er of w ires whic h c b e
feren t a sp ect ratios These a lternativ es are through this region and a n ber of rmtei
describ ed b y shap eunctions A shap e nals i e ins p on t he b o rders of the a djacen t
function is a l ist of f easible heigh twidth cells
com binations for the la y out of a single macro
cell f he T result of the orplan
Due to the complexit y t he routing is d one
ning phase is the s ized orplan whic hde
in t w o ubhases s In the glob r outing he
scrib es the p osition of the cells in the la y out
o o se routes for the nets are determined
and the c hosen implemen tations for the x
F or the computation of the g lobal outing r
ible cells the r outing space is represen ted as a g raph
the edges of t his g raph represen t t he rout
There exist man y d iren t pproac a hes to the ing regions and are w eigh ted with the corre
orplanning problem Wimer et al sp onding capacities f The global


routed an

use es
eenrouting is describ ed b y a list of routing re placemen t a en detailed routing are op
gions for e ac h et n of the c ircuit with none timized i n a single s tep there is no longer the
of the capacities of an y routing region b eing need for ompaction c T he main dirence o t
exceeded the c lassical approac h is that when building
an individual etailed d routing is d one ur d
ing lacemen p t f o the mo dules The global
routes and the g eneral placemen t a
mized b y he t genetic algorithm
The genot yp e
Figure A outing r graph eft and a
global route for a four ter
minal net righ t
After global r outing is d one for eac h outing r
region the n um b er f o nets routed through it
is kno wn In the detailed routing phase the
exact routes for t he wires h a v e to b e d eter
mined gure This is done incremen tally
i e one c hannel is routed at a ime t in a pre
deed order
Figure The slicing t ree for the l a y
out sho wn in ure
The genotyp e is enco ded b y a binary slicing
tree with additional sizing nd a routing infor
Figure The detailed routing inside
mation for eac h no de l v es of this tree
ac hannel
represen t the macro cells lo cks and the
inner no des represen t partial la y outs eta
blo cks ssoh wn in ure The tree is
The global routing can b e solv ed b y graph
constructed in a b ottomp fashion When
based tec hniques n I teger Programming or
building a m etalo c k o t w o blo c r
hierarc hical approac hes F or the d e
metalo c ks the arrangemen t a nd the ro
tailed routing there exist solutions based o n
tation of the t w o b lo c ks are xed The ex
Greedy Metho ds graph algorithms or hier
act r outing in the c hannel b t e w een hese t t w o
arc hical approac hes The complexit y and
blo c ks is done f i e nets b et w een
routabilit yofa la y out dep ends on the n um
the t w o lo b c ks are connected and outed r
ber of la y ers whic h can b e used for the com
Nets whic h onnect c other terminals han t
pletion of the in terconnections Usually in
those on the b orders f o the t w o b lo c ks are
macro cell la y out there are t w ola y ers and
passed on as terminals to the b orders of the
the routing is done in the manhattan o d
resulting metalo c k
i e one la y er is for he t v ertical he t other for
the horizon tal w ires and the nets c hange the
If the b lo c ks ha v e d iren tla youtlter
la y er when c hanging their direction
nativ es all necessary com binations of alter
nativ es are stored in the shap eunction of
the resulting etalo m c k The n ber of
com binations do es ot n gro wexponen tially
Our genetic algorithm com bines the or in the n b er f o blo c ks con tained in a sin
planning w ith he t routing phases Because gle m etalo c k b e cause some f o the com bi


ks of ut

ea The
opti re
ev nduals Here an iterated atc m hing approac h
4 6
is implem en ted w hic h ields y densely pac k ed
10 7
metalo c ks in the individuals F or this ll a
2 B2
p ossible pairs of mo dules a re built nd a v al
ued b yteh w asted space nside i the result
7 8 5
13 8
ing etalo m c ks Then a s et of pairs ith w
4 6
4 6
minim al o v erall w aste is c hosen to uilt b the
1 elemen ts for the next iteration of atc m h
ing This iteration results n i a set o f ensely d
pac k ed metalo c ks with four blo c ks inside
The m atc hingro cess is iterated un til the
11 11
slicingree for a ingle s individual is com
10 12
10 12
Figure Com bining t w o lo b c ks to a
There are diren t k m utations whic h
metalo c k
are applied ith w diren t frequencies hey T
c hange the structure of the slicing tree b y
exc hanging blo c ks or metalo c ks and mo v
ing subtrees to other p ositions n i t he tree
nations are redundan t cf ig F toring S
whic h corresp onds to mo ving partial la y
all alternativ es for he t metalo c ks is use
on the la y out surface F urther the m utation
ful b ecause one an c not d ecide in the lo w er
op erator rotates lo b c c hanges the p osi
lev el of the ree t whic h implemen tatio nof a
tion of t w o lo b c ks inside a metalo c k
metalo c kw ould b e the b st e to minim
co ding diren t implem en tations for eac h
the o v erall area of the la y out
metalo c k inagento yp e h ere nhances e the
p erformance to o b cause e fter a m utation
the b est implemen tati on ofamo v ed blo c k

t y out alternativ es

in its new en vironmen t c an b e c hosen This

for metalo c k M

migh t ir d from the b est implemen tation

d redundan t

at its old p osition


y out alternativ es


h B

e d d

Crosso v er



t d

M The c rosso v erp erator c ho oses t w o paren t




individuals f o whic h one opring is pro


duced b ycmo bining t w o d isjunct meta


blo c ks e subtrees from b oth individu

als It has turned out to b e not helpful
to do some n telligen t crosso v er i e c ho os
ing d ensely pac k ed metalo c ks in the ar p
en t i ndividuals so the m etalo c ks are c ho
sen randomly in the ctual a implemen tatio n
It is unlik ely to g et a complete la y out hen w
Figure The construction
com bining the etalo m c ks s o the missing
shap eunction for a meta
blo c v e to b e a dded When doing this
blo c k M b c k B b eing

the iterated atc m hing metho d is used again
p sitioned o up o n B or vice

to tak e c are that the a dded blo c ks built a
v ersa
densely pac k ed part in the la y out hicw his
represen ted b y t he opring
After the execution of a genetic op erator
Creation of the initial p opulatio n
the slicing tree is tra v ersed o t compute the
It has pro v ed to b e useful to start with a c hanged routing information and he t shap e
p opulation of not randomly created ndivid i functions for all inner no des

lo for
ha ks
the of

or ks
of indsRESUL TS




i p er c

la y out creation



T able The b enc hmark nstances i

The algorithm has b een tested on realife

iterated m atc hing
circuits c hosen rom f a la y out enc hmark

suite main tained b y MCNC North C ar
olina micro electronics computing nd a net

w orking cen ter see table The instances
are la y outroblems o f t he ld of full
custom macroell la y out
Figure The p erformance with re
sp ect to the creation of the
initial p opulation ami
p opulationize w as individuals The u p
p er curv e d escrib e s t he progress of the
ness a y out area or f runs of the algorithm
started ith w p opulations of totally random
generated individuals The lo w er curv e de
scrib es the p erformance for runs whic hha v e
started ith w a set o f v ery o g o d individuals
whic hha v e b een generated b y a pplication of
the i terated matc hing F or an impression of
the solution qualit y whic hw as on a v erage

mm for the r uns with the n telli
gen t creation of the initial p opulation note
Figure La y out for rea
that the la y out sho wn in ure h as an area

of mm
F or circuits with xible cells it is helpful to
Figure s ho ws a a l y out for the instance store ll a nonedundan tla y outlternativ es
ami a problem with only edize c ells for the metalo c ks in shap eunctions to en
The dark blo c ks sho w the cells the ligh ter hance the qualit y f o the initial p opulation
surface represen ts the routing space while This also increases the p erformance o f the
the white area sho ws the w asted space inside m utationp erator b ecause fter a the mo v e
the la y out The ctual a implemen tation do es men t of a metalo c k its b e st implemen ta
not do the detailed routing but adds an es tion n o the new p osition an c b e c hosen Fig
timated routing s pace when com bining t w o ho ure ws the b ene o f storing shap e
blo c ks The estimation is quite bad b ecause functions e v en for the metalo c ks for the
actually one trac k is reserv ed for eac h net in circuit with xible cells eac h
the c hannel b et w een t w o lo b c ks mplemen I t ha ving three diren t implemen tatio It is
ing a b etter heuristic for the etailed d outing r seen t hat the v ersion whic h tores s ll a alter
w ould further reduce the c hannel width nativ es for the metalo c ks clearly outp er
formes the v ersion of the algorithm whic his
Figure s ho ws the p erformance of the ge describ ed in the upp er curv e Here hen w
netic algorithm for circuit ami The pairing t w o exible b lo c ks to a metalo c k
b est ness a v eraged o v er runs s i sho wn only the i mplem en tation with the minima l
for b oth cases up to enerations g the area i s stored



ell mpl

amithe global view remains to the genetic al
gorithm whic h o ptimizes t he general place

only b est
men t a nd the g lobal routes on the la y out

com bination



la y out
J P Coho on W D P aris Genetic


Plac ement Pro c of IEEE In t Conf n o


shap eunctions lso a

for metalo c ks

J P oho C n o S U Hegde W N Mar

tin D S Ric hards Distribute d Ge
netic A lgorithms for the F lo orplan De

sign Pr oblem EEE T rans on CAD
V ol April
H Esb ensen A Macr oel l Glob al
Figure The b ene of shap eunc
R outer b ase d on wo t Genetic A lgo
tions for metalo c ks a v er
rithms Pro c of Europ e an Design
age of runs
Automation Conf Euro A C
Grenoble F rance Sep

A G eist A Beguelin J Dongarra
W Jiang R Manc hek V Sunderam
F uture w ork o n his t ro p ject will include the PVM Par al lel V irtual Machine IT
computation and visualization of the ex Press
act wiring whic h will replace the adding
T L engauer Combinatorial A lgorithms
of routingpace lik eit sdi neo ta hte mo
for Inte gr ate dCir cuit L ayout ohnWi
men t With this it will b e p ssible o to com
ley Sons
prise the wirelength in the ness whic h
only describ es he t la y out area n i the actual D Sc hlierk amp o osen H M uhlen
implem tation F or p erformance nhance e b e Str ate gy A daption by Comp et
men t he t concept of Comp eting ubp S opu ing S ubp opulations d Conf on P ar
lations n tro d uced b ySc hlierk amp o osen allel P roblem Solving from Nature
and M uhlen b ein will b e implemen ted Jerusalem Israel Oct
Though in this pap er only results of sequen Springer L ecture Notes in omputer C
tial runs are presen ted the algorithm is al Science
ready parallelized with the use of the PVM
R O tten Eient Flo orplan ptimiza O
ar al lel Virtual Machine messageassing
tion Pro c of In t Conf o n Comp De
in terface but t here will b e a sp e cial ert
in a more eien t parallelization
C Sec hen A Sangio v anniincen telli
The t imb erwolf plac ement a nd r outing
p ackage IEEE J of Solidtate Cir
cuits V ol SC
An ingenious a pproac h orf the al y outesign
of VLSI hips has b een presen ted It is con
N Sherw ani A lgorithms for VLSI
trary to the classical serial pro cess where
Physic al Design A utomation lu w er
st the cells are placed and global routes
Academic Publishers
for the nets are etermined d b efore the d e
S Wimer I Koren I Cederbaum
tailed routing is done There g lobal rout
timal asp e ct r atios f o building lo b cks
ing and orplanning is done with ha ving
in VLSI h A CMEEE Design Au
a global view on the dev eloping a l y out In
tomation onference C
the describ ed algorithm the detailed rout
ing is done during the omp c o sition o f par
D F W ong H W Leong C L Liu
tial la y outs whic h re a joined to a omplete c
Simulate dA nne aling for VLSI Design
solution during the construction of the geno
Klu w er Academic Publishers
t yp e a inary b licing s tree In this a pproac h


in en