Results for simulated annealing and evolutionary algorithm

evolution-ary algorithm

Forthemeta-heuristi algorithmwerstneedtoadjustthemetaheuristi parameters

for the algorithms. This is in many asesmore of an art, than a s ien e. In the

following we will experimentally ndthe best parametersetting. The test asewe

use to adjust the parametersfrom, is the HAL omputation with a time frame of

T = 20

^{. This is an arbitrary ase, and there is no guarantee this will leadto the}

−1 0 1 2 3 4 5 6 7

Figure 7.4: Solution (HAL

T = 20

^{) from simulated annealing asa fun tion of the}

α

temperature hange oe ientand thenumber

N

^{of iterationsto rea hthermal}

equilibrium.

Figure7.5: Solution(HAL

T = 20

^)fromevolutionaryalgorithmasafun tion ofthe

G stop

^{generation ountandthepopulationsize (}

N

^).

optimal set of parameters for all other ases. In parti ular one should beware of

ne-tuningthe algorithmpre isely tothis aseasit mightmeanthemeta-heuristi

algorithmsis reallygoodatndingthissolution,butterribleforallother asesand

ALU

Figure7.6: S hedule,FUallo ationandoperatorassignmentgeneratedbysimulated

annealingforHALwith

T = 20

onstraint,givingatotalbalsa- ost areaof

59700

^.

smallexamplewheretotheexa toptimumisknownisgoodtestfornarrowingdown

theparametersetting.

Webeginwithsimulatedannealing,whereweneedtondthetemperature hange

oe ient

α

^{andthethermal}equilibrium number

N

^{. InFigure7.4wehaveshown}

severalrunsofthealgorithmforvariousparametersettingsandplottedthesolution

thealgorithmnds. Ea hpointrepresentsanentirelynewrun. As anbeseenthe

simulatedalgorithm isratherunstable apableofgettingstu katalo alminimum.

Howeverfor

N = 500

^{and larger, the algorithm tends to be ome more stable and}

produ e good solutions(a tually the optimalsolution) at everyrun. The best

pa-rameter setting for

α

^{seems to be}

α = 1.250

^{for larger}

α

^{the algorithm does not}

produ e better solutions, only taking exponentiallymore time to omplete. These

settingalsoseemtoprodu egoodsolutionsfortheotherproblemsintheben hmark

set.

Nextis the evolutionaryalgorithm, whereweneed to ndthe

G stop

^generation

ount and the

N

^{population ount. In Figure 7.5 we have shown several runs of}

thealgorithmforvarious parametersettings andplotted thesolutionthealgorithm

nds. Againea hpointrepresentsanentirelynewrun. As anbeseenthesimulated

algorithm is rather stable apable of produ ing reliable results. Another fa tor is

the high-dependen y on the population size. With a population around

512

^the

algorithm starts onverging towardsthe global optimumwith the fast onvergen e

and hoosing a large population size doesnot in rease the onvergen e. The best

value for the maximum generation ount

G stop

^{seems to be around in the range}

from

320

^to

640

^{. To be on the safe side we hose}

640

generations. Again these parameterssettingsseemstoprodu egoodsolutionsfortheotheralgorithmsin the

someparti ularsolutions.

We have ben hmarked the algorithms on two DFGs: HAL (

T ASAP = 10

^{) and}

COSINE(

T ASAP = 11

^{). WeareinterestedintheCPU-timei.e.. theamountoftime}

ittakesrunningthealgorithmstogetasolutionsatisfyingourarearequirements. For

the twoDFGs weapply thetwometa-heuristi algorithms, givingus four primary

test ases(shownintable7.4). Forea htest asewesetvesili onarearequirements

and sixtime framerequirements

T = dt + T ASAP

^{,(the blanks arewhere the}

meta-heuristi -algorithmsfailtondasolutioneitherbe ausethereisnooptimalsolution

satisfyingtherequirementorin border asesbe ausethealgorithmsareheuristi ).

Again,alltestsareperformedona200MHzPentiumII,with96MBmemoryand

allnumbersree tastatisti alaverageofrunningthealgorithms500timesonea h

problem instan e.

In general the simulated annealing out-performs the evolutionary algorithm in

termsofCPUtimerequiredtondasolutionforlargeproblems(i.e. COSINE).The

primary reasonstems from the evolutionary algorithm working on a large

popula-tion,whi hineveryiterationhastobemadefeasibleand ostevaluated,whereasthe

simulatedannealing onlyworks withoneproblem instan e. Ontheother-handthe

evolutionaryalgorithm seems to performmore stable,unlikesimulated annealing

whi h is apable of getting stu k in lo al-minimums for some runs. Comparing

theevolutionaryalgorithmwiththesimulatedannealingtheevolutionaryalgorithm

takes signi antlylonger time torun anddoes ndjust asgood solutionsas

simu-lated annealing. Inparti ular in the COSINE ase theevolutionaryalgorithm has

problems. Thisdoesnotmeantheevolutionaryalgorithm annot ndthesolutions

eg. if runfree the evolutionary algorithm is apable of nding a solution for

CO-SINE,

T = 107

^{, belowthe area}requirementof

49200

^{, howeverit took}

25857.4s

^or

approximately7.18hours. Theevolutionaryalgorithmdoesnothoweverhavesimilar

problemsforFIR orELLIPTIC.

A property of the proposed CDFG synthesis algorithm is that one of these

al-gorithms will be run for the DFG fragments, until the main synthesis algorithm

onverges,itisthereforeimportantthatthesealgorithmsgeneratethesolutionsfast.

This favoursthesimulatedannealingoverthetwootheralgorithms.

Finally in Figure 7.6 is shown the optimal s hedule generated by the

meta-heuristi algorithmsin theparameterinvestigation.

In document Behavioral synthesis of asynchronous circuits (Page 110-113)