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Bo Yang, Liang Guang, Tero Sntti, Juha Plosila

Parameter-Optimized SimulatedAnnealing for Application

Mapping on Networks-on-Chip


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Outline

Introduction

Application Mapping

Implementation of SA

Nelder-Mead Simplex Method

Experiment and Analysis

Conclusion


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Introduction

Moores Law is still valid (ITRSs perspective)

What could we do with billions of transistors?

Tens to hundreds of cores on a single chip

80-core Intel Terascale Chip

Tilera TILE-Gx Family with 16 to 100 processing cores

...

Intel: Why a 1,000-core chip is feasible. ZDNet, 2010

Manycore architecture has become the mainstreamfor parallel commputing


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Major Concern

Communication, instead of computation

Great impact on perfomance and energy consumption

Conventional bus, point-to-point connections-bottleneck

Networks-on-Chip (NoC)

Better scalability

Higher reliability

More reusability

Introduction


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Application

a set of concurrent tasks

modeled by the communication weighted graph (CWG)

Many-core NoC

a set of tiles and links

Modeled by the computation and communication resource graph(CCRG)

Application Mapping


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The role is to determine how to place each task on a tile of theNoC so that the specific design interests and costraints arefulfilled.

Objective: mapping solution to minimize the communicationenergy consumption

Application Mapping


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Energy model of NoC [Jingcao2005]

Energy consumped by one communication

where : data volume transferred from task i to j

: distance of communication channel from node i

to j on the NoC and : energy consumed by switch and link

for transferring one bit of data on the NoC

Application Mapping


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Objective Formulization

Communication energy consumption of an application

Given constants and , Eapp is linearly proportional to

the product of and of all communications .

Weghted Communication of an Application (WCA)

The objective of the application mapping is to findthe optimal solution with minimal WCA.

Application Mapping

SmallerWCA

Bettersolution


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NP-hard problem

to map m tasks on n cores (m n )

possible solutions

search space increases exponentionally withproblem size m and n

Exhaustive search is impossible. (e.g., n =m =25,

25!1.55e25 ) Heuristic search including Simulated Annealing

(SA), Tabu Search (TS), Greedy Incremental (GI),etc.

Application Mapping

)!1(! mn

n


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Pro and Con

Be able to find global optima

Numerous computions and evaluations-long runtime

Parameters and Functions

Initial temperature T0 Final temperature T f Cost fucntion Cost(S)

Temperature function T e m p ( i ) Acceptance function Accept ( C, T)

Termination function Term ina te ( i , R)

Move function Move( S, T)

etc.

Simulated Annealing


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Cost function Cost(S)

Cost(S) = WCA of solution S

Temperature function T e m p ( i )

i :

# of iterations,q: cooling ratio

L: # of iterations at each temperature

Simulated Annealing

LiqTiTemp 0)(


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Acceptance function Accept ( C, T)

C0: initial cost, C : cost difference

K: normalized ratio

Termination function Term ina t e ( i , R)

Move function Mov e( S, T)

Single random swapping

A task in current solution is randomly selected and swapped to arandomly selected tiles to generate a new solution

Simulated Annealing

ZNRRTiTemp Cf 0max)(

)exp(1

1

0

()TKC

Cprobrandom


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Initial temperature T0 and final temperature T f Solve the acceptance function for T

T0 and T f can be derived by:

p r ob 0:probability of accepting Cm ax at temperature T0 p r ob f:probability of accepting Cm in at temperature T f

Simulated Annealing

)11ln(

0

00

max

probKC

CT

)11ln(0

probKC

CT

)11ln(0

min

fprobKC

CfT


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To summary, we need to determine parameters:

q : colling ratio

K: normalizing ratio

p r ob 0: probability of accepting Cm ax at temperature T0 p r ob f: probability of accepting Cm in at temperature T f Cm a x , Cm in : coputed using a finite number of trial moves

Considerations on parameter selection

problem-specific

jointly afftect the performance of SA

The set of parameters should be selected in a systemway, instead of being set mannually and independently.

Simulated Annealing


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Method for minimization of a function f ( p )

Proposed by Nelder et.al in 1965

f ( p ) : function with n variables x1, x2, , xn n + 1 points form the initial simplex, each point p

kis a n-

tuple (xk1, xk2, , xkn)

Sort the n + 1 function values so that f ( p 0 ) f ( p 1 ) f ( p n )

To get the minimum off ( p ) , in each iteration:

a new simplex is formed:either by replacing the point p n with

the re fe lec t i on po in t , the expans ion po in t or thecon t r act i on po in t , or by updating all points when thepreceding replacements failed.

Sort the n + 1 function values of points in the new simplex andcontinue the process



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The process terminates until f ( p 0) , f ( p 1) , , f ( p n)converge to one value which is the approximation ofthe mimimum value of function f ( p )

For more detail, refer J.A.Nelder and R.Mead. Asimplex method for function minimization.



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Parameter-Optimized SA (POSA) algorithm

Variables: q, K , p r ob 0 and p r ob f Initial simplex:5 initial points consisting of selected

values of 4 variables

SA algorihm applies each set of parameters of onepoint and finds one mapping solution

The WCA of the mapping solution found by the SAalgorithm is defined as the value of function f ( p ) andcompared with others

The Nelder-Mead method terminates when all 5 pointsconverge to one point which represents the set ofoptimized parameters we try to find

This set of optimized parameters is then applied to theSA algorithm to find the best mapping solution



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Expereiment and Result

Setup

Four applications

video object plane decoder (VOPD, 16 tasks)

MPEG4 12 tasks

multimedia systems application (MMS, 25 tasks)H.264 decoder (H264, 16 tasks)

Reference work: NoCMap ([Jingcao2005])

Parameters are set manually

q:0.9, T0:100, Tf:unbounded

Exponential form of acceptance function

Random swapping move function

Simulator in NoCMap is used to obtain the communication energyconsumption for POSA and NoCMap


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Optimized Parameters

Application q prob0 probf K

VOPD 0.91 0.44 0.05 0.72

MPEG4 0.95 0.34 0.05 0.36

MMS 0.94 0.36 0.05 0.62

H264 0.89 0.42 0.05 0.49

Parameters are problem-specific

Instead of using identical set of parameters, for different problems, differentsets of parmaters should be applied to the SA algorithm


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Number of I terations

Application NoCMap POSA POSA/ NoCMap

VOPD 4.30e6 2.74e4 0.64%

MPEG4 2.61e6 2.77e4 1.06%

MMS 1.14e7 1.18e5 1.04%

H264 1.61e6 1.94e4 1.02%

Avg. 0.94%

POSA uses significantly less number of iterations

On average less than 1% of that in NoCMap


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Runtime of SA (seconds)

App NoCMap POSANoCMap/ POSA

POSANoCMap/ POSA

VOPD 31.69 15.50 2.04 0.087 364

MPEG4 15.74 9.67 1.63 0.059 267

MMS 171.74 181.75 0.94 1.17 147

H264 12.34 11.90 1.04 0.072 171

Avg. 1.41 237

POSA includes the runtime of the Nelder-Mead method

POSA is the runtime of SA applying the optimized parameters

On average, a 237 times of speedup is achieved


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Weighted Communication (WCA)

The mapping solution of POSA yields comparable WCA with that of NoCMap


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Energy Consumption(EC)

Be consistent with the result of WCA

The mapping solution of POSA yields comparable communication energy consumption withthat of NoCMap


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Conclusion

A method to systematically select the parameters of the SAalgorithm for the application mapping problem is proposed.

With the set of optimized parameters, significantly less numberof evaluations are processed in the POSA and the SA algorithmis accelerated.

The accelerated POSA algorithm achieves comparable energyconsumption with NoCMap.

For the set of benchmarks, the POSA obtains the same qualitymapping solutions while using less than 1% of iterations ofNoCMap and achieving an average of 237 times of speedup.


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Thank for your attention!

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