An Analytical Study of GPU Computation for Solving QAPs by Parallel Evolutionary Computation with Independent Run

Transcription

1 An Analyical Sudy of GPU Comuaion for Solving QAPs by Parallel Evoluionary Comuaion wih Indeenden Run Shigeyoshi Tsusui Hannan Univ., JAPAN Noriyuki Fujimoo Osaka Prefecure Univ., JAPAN 1

2 Ouline of This Talk Background of he research Effec of arallel indeenden run on GPU Quadraic Assignmen Problem QAP) Imlemenaion Deails on GPU Resuls Analyical sudy Conclusions and Fuure Work 2

3 Background In a revious sudy CIGPU 2009), we alied GPU comuaion o solve quadraic assignmen roblems QAPs) wih arallel EC on a single GPU The resuls in ha sudy showed ha arallel EC wih he GTX285 GPU roduce a seedu of x3 o x12 comared o he i GHz) However, he analysis of he resuls was osoned for fuure work In his sudy, we roose a simlified arallel EC model and analyze how he seedu is obained using a saisical model of arallel runs of he algorihm

4 Parallel EC Models Maser-Slave Model Coarse-grained Model Disribued EC) Maser Slave Slave Slave Fine-grained Model Hybrid Model Individual-level Model

5 Parallel EC Model on GPU Shared Memory SM) Shared Memory SM) Shared Memory SM) Parallel Indeenden Run Model A varian of he coarse-grained model Gives a lower bound erformance of he coarse-grained model Each sub-oulaion runs on each MP indeendenly On an MP, individual level arallel run is erformed sub-oulaions 1 2 Muli-Processor 30) VRAM Global Memory)

6 Run ime Run ime Effec of Parallel Indeenden Run Sequenial run T avg Parallel indeenden run Obviously, T avg >T,avg

7 Quadraic Assignmen Problem QAP) One of he hardes combinaorial oimizaion roblem Problem size is a mos 150 Given l locaions and l faciliies, he ask is o assign he faciliies o he locaions o minimize he cos For each air of locaions i and j, he disance is d ij For each air of faciliies r and s, he flow is f rs The cos is defined as: cos l l ) f ij d i) i1 j1 j) 7

8 locaion faciliy CEC/CIGPU 2010, Barcelona, July 2010 An Examle of QAP l=4) locaion 1 faciliy locaion locaion faciliy 2 locaion 3 44 faciliy faciliy 3 locaion disance marix d ij faciliy flow marix f rs an assignmen = cos ) 4 4 i1 j f ij d i) j) 8

9 The Base EC Model of a Sub-oulaion We use oulaion ool P and working ool W Each individual i i=1,2,, N) is rocessed indeendenly of oher individuals. Re-iniialize if number of individuals which have curren bes funcional value is greaer han N0.6 Pair wise selecion beer P I 1 I 2 I N W I 1 ' I' 2 Aly Crossover and muaion I i Selec anoher aren randomly I' N 9

10 Imlemenaion Deails on GPUs MP 1 shared memory16kb) Assume roblem size a mos 56 subo size N=128 Sring is array of unsigned char MP 30 shared memory16kb) Check or se soluion was found consan memory Consan daa for QAPf ij, d ij ) Foundflag=0 VRAM 10

11 Exerimenal Condiions CPU Inel Core i7 965 GPU NVIDIA GeForce GTX rocs, VRAM 1GB) 2 OS Windows XP Comiler Visual Sudio 2005 wih /O2 SDK CUDA 2.3 Number of runs 30 Problem insances ai25b, kra30a, kra30b, ai30b, kra32, ai35b, se36b, ai40b, ai50b from QAPLIB 11

12 The run ime gain obained by gain -block arallel runs o single block runs The values of gain are differen from insance o insance They are in he range [10, 35] for = 30, and [10, 70] for = 60, and are nearly roorional o, exce for some insances GPU =30) 2GPUs =60) 0 ai25b kra30a kra30b ai30b kra32 ai35b se36b ai40b ai50b QAP Insances

13 Run Time Esimaion of Indeenden Parallel Run 1) Sequenial run f), F) Parallel indeenden run g,), G,)

14 Run Time Esimaion of Indeenden Parallel Run 2) d f F M f F G d d g F G d f F ) )) 1 ) ) )) 1 ), ), )) 1 1 ), ) ) blocks indeenden run wih arallel Run imeof ) 1) Run imewih single block run d f M ) )) 1 ) ) 1) blocks indeenden run wih by arallel Gain obained d f F d f M M Gain

15 Run ime disribuion on a single block ai25b kra30a kra30b ai30b kra32 ai35b se36b ai40b ai50b ime sec) QAP Insances

16 F) G disribuion reflecs run ime well ai25b 0.4 kra30a kra30b f ) ex ) 0.2 f ) ex ) 0.2 f ) ex ) ai30b 0.4 kra ai35b 0.2 f ) ex ) 0.2 f ) ex ) 0.2 f ) ex ) se36b 0.4 ai40b 0.4 ai50b 0.2 f ) ex ) f ) ex ) 0.2 f ) ex )

17 An examle of G disribuion ai25b

18 Comarison beween Exerimenal and GPU GPU1 Insances Analyical Resuls No of GPU G GPU G GPU G blocks T,avg M P ) T,avg M P ) T,avg M P ) GPU GPU GPU1 Insances GPU G GPU G GPU T,avg M P ) T,avg M P ) T,avg M P ) GPU GPU GPU1 No of blocks Insances No of blocks ai25b ai30b se36b kra30a kra32 ai40b GPU G GPU G GPU kra30b ai35b ai50b T,avg M P ) T,avg M P ) T,avg M P ) GPU G G

19 Comarison beween GPU and CPU Comuaion QAP insances GPU Comuaion GPU1 T 30,avg ) GPU2 T 60,avg ) CPU Comuaion CPU T avg ) Poulaion Size GPU1 seedu GPU2 ai25b kra30a kra30b ai30b kra ai35b se36b ai40b ai50b Values of T 30,avg, T 60,avg and M P ) are in seconds 19

20 Conclusions We roosed an EA for solving QAPs wih arallel indeenden runs using GPU comuaion and gave an analysis of he resuls In his arallel model, a se of small-size suboulaions was run in arallel in each block in CUDA indeendenly Wih his scheme, we go a erformance of GPU comuaion ha is almos roorional o he number of equied mulirocessors MPs) in he GPUs We exlained hese comuaional resuls by erforming saisical analysis Regarding erformance comarison o CPU comuaions, GPU comuaion showed a seedu of x4.4 and x7.9 on average using a single GPU and wo GPUs, resecively

21 Fuure Work To obain higher seedu values, we need o imrove he imlemenaion of variaion oeraor used in each hread in he blocks Each war of 32 hreads is essenially run in a SIMD fashion in a MP; high erformance can only be achieved if all of a war s hreads execue he same insrucion We can consider many arallel evoluionary models for GPU comuaion. To imlemen hese models and analyze hem remain for fuure work

22 kra30a M[1]/ M[]

23 ai50b

24 ai40b 系列

25 ai35b

26 ai30b

27 ai25b

28 se36b

29 kra

30 kra30b