Master Thesis Defense

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An Evolutionary Approach for the Task Mapping Problem

Filipo Novo MrSupervisor: Dr. Csar Augusto Missio MarconCo-supervisor: Dr. Andrew Rau-Chaplin

www.filipomor.commaster thesis defense

Presentation Outline1IntroductionTheoretical BackgroundRelated WorkProject MethodologyExperimental Results

Conclusions

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Introduction Some concepts NoC - Network on Chip Tasks

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t0t1t3t4t2t5

Introduction The Task Mapping Problem

3t0t1t3t4t2TASKSt5

NP-Hard problem!

power consumption communication profile execution timeFilipo Novo Mr

IntroductionBrute-force algorithms are not feasible for solving NP-Hard problemsAlternative: to use heuristic methodsBest solution possible, although there is no guarantee the best global solution will be foundEvolutionary AlgorithmsDifferential Evolution (DE)4

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IntroductionMotivation Previous works Considering the DE features of: Optimization of non-linear problems Simplicity and flexibility of its code Try finding a more efficient task mapping solver using DE5

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IntroductionObjective Implement a new elitist strategy on Single Objective DE to efficiently solve the Task Mapping onto NoC Problem6

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Theoretical Background7Filipo Novo MrIntroductionTheoretical BackgroundRelated WorkProject MethodologyExperimental Results

Conclusions

Theoretical Background Task Mapping onto NoC ProblemTraditional approaches:PartitioningMappingFilipo Novo Mr8

C.A.M.Marcon, 2005

Theoretical Background Task Mapping AlgorithmsFilipo Novo Mr9

Network Flow Algorithm Shortest Tree Algorithm A* Algorithm Mathematical Inequalities Linear programming Evolutionary Algorithms Genetic programming Simulated Annealing

Theoretical Background Evolutionary AlgorithmsFilipo Novo Mr10

Theoretical BackgroundDifferential Evolution (DE)Filipo Novo Mr11


vector initialization Population is randomly initialized Uniform probabilistic distribution If a preliminary solution is available, must add distributed random deviations to it Each individual on the population represent a solution candidate

Theoretical BackgroundFilipo Novo Mr13

NPPopulation

(solution candidate)1



(solution candidate)n


mutation generate a new mutate vector a new parameter vector is generated by the DE by adding the weighted difference between two population vectors to a third vector


D. Bingham, 2015


X2X1

target vector

mutation factor


mutation generate a new mutate vector a new parameter vector is generated by the DE by adding the weighted difference between two population vectors to a third vector the resulting vector will be used as a donor on the next step keeps pacing throughout the solution space


recombination enhance the Population diversity keep track of good candidate solutions from previous generations


D


selection only the best individuals will be kept in the Population


Population

Xi,G



(solution candidate)n

Uj,i,G+1


DE complete steps

Theoretical BackgroundPopulation Evaluation on DEFilipo Novo Mr23

Filipo Novo Mr24Theoretical BackgroundTested algorithms:Brute Force Nave: N2 two independent nested loops.Brute Force Smart: N2 two dependent nested loops.Mishra & Sandeep: heapsort + 1 outer loop with a dynamic variant linked list.

Tested in a I5 CPU, 8GB RAM, running Kubuntu 14.04. All tests performed using nice -20 prioritization.To generate the data set:

Filipo Novo Mr25Theoretical BackgroundManaging the DE archive

truncate the archive using the Crowding Distance metricKumar and Kesavan, 2015

Theoretical BackgroundSimulated Annealing (SA)Filipo Novo Mr26

FCE Frankfurt Consulting Engineers GmbH, 2015

Theoretical BackgroundNASA Numerical Aerodynamic Simulation (NAS)Filipo Novo Mr27

CG - Conjugate Gradient, irregular memory access and communicationFT - discrete 3D fast Fourier Transform, all-to-all communicationIS - Integer Sort, random memory accessLU - Lower-Upper Gauss-Seidel solver. Large number of short messagesMG - Multi-Grid on a sequence of meshes, long- and short-distance communication, memory intensiveThese applications were selected because they have task communication based profiles. Therefore they are ideal for the purposes of this work.

Related Work28Filipo Novo MrIntroductionTheoretical BackgroundRelated WorkProject MethodologyExperimental Results

Conclusions

Related WorkJ. R. Ku and S. G. Ku [34]Two phases: clustered high communicating tasks into partitionsUsed NSGA-II algorithmMapped these partitions onto NoC processors.Tried to keep high communicating partitions close to each otherUsed a second version of the NSGA-II algorithm15% more efficient then Physical Mapping AlgorithmC. Deng et al. [41]Changed the classical DEIncluded a sorting step before chromosomes recombinationFor high-level task graphs, free of a target hardware architectureFilipo Novo Mr29

Related WorkSen Zhao et al. [45]Proposed a MODE using an adaptative mutation operator.The strategy is changed during runtime to try achieving better solutions on the flyThe resulting vector is now compared with the whole population, not only with your fatherTested using benchmark ZDT functions onlyD. Das, M. Verma and A. Das [58]Hardware/software partitioning problem using DEObjective functions: execution time, area cost and communication costDE ran 16% faster than PSOQuality of acieved solutions were not describedZhuo Qingqi et al. [51]Solving Task Mapping problem combining two evolutionary algorithms (not DE)Parallel approach for searching the solution spaceMPEG-4 and VOPD (Video Objective Plane Decoder) benchmark applicationsSaves 13% on energy and is 3% more efficient in communication latencyFilipo Novo Mr30

Project Methodology31Filipo Novo MrIntroductionTheoretical BackgroundRelated WorkProject MethodologyExperimental Results

Conclusions

Project MethodologyFilipo Novo Mr32

resulting task mapEACFBD012345678chromosomes

individual

task mapping step

Project MethodologyFilipo Novo Mr33

Project Methodology Data Structures ModellingFilipo Novo Mr34

00342132444221034011t0t1t2t3t4

Population size (NP)

Population Dimension (D)

D = number of existing tasksAdherent to SODE and MODE

Project Methodology Communication Volume MetricFilipo Novo Mr35

fo3(solution 1) = 10+0+25+20+15 = 70

fo3(solution 2) = 10+10+10+10+10+10+10+25+20+15 = 130

Project Methodology Load Balance MetricFilipo Novo Mr36

fo2(solution 1) = 29.45fo2(solution 2) = 54.11

Project Methodology Modifying DE: rewarding good individuals Identify most communicating tasks proposal 1:Reward individuals keeping most communicating tasks near to each other Proposal 2: Try generate good individuals during mutation or recombination operationsFilipo Novo Mr37

Project Methodology Identifying most communicating tasksFilipo Novo Mr38

ACEBDF55325341A, B: 5A, C: 5B, D: 3D, F: 1F, D: 4C, E: 5E, A: 3E, B: 2

A, B: 5A, C: 5B, D: 3D, F: 1+4C, E: 5E, A: 3E, B: 2

A, B, C,E: 5+5+3B, D, A, E: 3+5+2D, F, B: 5+3C, E, A: 5+5E, A, C, B: 3+5+2

A, B, C,E: 13B, D, A, E: 10D, F, B: 8C, E, A: 10E, A, C, B: 10

tA, tB, tC and tE

Project Methodology Proposal 1Filipo Novo Mr39

Ideal bonus value is 10%Different bonus values tend to stuck the evolution (no more convergence is reach)On average, 14% of solutions at the final Generation had been rewarded

Project Methodology Proposal 2Filipo Novo Mr40

Proposal 2 was halted:No more convergence after 4 generations on averageToo few tasks? Too small NoC?

Project Methodology Validating the DE (Single Objective)Filipo Novo Mr41

SO_Proc36_T36_CR0_50_F0_40_Gen1000_Noc6_6_1_Pop20_Test2016061716017308_ft32x1_v2ap01

Project Methodology Validating the DE (Multiple Objective)Filipo Novo Mr42

Function ZDT1

ETH Zrich, 2008

Project Methodology Validating the DE (Multiple Objective)Filipo Novo Mr43

Function ZDT2ETH Zrich, 2008

Project Methodology Validating the DE (Multiple Objective) Hypervolume metricFilipo Novo Mr44

Kian Sheng Lim et al, 2013

Experimental Results45Filipo Novo MrIntroductionTheoretical BackgroundRelated WorkProject MethodologyExperimental Results

Conclusions

Experimental ResultsParametersRangeNP10 and 20G100, 300, 500, 100, 5000 and 10000CR0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 06, 0.7, 0.8 and 0.9F0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 06, 0.7, 0.8 and 0.9

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Single Objective DENASA NAS applications: IS, CG, FT, MG, LUEach test case was executed at least 30 timesGoal: reduce communication volume

Experimental ResultsFilipo Novo Mr47

Single Objective DE NASA NAS benchmark





FT e IS COM MUITAS TROCAS DE MENSAGENS49


SODE vs CAFES NASA NAS benchmarkNASA NAS applications: IS, CG, FT, MG, LUEach test case was executed at least 30 timesCAFES was set to the best execution parameters found during preparation tests.The same formula was used by CAFES and SODE to calculate the fitness valueThe comparison focused on the quality of the best candidate solutionsThe comparison considered the five best candidate solutions of each test case for both tested algorithms



SODE vs CAFES NASA NAS benchmarkMean Values: absolute scalar value for the communication volumeStandard Deviation: how close are the best solutions from each other


Conclusions52Filipo Novo MrIntroductionTheoretical BackgroundRelated WorkProject MethodologyExperimental Results

Conclusions

ConclusionsA new adaptation for the SODE was proposed, rewarding individuals who kept related communicating tasks close to each otherTestes were executed using the NASA NAS benchmark, showing our implementation was able to generate feasible solutions.Our algorithm was compared to the SA implementation existing on the CAFES Framework.Our implementation reached better solutions on two of five benchmark applications; achieve similar results on one application. CAFES achieved better solution on other two tested applicationsOur implementation has proved to be important on solving the Task Mapping onto NoC problem, specially for applications with similar NASA NAS message exchange profiles Filipo Novo Mr53

An Evolutionary Approach for the Task Mapping Problem

Filipo Novo MrSupervisor: Dr. Csar Augusto Missio MarconCo-supervisor: Dr. Andrew Rau-Chaplin2016, August 18th

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