Master Thesis Defense
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This document outlines the presentation for a master's thesis defense. It includes sections on the introduction, theoretical background, related work, project methodology, experimental results, and conclusions. The introduction discusses concepts like network-on-chip and the task mapping problem. The theoretical background section covers task mapping algorithms including differential evolution. The related work section summarizes previous research applying evolutionary algorithms to task mapping. The project methodology describes how the data is modeled and the metrics used to evaluate communication volume and load balance.
![Related Work
• J. R. Ku and S. G. Ku [34]
• Two phases:
• clustered high communicating tasks into partitions
• Used NSGA-II algorithm
• Mapped these partitions onto NoC processors.
• Tried to keep high communicating partitions close to each other
• Used a second version of the NSGA-II algorithm
• 15% more efficient then Physical Mapping Algorithm
• C. Deng et al. [41]
• Changed the classical DE
• Included a sorting step before chromosomes recombination
• For high-level task graphs, free of a target hardware architecture
Filipo Novo Mór 29](https://image.slidesharecdn.com/masterthesisfilipodefensev1publicavel-160901043353/85/Master-Thesis-Defense-30-320.jpg)
![Related Work
• Sen 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
fly
• The resulting vector is now compared with the whole population, not only with
your ’father’
• Tested using benchmark ZDT functions only
• D. Das, M. Verma and A. Das [58]
• Hardware/software partitioning problem using DE
• Objective functions: execution time, area cost and communication cost
• DE ran 16% faster than PSO
• Quality of acieved solutions were not described
• Zhuo Qingqi et al. [51]
• Solving Task Mapping problem combining two evolutionary algorithms (not DE)
• Parallel approach for searching the solution space
• MPEG-4 and VOPD (Video Objective Plane Decoder) benchmark applications
• Saves 13% on energy and is 3% more efficient in communication latency
Filipo Novo Mór 30](https://image.slidesharecdn.com/masterthesisfilipodefensev1publicavel-160901043353/85/Master-Thesis-Defense-31-320.jpg)
Master Thesis Defense
- 1. Filipo Novo Mór Supervisor: Dr. César Augusto Missio Marcon Co-supervisor: Dr. Andrew Rau-Chaplin www.filipomor.com master thesis defense
- 3. Introduction Some concepts NoC - Network on Chip Tasks 2Filipo Novo Mór NoC t0 t1 t3 t4 t2 t5
- 4. Introduction The Task Mapping Problem 3 t0 t1 t3 t4 t2 TASKS t5 NP-Hard problem! power consumption communication profile execution time Filipo Novo Mór
- 5. Introduction Brute-force algorithms are not feasible for solving NP-Hard problems Alternative: to use heuristic methods Best solution possible, although there is no guarantee the best global solution will be found Evolutionary Algorithms Differential Evolution (DE) 4Filipo Novo Mór
- 6. Introduction Motivation 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 DE 5Filipo Novo Mór
- 7. Introduction Objective Implement a new elitist strategy on Single Objective DE to efficiently solve the Task Mapping onto NoC Problem 6Filipo Novo Mór
- 8. Theoretical Background 7Filipo Novo Mór Introduction Theoretical Background Related Work Project Methodology Experimental Results Conclusions
- 9. Theoretical Background Task Mapping onto NoC Problem Traditional approaches: Partitioning Mapping Filipo Novo Mór 8 6 Application App1 t1 t4 t2 t6 t5 t7 t9 t10 t11 t12 t22 t16 t20 t21t18 t17 t19 t15 t14 t13 t12t2 t14 t11 t10 t16 t22 t7t19 t9 t1 t15 t13 t3 t20 t17 t21 t4 n1 n2 n3 n4 n5 n6 Communication Infrastructure Application App3 pA1 n3 1 pA2 pA3 pA4 pA5 pA6 Application App2 t5t18 t6 Partitioning Mapping 2 3 4 5 n5 n1 n6 n4 n2 t8 t8 t3 C.A.M.Marcon, 2005
- 10. Theoretical Background Task Mapping Algorithms Filipo Novo Mór 9 Network Flow Algorithm Shortest Tree Algorithm A* Algorithm Mathematical Inequalities Linear programming Evolutionary Algorithms Genetic programming Simulated Annealing
- 11. Theoretical Background Evolutionary Algorithms Filipo Novo Mór 10 SearchingTechniques EvolutionaryAlgorithmsCalculation Based Enumerative SingleObjective MultiObjective SimulatedAnnealing EvolutionaryStrategies Genetic ProgrammingDifferentialEvolution Genetic Algorithms
- 12. Theoretical Background Differential Evolution (DE) Filipo Novo Mór 11 vector initialization mutation recombination selection
- 13. Theoretical Background Differential Evolution (DE) Filipo Novo Mór 12 vector initialization mutation recombination selection 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
- 14. Theoretical Background Filipo Novo Mór 13 𝑿𝒊,𝑮 , 𝐢 = {𝟏, 𝟐, … , 𝑵𝑷} … NP Population (solution candidate)1 (solution candidate)2 (solution candidate)3 (solution candidate)n
- 15. Theoretical Background Differential Evolution (DE) Filipo Novo Mór 14 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 vector initialization mutation recombination selection
- 16. Theoretical Background Filipo Novo Mór 15 𝒇 𝒙 = 𝒊=𝟏 𝒅 𝒙𝒊 𝟐 D. Bingham, 2015
- 17. Theoretical Background Filipo Novo Mór 16 X2 X1 𝑿 𝒓 𝟐 𝒊 𝑿 𝒓 𝟑 𝒊 𝑿 𝒓 𝟏 𝒊 α δ 𝑽 𝒊,𝑮 target vector 𝑽𝒊,𝑮+𝟏 = 𝑿 𝒓 𝟏,𝑮 𝒊 + 𝑭 𝑿 𝒓 𝟐,𝑮 𝒊 − 𝑿 𝒓 𝟑,𝑮 𝒊 mutation factor
- 18. Theoretical Background Differential Evolution (DE) Filipo Novo Mór 17 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 vector initialization mutation recombination selection
- 19. Theoretical Background Differential Evolution (DE) Filipo Novo Mór 18 recombination enhance the Population diversity keep track of good candidate solutions from previous generations vector initialization mutation recombination selection
- 20. Theoretical Background Filipo Novo Mór 19 𝑽 𝒊,𝑮+𝟏 𝑿 𝒊,𝑮 𝑼 𝒋,𝒊,𝑮+𝟏 D 𝑼𝒋,𝒊,𝑮+𝟏 = 𝑽𝒋,𝒊,𝑮+𝟏 if 𝒓𝒂𝒏𝒅𝒋,𝒊 ≤ 𝑪𝑹 𝑿𝒋,𝒊,𝑮 if 𝒓𝒂𝒏𝒅𝒋,𝒊 > 𝑪𝑹 i = 1, 2, … , 𝑁𝑃 j = 1, 2, … , 𝐷 𝑉𝑖,𝐺+1 ≠ 𝑋𝑖,𝐺
- 21. Theoretical Background Differential Evolution (DE) Filipo Novo Mór 20 selection only the best individuals will be kept in the Population vector initialization mutation recombination selection
- 22. Theoretical Background Filipo Novo Mór 21 𝑿 𝒊,𝑮 𝑼 𝒋,𝒊,𝑮+𝟏 … Population Xi,G (solution candidate)2 (solution candidate)3 (solution candidate)n Uj,i,G+1
- 23. Theoretical Background Filipo Novo Mór 22 A - Population Initialization Is ui,G+1 better than xi,G ? H - Update Population B – Population Evaluation C - Select xr1,G, xr2,G and xr3,G D - Mutation E - Recombination F - Evaluates ui,G+1 no yes repeat for n generations for each individual i in the Population, repeatI - Select Dominant Solutions from Archieve G DE – complete steps
- 24. Theoretical Background Population Evaluation on DE Filipo Novo Mór 23 ≅ 𝑶 𝒏 𝟐 how deep would be the impact on the overall performance? X2 X1
- 25. Filipo Novo Mór 24 Theoretical Background 0 200 400 600 800 1000 1200 1400 1600 50 100 500 1000 2000 5000 7500 10000 milliseconds N Dominance Algorithms Execution Time M&S BF Naive BF Smart 0 1 2 3 4 5 6 50 100 500 1000 2000 5000 7500 10000 milliseconds N Mishra & Sandeep Dominance Algorithm Execution Time 3 5 21 32 63 146 210 287 0 50 100 150 200 250 300 350 50 100 500 1000 2000 5000 7500 10000 Speedup N M&S Dominance Algorithm Tested algorithms: Brute Force “Naïve”: 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: 𝑓1 = 1 − 𝑥2, 𝑥 = 𝑟𝑎𝑛𝑑48() 𝑓2 = 1 − 𝑥2, 𝑥 = 𝑟𝑎𝑛𝑑48()
- 26. Filipo Novo Mór 25 Theoretical Background Managing the DE archive truncate the archive using the Crowding Distance metric Kumar and Kesavan, 2015
- 27. Theoretical Background Simulated Annealing (SA) Filipo Novo Mór 26 FCE Frankfurt Consulting Engineers GmbH, 2015
- 28. Theoretical Background NASA Numerical Aerodynamic Simulation (NAS) Filipo Novo Mór 27 CG - Conjugate Gradient, irregular memory access and communication FT - discrete 3D fast Fourier Transform, all-to-all communication IS - Integer Sort, random memory access LU - Lower-Upper Gauss-Seidel solver. Large number of short messages MG - Multi-Grid on a sequence of meshes, long- and short-distance communication, memory intensive These applications were selected because they have task communication based profiles. Therefore they are ideal for the purposes of this work.
- 29. Related Work 28Filipo Novo Mór Introduction Theoretical Background Related Work Project Methodology Experimental Results Conclusions
- 30. Related Work • J. R. Ku and S. G. Ku [34] • Two phases: • clustered high communicating tasks into partitions • Used NSGA-II algorithm • Mapped these partitions onto NoC processors. • Tried to keep high communicating partitions close to each other • Used a second version of the NSGA-II algorithm • 15% more efficient then Physical Mapping Algorithm • C. Deng et al. [41] • Changed the classical DE • Included a sorting step before chromosomes recombination • For high-level task graphs, free of a target hardware architecture Filipo Novo Mór 29
- 31. Related Work • Sen 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 fly • The resulting vector is now compared with the whole population, not only with your ’father’ • Tested using benchmark ZDT functions only • D. Das, M. Verma and A. Das [58] • Hardware/software partitioning problem using DE • Objective functions: execution time, area cost and communication cost • DE ran 16% faster than PSO • Quality of acieved solutions were not described • Zhuo Qingqi et al. [51] • Solving Task Mapping problem combining two evolutionary algorithms (not DE) • Parallel approach for searching the solution space • MPEG-4 and VOPD (Video Objective Plane Decoder) benchmark applications • Saves 13% on energy and is 3% more efficient in communication latency Filipo Novo Mór 30
- 32. Project Methodology 31Filipo Novo Mór Introduction Theoretical Background Related Work Project Methodology Experimental Results Conclusions
- 33. Project Methodology Filipo Novo Mór 32 E A C F B D 0 1 2 0 1 2 0 1 2 3 4 5 6 7 8 resulting task map E A C F B D 0 1 2 3 4 5 6 7 8 chromosomes individual 0 1 2 0 1 2 0 1 2 3 4 5 6 7 8 task mapping step A C E B D F 5 5 3 2 5 3 4 1
- 34. Project Methodology Filipo Novo Mór 33 E A C F B D B A C D F E C A B E D F F D A B E C 0 1 2 3 4 5 6 7 8 0 1 2 3 0 1 2 0 1 2 0 1 2 3 4 5 6 7 8 A C E B D F 5 5 3 2 5 3 4 1
- 35. Project Methodology Data Structures Modelling Filipo Novo Mór 34 0 0 3 4 2 1 3 2 4 4 4 2 2 1 0 3 4 0 1 1 t0 t1 t2 t3 t4 Populationsize(NP)Population Dimension (D) 0 1 2 0 1 2 0 1 2 3 4 5 6 7 8 D = number of existing tasks Adherent to SODE and MODE
- 36. Project Methodology Communication Volume Metric Filipo Novo Mór 35 Manhattan Distance 𝑴 𝒅 = 𝒙 𝟏 − 𝒙 𝟐 + 𝒚 𝟏 − 𝒚 𝟐 15 2025 10 10 t0 t1 t3 t4 t2 TASKS t5 10 20 25 15 0 Candidate Solution 1 fo3(solution 1) = 10+0+25+20+15 = 70 1020 25 15 10 10 10 10 1010 Candidate Solution 2 fo3(solution 2) = 10+10+10+10+10+10+10+25+20+15 = 130
- 37. Project Methodology Load Balance Metric Filipo Novo Mór 36 75 t0 t1 t3 t4 t2 TASKS t5 53 75 50 10 65 Candidate Solution 1 Candidate Solution 2 fo2(solution 1) = 29.45 fo2(solution 2) = 54.11 𝑹𝑴𝑺𝑫 = 𝟏 𝒏 𝒊=𝟏 𝒏 𝑿𝒊 − 𝑿 𝟐
- 38. 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 operations Filipo Novo Mór 37
- 39. Project Methodology Identifying most communicating tasks Filipo Novo Mór 38 A C E B D F 5 5 3 2 5 3 4 1 A, B: 5 A, C: 5 B, D: 3 D, F: 1 F, D: 4 C, E: 5 E, A: 3 E, B: 2 A, B: 5 A, C: 5 B, D: 3 D, F: 1+4 C, E: 5 E, A: 3 E, B: 2 A, B, C,E: 5+5+3 B, D, A, E: 3+5+2 D, F, B: 5+3 C, E, A: 5+5 E, A, C, B: 3+5+2 A, B, C,E: 13 B, D, A, E: 10 D, F, B: 8 C, E, A: 10 E, A, C, B: 10 tA, tB, tC and tE
- 40. Project Methodology Proposal 1 Filipo Novo Mór 39 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
- 41. Project Methodology Proposal 2 Filipo Novo Mór 40 Proposal 2 was halted: No more convergence after 4 generations on average Too few tasks? Too small NoC?
- 42. Project Methodology Validating the DE (Single Objective) Filipo Novo Mór 41 SO_Proc36_T36_CR0_50_F0_40_Gen1000_Noc6_6_1_Pop20_Test2016061716017308_ft32x1_v2ap01
- 43. Project Methodology Validating the DE (Multiple Objective) Filipo Novo Mór 42 Function ZDT1 ETH Zürich, 2008
- 44. Project Methodology Validating the DE (Multiple Objective) Filipo Novo Mór 43 Function ZDT2 ETH Zürich, 2008
- 45. Project Methodology Validating the DE (Multiple Objective) Hypervolume metric Filipo Novo Mór 44 Kian Sheng Lim et al, 2013
- 46. Experimental Results 45Filipo Novo Mór Introduction Theoretical Background Related Work Project Methodology Experimental Results Conclusions
- 47. Experimental Results Parameters Range NP 10 and 20 G 100, 300, 500, 100, 5000 and 10000 CR 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 06, 0.7, 0.8 and 0.9 F 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 06, 0.7, 0.8 and 0.9 Filipo Novo Mór 46 Single Objective DE NASA NAS applications: IS, CG, FT, MG, LU Each test case was executed at least 30 times Goal: reduce communication volume
- 48. Experimental Results Filipo Novo Mór 47 Single Objective DE – NASA NAS benchmark
- 49. Experimental Results Filipo Novo Mór 48 Single Objective DE – NASA NAS benchmark 0 5000 10000 15000 20000 25000 CG - 10 - 100 CG - 10 - 500 CG - 10 - 5000 CG - 20 - 100 CG - 20 - 500 CG - 20 - 5000 121 367 615 1233 6078 12194 245 735 1226 2462 12124 24049 0 20000 40000 60000 FT - 10 - 100 FT - 10 - 500 FT - 10 - 5000 FT - 20 - 100 FT - 20 - 500 FT - 20 - 5000 269 812 1336 2684 13596 27099 550 1595 2709 5428 26841 53608 0 20000 40000 60000 IS - 10 - 100 IS - 10 - 500 IS - 10 - 5000 IS - 20 - 100 IS - 20 - 500 IS - 20 - 5000 279 842 1388 2769 13765 27320 553 1671 2768 5387 27091 54840 0 5000 10000 15000 20000 25000 LU - 10 - 100 LU - 10 - 500 LU - 10 - 5000 LU - 20 - 100 LU - 20 - 500 LU - 20 - 5000 123 372 607 1170 6076 11490 239 721 1196 2375 11971 24141 0 5000 10000 15000 20000 25000 MG - 10 - 100 MG - 10 - 500 MG - 10 - 5000 MG - 20 - 100 MG - 20 - 500 MG - 20 - 5000 127 375 629 1265 6079 12402 245 742 1253 2474 12173 24000
- 50. Experimental Results Filipo Novo Mór 49 Single Objective DE – NASA NAS benchmark 5120 11377 11556 5040 5147 0 2000 4000 6000 8000 10000 12000 14000 CG FT IS LU MG Average Execution Time by benchmark application
- 51. Experimental Results Filipo Novo Mór 50 SODE vs CAFES – NASA NAS benchmark NASA NAS applications: IS, CG, FT, MG, LU Each test case was executed at least 30 times CAFES was set to the best execution parameters found during preparation tests. The same formula was used by CAFES and SODE to calculate the fitness value The comparison focused on the quality of the best candidate solutions The comparison considered the five best candidate solutions of each test case for both tested algorithms
- 52. Experimental Results Filipo Novo Mór 51 SODE vs CAFES – NASA NAS benchmark 969114 989330 2616473 3020149 1124121 1109178 3858343 2503478 655376 485965 SODE CAFES SODE CAFES SODE CAFES SODE CAFES SODE CAFES CGFTISLUMG SODE vs CAFES Top 5 Best Solutions - Mean Values SODE CAFES SODE CAFES SODE CAFES SODE CAFES SODE CAFES CG FT IS LU MG 8766 11537 9954 100 914 574 92400 51726 14357 4950 SODE vs CAFES Top 5 Best Solutions - Standard Deviation Mean Values: absolute scalar value for the communication volume Standard Deviation: how close are the best solutions from each other
- 54. Conclusions A new adaptation for the SODE was proposed, rewarding individuals who kept related communicating tasks close to each other Testes 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 applications Our 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 Mór 53
- 55. Filipo Novo Mór Supervisor: Dr. César Augusto Missio Marcon Co-supervisor: Dr. Andrew Rau-Chaplin 2016, August 18th www.filipomor.com master thesis defense Thank you!