ILP model and HeuristicAuthors:   Josep Subirats           Arinto Murdopo           Ioanna Tsalouchidou
ContentResultProblem DescriptionThe ILP modelHeuristic DesignData-Set GenerationResultsConclusions
Problem DescriptionGrid data-center scheduling problemOptimal solution          economic revenue          power saving  ...
Problem Description
Problem Description                      Revenue                      QoS Health                      Power               ...
ILPJob allocation in data-grid•   Power consumption based on used CPUs•   CPUs in each host•   Min CPUs required by each j...
ILPObjective Function             Benefit ofMax:         Execution              QoS Penalty             Power             ...
ILPS.T:          Processor switched on/off in order: keep consistency          Relaxation: job scheduled or not schedul...
Data GenerationGenerate an array of numHosts components: cpus[]: CPUs in each host, each with 1, 2, 4 or 8 CPUs  (random...
CPU : Intel i7 @ 2.8 GHzOS: Windows 7RAM: 8 GBCPLEX: IBM ILOG CPLEX Optimization Studio 12.4Heuristic: Java in JRE 1.6.0_2...
Multiple Alpha: 0, 0.1, 0.2 … 1Multiple Problem Sizes:5H10J, 15H30J, 20H40J, 30H40J, 40H80J, 100H200JMultiple Iterations:1...
CPLEX Execution Time           250           200           150Time (s)           100                                      ...
Heuristic Random 100H200J - Time (s)           350           300           250           200Time (s)           150        ...
Alpha vs Benefit 20H40J NR                                  Alpha vs Benefit 40H 80J NR          101                      ...
Alpha vs Benefit 20H40J NR          97          95          93          91                                                ...
Alpha vs Benefit 100H 200J NR          570          560          550          540                                         ...
Solution Quality - Alpha 0.1 - 100H - 200J - 100000 Iterations                         100            12377               ...
Solution Quality - Zoomed In - Alpha 0.1 - 100H - 200J - 100000                                                         It...
Alpha vs Benefit 20H40J R                                          Alpha vs Benefit 40H80J R          105                 ...
Alpha vs Benefit 20H40J R          105          100           95                                                          ...
Alpha vs Benefit H100 J200 R          610          590          570          550                                          ...
Solution Quality - Alpha 0.0 - 100H - 200J - 100000 Iterations                         100                                ...
Solution Quality - Zoomed In -Alpha 0.0 - 100H - 200J - 100000                                                       Itera...
Problem Size vs Methodology vs Benefit          700                                                         CPLEX         ...
ConclusionsDatacenter job scheduling and management can be optimized using ILPs.Complex ILP restrictions can be translat...
ConclusionsLower alpha values achieve better results. Alpha of 0 is the best when using random node selection.Random nod...
ReferenceJ. L. Berral García, R. Gavaldà Mestre, J. TorresViñals, and others, “An integer linearprogramming representation...
ILP model and HeuristicAuthors:   Josep Subirats           Arinto Murdopo           Ioanna Tsalouchidou
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
An Integer Programming Representation for Data Center Power-Aware Management - slides
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An Integer Programming Representation for Data Center Power-Aware Management - slides

  1. 1. ILP model and HeuristicAuthors: Josep Subirats Arinto Murdopo Ioanna Tsalouchidou
  2. 2. ContentResultProblem DescriptionThe ILP modelHeuristic DesignData-Set GenerationResultsConclusions
  3. 3. Problem DescriptionGrid data-center scheduling problemOptimal solution  economic revenue  power saving  QoSSet of elements  machines  processors  jobs
  4. 4. Problem Description
  5. 5. Problem Description Revenue QoS Health Power Migration
  6. 6. ILPJob allocation in data-grid• Power consumption based on used CPUs• CPUs in each host• Min CPUs required by each job• Max CPUs required by each job
  7. 7. ILPObjective Function Benefit ofMax: Execution QoS Penalty Power Consumption Migration Cost
  8. 8. ILPS.T:  Processor switched on/off in order: keep consistency  Relaxation: job scheduled or not scheduled  Available CPUs in each host not exceedOutput:  Max. Benefit  Placement of each job in the infrastracture  CPU assignment for each job  CPUs used in each host
  9. 9. Data GenerationGenerate an array of numHosts components: cpus[]: CPUs in each host, each with 1, 2, 4 or 8 CPUs (random).Generate two arrays of numJobs components: consMin[]: minimum CPU required, between 1 and 10 (random). consMax[]: maximum CPU required, randomly between consMin[j] + 1 to 2 extra CPUs (random).
  10. 10. CPU : Intel i7 @ 2.8 GHzOS: Windows 7RAM: 8 GBCPLEX: IBM ILOG CPLEX Optimization Studio 12.4Heuristic: Java in JRE 1.6.0_24-b07
  11. 11. Multiple Alpha: 0, 0.1, 0.2 … 1Multiple Problem Sizes:5H10J, 15H30J, 20H40J, 30H40J, 40H80J, 100H200JMultiple Iterations:10, 100, 1000, 10000, 100000
  12. 12. CPLEX Execution Time 250 200 150Time (s) 100 Execution Time 50 0 5H10J 10H20J 15H30J 20H40J Problem Size
  13. 13. Heuristic Random 100H200J - Time (s) 350 300 250 200Time (s) 150 Time (s) 100 50 0 10 100 1000 10000 100000 Number of Iteration
  14. 14. Alpha vs Benefit 20H40J NR Alpha vs Benefit 40H 80J NR 101 195 96 190 10 185 10Benefit Benefit 91 100 180 100 1000 175 1000 86 10000 170 10000 81 165 100000 100000 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 Alpha Alpha Alpha vs Benefit 30H60J NR Alpha vs Benefit 100H 200J NR 140 580 10 560 10 Benefit 130 Benefit 100 540 100 120 520 1000 1000 110 500 10000 10000 0 0.2 0.4 0.6 0.8 1 480 100000 0 0.5 1 100000 Alpha Alpha
  15. 15. Alpha vs Benefit 20H40J NR 97 95 93 91 10Benefit 89 100 1000 87 10000 85 100000 83 81 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Alpha
  16. 16. Alpha vs Benefit 100H 200J NR 570 560 550 540 10Benefit 530 100 1000 520 10000 100000 510 500 490 0 0.2 0.4 0.6 0.8 1 Alpha
  17. 17. Solution Quality - Alpha 0.1 - 100H - 200J - 100000 Iterations 100 12377 133566 683 99.5 69Normalized Benefit (%) 99 24 98.5 Normalized 17 Benefit (%) 14 98 97.5 11 7 97 Time (mili seconds)
  18. 18. Solution Quality - Zoomed In - Alpha 0.1 - 100H - 200J - 100000 Iterations 100 99.5 69Normalized Benefit (%) 99 24 98.5 Normalized 17 Benefit (%) 14 98 97.5 11 7 97 Time (mili-seconds)
  19. 19. Alpha vs Benefit 20H40J R Alpha vs Benefit 40H80J R 105 220 100 10 10 200 BenefitBenefit 95 100 100 90 180 1000 1000 85 80 10000 160 10000 0 0.2 0.4 0.6 0.8 1 100000 0 0.2 0.4 0.6 0.8 1 100000 Alpha Alpha Alpha vs Benefit 30H60J R Alpha vs Benefit H100 J200 R 170 620 10 Benefit 150 570 10 Benefit 100 130 100 1000 520 1000 110 10000 0 0.2 0.4 0.6 0.8 1 10000 100000 470 Alpha 100000 0 0.2 0.4 0.6 0.8 1 Alpha
  20. 20. Alpha vs Benefit 20H40J R 105 100 95 10Benefit 100 90 1000 10000 100000 85 80 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Alpha
  21. 21. Alpha vs Benefit H100 J200 R 610 590 570 550 10Benefit 100 530 1000 10000 510 100000 490 470 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Alpha
  22. 22. Solution Quality - Alpha 0.0 - 100H - 200J - 100000 Iterations 100 224536 98 8813 112341 96Normalized Benefit (%) 2012 94 13 Normalized 92 Benefit (%) 90 9 88 3 86 Time (mili-seconds)
  23. 23. Solution Quality - Zoomed In -Alpha 0.0 - 100H - 200J - 100000 Iterations 99 97Normalized Benefit (%) 95 93 292 617 693 13 91 Normalized 9 Benefit (%) 89 3 87 85 Time(mili-seconds)
  24. 24. Problem Size vs Methodology vs Benefit 700 CPLEX 600 500 Heuristic Non- Random Initial 400 Selection (NR)Benefit Heuristic Random 300 Initial Selection(R) - 10000 Iter 200 Heuristic Random Initial Selection(R) - 100 100000 Iter 0 Problem Size
  25. 25. ConclusionsDatacenter job scheduling and management can be optimized using ILPs.Complex ILP restrictions can be translated into easy heuristic code.CPLEX does not scale well.Heuristics can cope with higher problem sizes.
  26. 26. ConclusionsLower alpha values achieve better results. Alpha of 0 is the best when using random node selection.Random node selection obtains the best results.More iterations achieve better benefits.
  27. 27. ReferenceJ. L. Berral García, R. Gavaldà Mestre, J. TorresViñals, and others, “An integer linearprogramming representation for data-centerpower-aware management,” 2011.http://upcommons.upc.edu/handle/2117/11061
  28. 28. ILP model and HeuristicAuthors: Josep Subirats Arinto Murdopo Ioanna Tsalouchidou

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