Slides for CANO (Communication Networks Optimization) project

1. ILP model and Heuristic
Authors: Josep Subirats
Arinto Murdopo
Ioanna Tsalouchidou

2. ContentResult
Problem Description
The ILP model
Heuristic Design
Data-Set Generation
Results
Conclusions

3. Problem Description
Grid data-center scheduling problem
Optimal solution
 economic revenue
 power saving
 QoS
Set of elements
 machines
 processors
 jobs

4. Problem Description

5. Problem Description
Revenue
QoS Health
Power
Migration

6. ILP
Job 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. ILP
Objective Function
Benefit of
Max: Execution
QoS Penalty
Power
Consumption
Migration
Cost

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

29. 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).

30. CPU : Intel i7 @ 2.8 GHz
OS: Windows 7
RAM: 8 GB
CPLEX: IBM ILOG CPLEX Optimization Studio 12.4
Heuristic: Java in JRE 1.6.0_24-b07

31. Multiple Alpha: 0, 0.1, 0.2 … 1
Multiple Problem Sizes:
5H10J, 15H30J, 20H40J, 30H40J, 40H80J, 100H200J
Multiple Iterations:
10, 100, 1000, 10000, 100000

32. CPLEX Execution Time
250
200
150
Time (s)
100 Execution Time
50
0
5H10J 10H20J 15H30J 20H40J
Problem Size

33. Heuristic Random 100H200J - Time (s)
350
300
250
200
Time (s)
150 Time (s)
100
50
0
10 100 1000 10000 100000
Number of Iteration

34. Alpha vs Benefit 20H40J NR Alpha vs Benefit 40H 80J NR
101 195
96 190
10 185 10
Benefit
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

35. Alpha vs Benefit 20H40J NR
97
95
93
91
10
Benefit
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

36. Alpha vs Benefit 100H 200J NR
570
560
550
540
10
Benefit
530 100
1000
520 10000
100000
510
500
490
0 0.2 0.4 0.6 0.8 1
Alpha

37. Solution Quality - Alpha 0.1 - 100H - 200J - 100000 Iterations
100 12377 133566
683
99.5
69
Normalized Benefit (%)
99
24
98.5
Normalized
17 Benefit (%)
14
98
97.5 11
7
97
Time (mili seconds)

38. Solution Quality - Zoomed In - Alpha 0.1 - 100H - 200J - 100000
Iterations
100
99.5
69
Normalized Benefit (%)
99
24
98.5
Normalized
17 Benefit (%)
14
98
97.5 11
7
97
Time (mili-seconds)

39. Alpha vs Benefit 20H40J R Alpha vs Benefit 40H80J R
105 220
100 10 10
200
Benefit
Benefit
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

40. Alpha vs Benefit 20H40J R
105
100
95 10
Benefit
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

41. Alpha vs Benefit H100 J200 R
610
590
570
550 10
Benefit
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

42. Solution Quality - Alpha 0.0 - 100H - 200J - 100000 Iterations
100 224536
98
8813 112341
96
Normalized Benefit (%)
2012
94
13 Normalized
92 Benefit (%)
90
9
88
3
86
Time (mili-seconds)

43. Solution Quality - Zoomed In -Alpha 0.0 - 100H - 200J - 100000
Iterations
99
97
Normalized Benefit (%)
95
93 292 617 693
13
91 Normalized
9 Benefit (%)
89
3
87
85
Time(mili-seconds)

44. 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

45. 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.

46. 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.

47. Reference
J. L. Berral García, R. Gavaldà Mestre, J. Torres
Viñals, and others, “An integer linear
programming representation for data-center
power-aware management,” 2011.
http://upcommons.upc.edu/handle/2117/11061

48. ILP model and Heuristic
Authors: Josep Subirats
Arinto Murdopo
Ioanna Tsalouchidou