Chapter 4 Experimental Results
4.2 Analysis
1. 2-step VS. 1-step
We compare three crossover schemes here. The curve “Shape” is the crossover scheme as presented in [17]. Curve “Shape + Partition” means using partition cross through the evolution process and curve “2-step” is our crossover scheme. As we can see in
Figure 4.3, if we change the crossover method in the 200th generation, we can get better performance in the later generation. In this case, we can get 4.6% throughput improvement in 1,000th generation, and the throughput of 2-step method is always better than the shape method.
Table 4.2：2-step method (Task 300/Ratio 2)
2-step Shape + Partition Shape
Generation 100 200 600 1000 100 200 600 1000 100 200 600 1000
Throughput 479 536 645 697 479 536 616 666 435 489 615 674
400 450 500 550 600 650 700
100 200 600 1000
Generation Throughput
2-step Shape+Partition shape
Figure 4.3：Improvement of 2-step method (Task 300/Ratio 2)
2. Partition Method
As shown in Figure 4.4, three curves show the throughput in 100th, 200th and 1,000th generation. Since we use partition cross with control of communication overhead, we can get a raising trend when partition number increases. But partition number influences the run time of system, so we pick a proper value of partition by the improvement curve. Take Figure 4.4 as an example, when partition number is more than 6, the throughput improvement curve becomes flat.
Table 4.3：Partition (Task 200/Ratio 2)
Partition 1 2 3 4 5
Throughput at 100gen 621 663.1 671.8 671.4 682.6 Throughput at 200gen 679.3 740.7 749.7 746.1 749.4 Throughput at 1000gen 783.1 845 852.8 857.5 840
Partition 6 7 8 9 10
Throughput at 100gen 685 679.6 694 691.7 700.8 Throughput at 200gen 755.8 760.3 767.6 767.8 766 Throughput at 1000gen 863.9 873.4 884.2 871.6 890.3
600 650 700 750 800 850 900
1 2 3 4 5 6 7 8 9 10
Partition number
Throughput 1000 gen
200 gen 100 gen
Figure 4.4：Partition (Task 200/Ratio 2)
3. Comparison under Different Throughput Demand
We compare three crossover schemes under 3 task ranges including two-point crossover, shape crossover [17] and our crossover method. The advantages of our algorithm are proved here. Because of great improvement of throughput in the beginning of evolution, we can save a lot of time compared with other crossover schemes under different throughput demands. Especially in terms of tasks of 300 and 400, the saving time is significant.
Table 4.4：Comparison under different throughput demand (Task 200/Ratio 1)
Task200
Throughput 250 350 450
2 point 29 243 837
Shape 13 233 631
2-step 16 146 533
0 100 200 300 400 500 600 700 800 900
250 350 450
Throughput Generation
2 point Shape 2-step
Figure 4.5：Throughput curves in 200 tasks (Ratio 1)
Table 4.5：Comparison under different throughput demand (Task 300/Ratio 1)
Task300
Throughput 200 250 300
2 point 105 364 868
Shape 88 259 672
2-step 34 157 447
0 100 200 300 400 500 600 700 800 900 1000
200 250 300
Throughput Generation
2 point Shape 2-step
Figure 4.6：Throughput curves in 300 tasks (Ratio 1)
Table 4.6：Comparison under different throughput demand (Task 400/Ratio 1)
Task400
Throughput 160 200 240
PP 12 150 713
Shape 5 161 469
PGA 4 51 278
0 100 200 300 400 500 600 700 800
160 200 240
Throughput Generation
2 point Shape 2-step
Figure 4.7：Throughput curves in 400 tasks (Ratio 1)
4. Throughput Comparison
In this section, we compare four crossover methods including random, two-point crossover, shape crossover [17] and our method. We normalize the throughput to random method. As we can see, we can get around 10% improvements in 100th generation in all cases. If we can get great improvement in the start of evolution, then we can save a lot of time to obtain a desired throughput.
In most cases, our algorithm can attain higher throughput in the whole evolution process, especially for the case of task number above 300, where 5% improvement can be attained at 1,000th generation.
Task200
100 200 400 600 800 900 1000
Generation
Figure 4.8：Improvement of 4 crossover schemes (Task 200/Ratio 1)
1
100 200 400 600 800 900 1000
Generation
Figure 4.9：Improvement of 4 crossover schemes (Task 200/Ratio 2)
1
100 200 400 600 800 900 1000
Generation
Figure 4.10：Improvement of 4 crossover schemes (Task 200/Ratio 3)
1
100 200 400 600 800 900 1000
Generation
Figure 4.11：Improvement of 4 crossover schemes (Task 200/Ratio 4)
There are 4 cases of task graphs containing 170~230 tasks under 4 ratios of computation time to communication time. Our algorithm can obtain 8%~10%
improvement in 100th generation, but in the later generation, the difference is decreased.
Task300
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
0 200 400 600 800 1000 1200
Generation Throughput
2-step Shape 2 point Random 12.9%
Figure 4.12：Improvement of 4 crossover schemes (Task 300/Ratio 1)
1
0 200 400 600 800 1000 1200
Generation
Figure 4.13：Improvement of 4 crossover schemes (Task 300/Ratio 2)
1
0 200 400 600 800 1000 1200
Generation
Figure 4.14：Improvement of 4 crossover schemes (Task 300/Ratio 3)
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
0 200 400 600 800 1000 1200
Generation Throughput
2-step Shape 2 point Random
Figure 4.15：Improvement of 4 crossover schemes (Task 300/Ratio 4)
There are 4 cases of task graphs containing 270~330 tasks under 4 ratios of computation time to communication time. Our algorithm can obtain 12%
improvement in 100th generation, and we can still have above 4% improvement in 1000th generation.
Task400
0 200 400 600 800 1000 1200
Generation
Figure 4.16：Improvement of 4 crossover schemes (Task 400/Ratio 1)
0 200 400 600 800 1000 1200
Generation
Figure 4.17：Improvement of 4 crossover schemes (Task 400/Ratio 2)
1
0 200 400 600 800 1000 1200
Generation
Figure 4.18：Improvement of 4 crossover schemes (Task 400/Ratio 3)
1
0 200 400 600 800 1000 1200
Generation
Figure 4.19：Improvement of 4 crossover schemes (Task 400/Ratio 4)
There are 4 cases of task graphs containing 370~430 tasks under 4 ratios of computation time to communication time. Our algorithm can attain above 12%
improvement in 100th generation, and we can still have above 5% improvement in 1000th generation.
5. Mutation Rate VS. Throughput
250 260 270 280 290 300 310 320 330 340 350
0 200 400 600 800 1000 1200
0 10%
20%
Figure 4.20：Mutation rate VS. Throughput (Task 300/Ratio 2)
In our algorithm, suitable mutation rate can raise throughput performance.
However, we think that crossover method dominates the throughput performance of genetic algorithm. Thus, we focus on the improvement of crossover method.
Chapter 5
Conclusions and future work
5.1 Conclusions
Our method can obtain great improvement in scheduling process. We can use the result according to our requirement. For instance, if we want to get a throughput in a short period, our method can attain around 10% improvement in 100th generation. If our requirement is met around here, we can save a lot of scheduling time. On the other hand, if we want a higher throughput, our method can also provide better throughput in the later generation. Especially for the case of task number above 300, our method can still obtain 5% improvement at the 1000th generation.
Traditional method can not handle the task graph well, and this kind of situation will become worse when task graph become larger. So we combine the partition scheme and graphic-base crossover to improve the partition method by finding suitable partition size and adjust boundary. Experimental result shows that the improvement in throughput is obvious and we can save a lot of scheduling time.
When applications become more complex, we think that our scheduling method can handle well and get great system performance.
5.2 Future work
Partition method for task graph is important for partition genetic algorithms, especially in the complex applications. If we can find better partition method to handle the task graph, we believe that we can speed up the scheduling program and obtain better performance in system throughput. In order to get better partition algorithm, we can further consider about the partition size, communication amount, and task topology.
We can find different improvement curves in different crossover methods. For example, our method can obtain great improvement at the start of evolution, but in later generation, there is still space for further improvement. In other traditional method, they have their own curves and trend. If we can do some detail analysis about all the crossover methods, maybe we can find a better crossover method by combining their advantage.
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Vita
Yan-Ting Mi was born in Taipei on June 4, 1983. He received the B.S. degree in Electronics Engineering from National Chiao Tung University in June 2006. From September 2006 to August 2008, he was a graduate student of Professor Jing-Yang Jou in the institute of Electronics, National Chiao Tung University. His research was related to Electronic Design Automation (EDA). He received the M.S. degree in Electronics Engineering from National Chiao Tung University in August 2008.