## 6 Experiment Result
### Performance Analysis of Different Algorithms  
In order to more clearly show the relative sizes of SL solved by different methods, Performance Improvement Ratio (PIR) was introduced to represent the relative difference of SL as follows:  
\[PIR=\frac{SL_{SA}-SL_{other}}{SL_{other}} \tag{11}\]  
When \(PIR=0\), SA-based algorithm had the same scheduling length as other algorithm;  
When \(PIR<0\), the scheduling length solved by SA-based algorithm was better than other algorithm, \(|PIR|\) means that the difference between SA-based algorithm and other algorithm accounted for the proportion of other algorithm;  
When \(PIR>0\), the scheduling length solved by SA-based algorithm was worse than other algorithm. \(|PIR|\) represents the proportion of the difference between SA-based algorithm and other algorithm accounts for the proportion of other algorithm. Table 2 shows data comparisons that RDNC-SA, RDC-SA compared to MILP [23], IS-k [23] and ACO [18]. The resource volume of the FPGA was set as 40% of the aggregate resource requirement of each application. Table 2 consists of five parts. The first part is the name of the application and the number of tasks for each application. The second, third and fourth parts are the solving time of MILP, IS-k and ACO algorithms and the PIR of SL compared with RANC-SA, RDC-SA. The fifth part is RANC-SA and RDC-SA solving time. To facilitate analysis, we divide all applications into three parts according to the number of tasks. The first part is application task number \(\in\) (0, 10]. From the data in the table, we can know that the PIR of MILP and IS-k were both \(-\)3%. The solving time of MILP, IS-k and RDC-SA were all less than 1 s, but RDNC-SA is 31.96 s.  
Figure 7: Iterative convergence. The second part is task number \(\in\) (10, 30). In this part, the average value of RDNC-SA PIR of all DAGs was \(-\)10%, \(-\)12%, \(-\)38% corresponding to MILP, IS-k and ACO. Most solving time in MILP reached timeout. Except for the application Cyber Shake, RDNC-SA solving time was longer than IS-k. Although the solving times of ACO were all about 4 s, there was a big gap that the PIR was \(-\)38% compared to RDNC. Compared with RDC-SA, the average values of PIR were \(-\)9%, \(-\)11%, \(-\)37% corresponding to MILP, IS-k and ACO, and the solution time of all DAGs was less than MILP, IS-k and ACO. This also means that the RDC-SA solved a better quality solution in a shorter time. The third part is task number \(\in\) (30, 50). As the number of tasks increased, the advantages of our proposed algorithms became more significant. For the other three algorithms, the average value of RDNC-SA PIR was \(-\)20%, \(-\)11%, \(-\)37%, and the average value of RDC-SA PIR reached \(-\)18%, \(-\)10%, \(-\)36% respectively. In terms of solving time, our proposed RDC-SA and RDNC-SA were shorter than MILP and IS-k.  
On the whole, the two algorithms proposed in this paper were more efficient in solution quality and solving time. Compared with MILP and IS-k, for RDNC-SA algorithm, the average solving time was 60.6s, which reduced 96% and 76% of the time cost respectively. In terms of solving quality, it was 11% better than MILP and IS-k. For RDC-SA algorithm, its average solving time was 1.26 s which was much shorter than the other two algorithms. This algorithm also got the same 11% higher solution quality almost instantly. Compared with ACO, the solving results of our two algorithms were 37% better than ACO. Therefore, although ACO had a shorter solving time, its solving results had no performance advantage. These two algorithms could efficiently solve the most approximate solution. Since our proposed algorithms were based on SA, the solving time of algorithms was only related to the number of tasks. In contrast, the ILP-based methods were related to multiple factors such as the number of variables, the number of tasks, and the data values of task attributes. Moreover, we utilized some optimization strategies to improve the solution quality. Hence, our results were better than the other algorithms.