## 5 Experiments
### Simulation Environment  
The experimental environment is based on python and geatpy [33], and the reference objectives are selected benchmark NSGA-II, INSGA2-TG(Transcription Gene) algorithm, INSGA2-HR(Heuristic Recombination) algorithm and extremums. Table 4 shows the Ablation of INSGA2-TGHR, where benchmark NSGA-II algorithm has a random initial population, using simulated binary crossover operator and polynomial mutation operator. INSGA2-TG has TG initial population, using simulated binary crossover operator and polynomial mutation operator, INSGA2-HR has random initial population, using swap mutation operator and HR crossover operator, INSGA2-TGHR has TG initial population, using swap mutation operator and HR crossover operator, and extremum of IRMWAP problem in both latency and cost directions are solved respectively by the gurobi [26]. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Params Type**} & \multicolumn{2}{c}{**Params Value**} \\ \hline \multirow{4}{*}{workflow} & Number of subtasks & 30–80 \\ \cline{2-3}  & instruction & 10–800 MI \\ \cline{2-3}  & memory & 100–500 MB \\ \cline{2-3}  & data dependency & 10–100 kB \\ \hline \multirow{4}{*}{Local Monitor} & CPU & 0.8 Ghz*1 \\ \cline{2-3}  & memory & 1 GB \\ \cline{2-3}  & bandwidth & 400 Mbps \\ \hline \multirow{4}{*}{Edge Server 1} & CPU & 3.0 Ghz*4 \\ \cline{2-3}  & memory & 8 GB \\ \cline{2-3}  & bandwidth & 2 Gbps \\ \cline{2-3}  & cost & 2 RMB/h \\ \hline \multirow{4}{*}{Cloud Server 1} & CPU & 3.0 Ghz*8 \\ \cline{2-3}  & memory & 16 GB \\ \cline{2-3}  & bandwidth & 4 Gbps \\ \cline{2-3}  & cost & 2 RMB/h \\ \hline \multirow{4}{*}{Local to Edge} & cost & 0.25 RMB/GB \\ \cline{2-3}  & Latency & 10 ms \\ \hline \multirow{2}{*}{Edge to Cloud} & cost & 0.75 RMB/GB \\ \cline{2-3}  & Latency & 30 ms \\ \hline \multirow{2}{*}{Local to Cloud} & cost & 1 RMB/GB \\ \cline{2-3}  & Latency & 40 ms \\ \hline \end{tabular}  
* Price reference is Huawei Cloud ECS and Huawei Cloud IEC [32].  
\end{table} 
Table 3: Experimental Parameters. Figure 7 compares the Pareto frontier of the four algorithms in the (6, 2, 1) resource setting, which has 6 local monitors, 2 edge servers and 1 cloud server. TGHR algorithm can obtain the solution closest to the extreme value and closer to the true Pareto frontier, and the convergence of its solution set is better than the other three algorithms. The TG algorithm is less exploratory than TGHR and HR, although it has a dominant initial population. The HR algorithm contains more monitor genes due to its initial gene population, so that its evolutionary direction will be more likely to favor the low-cost side. Benchmark NSGA-II algorithm does not reach convergence at 200 generations. It shows that the TG and HR algorithms have the advantage of dominant initial populations and evolutionary exploration, respectively, to find non-dominated solutions quickly and close to the Pareto frontier. In addition, the TGHR algorithm has the advantages of both TG and HR, and its solution set is balanced and closer to the real Pareto frontier. Impact of Evolution Generation  
Figure 8 shows the impact of comparing the number of evolutionary generations of the four algorithms in the (6, 2, 1) resource setting. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Initial Population** & **Mutation and Crossover Operator** \\ \hline Benchmark NSGA-II & random & simulated binary and polynomial mutation \\ \hline INSGA2-TG & TG & simulated binary and polynomial mutation \\ \hline INSGA2-HR & random & Swap and HR \\ \hline INSGA2-TGHR & TG & Swap and HR \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Ablation of INSGA2-TGHR. Figure 7: Comparison of Pareto frontier. (**a**) Comparison of four algorithms; (**b**) Comparison of TGHR and benchmark NSGA-II; (**c**) Comparison of TGHR and TG; (**d**) Comparison of a and TGHR and HR. The Figure 8a shows the number of non-dominated solutions, as shown in the figure, the TGHR algorithm works best and is the first to obtain close to 100 non-dominated solutions.