## 5 Experiment
### Selected Algorithm  
For the multi-objective scheduling problem, the most popular algorithm is NSGA-II. However, it lacks a better local search capability. It means that, when solving some cases, its results usually fall into a locally optimal solution. To make experimental results more accurate and better, this study used the NSGA-II combined with simulated annealing (SA). The following introduces the NSGA-II and SA algorithm and the parameters used.  
1. Nondominated sorting genetic algorithm II (NSGA-II)  
Based on NSGA, developed by [PERSON] et al. [PERSON] et al. (2018), NSGA-II has the advantage of fast running speed, good robustness, and fast convergence. The encoding method is consistent with the above described. Each gene means an operation. Each chromosome/individual represents a solution or a sequence of all the operations waiting to be scheduled. NSGA-II combines parent and offspring  
Figure 4: Framework of ADSM.  
into a new population and then obtains the non-dominated solutions by fast non-dominated sorting. The parent is generated by disrupting genes in the chromosome. The offspring is generated by the crossover and mutation method. The parameters are shown in Table 5.
2. Simulated annealing (SA) Simulated annealing is an approximate method based on Monte Carlo design. It was first introduced by [PERSON] et al. [37] to solve the optimization problem. SA accepts a solution that is worse than the current solution by the Metropolis criterion, thus it is possible to jump out of this local optimal solution to reach the global optimal solution. Table 6 lists the parameters used in SA.  
The non-dominated solutions were obtained by NSGA-II, and then SA was used to local search. Because of the multi-objective reasons, an objective function was randomly selected as the direction of a search, and the obtained non-dominated solutions were stored in the external archive. SA was applied to local search every 50 generations in this experiment.  
To obtain better initial population rules, the data source of data mining must be the optimal or near-optimal solution set, so that accurate and reliable rules can be discovered. In Tables 7 and 8, we can see that the data obtained by NSGA-II hybrid with SA are more effective, thus the results obtained by this algorithm were selected as the data source of knowledge mining. More comparisons between this algorithm and other algorithms can be seen in [38].  
To verify the knowledge mining method, three different initial populations of NSGA-II combined with simulated annealing were considered as follows:  
* Knowledge mining heuristic optimization method (rule) The initial population was generated using the proposed hybrid machine learning and population knowledge mining method.
* Heuristic optimization method (random) The initial population of this method was completely randomized.
* Hybrid population optimization method (mixed) Half of the initial population was generated by knowledge mining and the other half was randomly generated.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Values** \\ \hline population size & 25, 50, 100 \\ initial temperature & 100 \\ end temperature & 0.01 \\ cooling rate & 0.001 \\ number of iterations & \(100,300\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Parameters used in SA.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Values** \\ \hline population size & 25, 50, 100 \\ mutation rate & 0.002 \\ crossover rate & 0.9 \\ size of tournament selection & 10 \\ number of iterations & \(100,300\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Parameters used in NSGA-II.