## 6 Computational Results of the Developed Algorithms
### Discussion of the Experimental Results  
The optimization criteria of the developed metaheuristics are based on the quality of the solutions and rapidity. The quality and efficiency of the metaheuristics were proven by comparing the solutions obtained with these algorithms and the optimal solutions of the mathematical model. Regarding the rapidity, the computation times of the algorithms were compared with those of the mathematical model. From the results presented above (Tables 5-9), we remark that the two genetic algorithms are efficient in terms of quality and rapidity. The performance of the developed resolution methods depends on the types of instances and their sizes, and it also depends on the choice of heuristics for the generation of initial solutions. The first genetic algorithm is more efficient in terms of quality with the MMWA assignment heuristic and the SPT sequence heuristic, while the second genetic algorithm is more efficient with the MMWA and MNOR heuristics. For the iterated local search algorithms, the first algorithm gives better solutions with the SPT assignment heuristic and the MNOR sequence heuristic, while the second algorithm finds good solutions with the MMWA and MNOR heuristics. Regarding the rapidity, the four metaheuristics are more faster with the RA assignment heuristic and the RS sequence heuristic. The results of the genetic algorithms for different types of instances (Tables 5-9) show that the developed metaheuristics are efficient relative to the quality of solutions. Table 5 represents the results of the different methods developed on a real instance with 82 jobs, 92 sub-lots, 370 operations, and 29 machines. From these instances, several sub-instances were built by increasing the number of jobs, sub-lots, and operations each time to see from what number of jobs, sub-lots, and operations the model is not able to find solutions. From Table 5, we observe that for the real instances of the HCT, the mathematical model quickly found solutions for the small instances with less than five dishes, five sub-lots, 24 operations, and 29 machines. It took a little longer for the instances with more than six dishes, six sub-lots, 29 operations, and 29 machines. However, for the instances with more than nine jobs, 44 operations, and 29 machines, after more than 3 h of execution, the \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & **PS** & **MNG** & **NEI** & **NILS** & **Pc** & **Pm** & **DOS** & **MISO** & **MIAO** & **MPPO** \\ \hline GA 1 & 500 & 1000 & 50 & 50 & 0.8 & 0.2 & ILS 1 & 0.05 & 100 & 100 & 50 \\ \hline GA 2 & 800 & 1200 & 80 & 80 & 0.8 & 0.2 & ILS 2 & 0.07 & 200 & 200 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimal parameters of the genetic and iterated local search algorithms. mathematical model did not find solutions. For these instances, the two genetic algorithms succeeded in finding feasible solutions in very short computation times. For example, for the large instance with 82 jobs, 92 sub-lots, 370 operations, and 29 machines, the first genetic algorithm found a feasible solution that respected all the constraints after 5 min of execution. Tables 6-8 present the performances of the resolution methods in terms of quality and rapidity for randomly generated instances and a comparison between the solutions obtained by these different methods. From the results presented in these tables, we remark that the genetic algorithms found feasible solutions for the large-size instances in reasonable resolution times. In Table 9, we observe that for the instances adapted from the literature, the genetic algorithms make it possible to improve the solutions of the instances adapted from the literature. For example, for the instance from [PERSON] et al. [35], the genetic algorithms brought about an improvement of 3.92% over the solutions obtained with the methods proposed by [PERSON] et al. [35].