## 6 Conclusions and Future Work  
This paper proposes a new Cellular Processing Algorithm that uses a GRASP construction, called GRASP-CPA, for scheduling precedence-constraint tasks on heterogeneous systems. Experimental results showed that GRASP-CPA outperformed a high-performance algorithm from the state-of-the-art called EFT-ILS, regarding optimal and median values with statistical significance for the proposed set of instances. Two main features of the GRASP-CPA contribute to its performance. The first is the generation of tasks' execution orders using a GRASP algorithm, conversely to a completely random order generation in EFT-ILS. The second is the communication between different Processing Cells to help explore the search space. We encourage researches to apply the Cellular Processing Algorithm approach to their problems. This approach is more a framework than a strict algorithm that allows flexible implementations with homogeneous or heterogeneous Processing Cells. Despite being a novel approach, it has proven to be effective for several problems and still has many open research areas. As future work, we would like to research other methods to produce tasks' execution orderings, to improve the results yielded by GRASP-CPA. Conceptualization, formal analysis, investigation, methodology, resources, software, supervision, validation, writing--original draft, writing--review and editing, A.S.; data curation, project administration, software, validation, writing--original draft, and writing--review and editing, J.D.T.-V.; funding acquisition, project administration, visualization, S.I.M. ; writing--review and editing, J.A.C.R., J.L.M., M.G.T.B., and M.P.-F. All authors have read and agreed to the published version of the manuscript. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Problem** & **EFT-ILS** & **GRASP-CPA** & **Optimum** & **Reference** & **Time\({}_{\text{Enum}}\)** & **Time\({}_{\text{ET-ILS}}\)** & **Time\({}_{\text{GRASP-CPA}}\)** \\ \hline Ahmad-3-9 & 27\({}_{0.0}-\) & 27\({}_{0.0}\) & 27 & [42] & 8s & 0s & 0s \\ Daoud-2-11 & 60\({}_{1.5}\)**A** & 58.5\({}_{0.0}\) & 56 & [43] & 46s & 0s & 0s \\ Eswari-2-11 & 60\({}_{0.5}\)**A** & 58.5\({}_{0.0}\) & 56 & [44] & 46s & 0s & 0s \\ Hamid-3-10 & 100\({}_{0.0}\)**A** & 100\({}_{0.0}\) & 100 & [45] & 71s & 0s & 0s \\ Heteropar-4-12 & 136\({}_{0.0}\)**A** & 124\({}_{12}\) & 124 & [46] & 1677s & 0s & 0s \\ Hsu-3-10 & 80\({}_{0.0}\)**A** & 80\({}_{0.0}\) & 80 & [47] & 64s & 0s & 0s \\ Iavarasan-3-10 & 73\({}_{0.0}\)**A** & 73\({}_{0.0}\) & 73 & [48] & 65s & 0s & 0s \\ Kang1-3-10 & 760\({}_{0.0}\)**A** & 76\({}_{1.0}\) & 73 & [49] & 67s & 0s & 0s \\ Kang2-3-10 & 83\({}_{0.0}\)**A** & 83\({}_{0.0}\) & 79 & [50] & 68s & 0s & 0s \\ Kuan-3-10 & 27\({}_{0.0}\)**A** & 27\({}_{0.0}\) & 26 & [51] & 25s & 0s & 0s \\ Liang-3-10 & 73\({}_{0.0}\)**A** & 73\({}_{3.0}\) & 73 & [52] & 67s & 0s & 0s \\ Sample-3-8 & 84\({}_{2.0}\)**A** & 82\({}_{3.0}\) & 81 & [11] & 0s & 0s & 0s \\ SampleFig-3-8 & 66\({}_{0.0}-\) & 66\({}_{0.0}\) & 66 & [11] & 0s & 0s & 0s \\ YClee-3-8 & 66\({}_{0.0}-\) & 66\({}_{0.0}\) & 66 & [53] & 0s & 0s & 0s \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Small synthetic benchmark instances median and IQR of EFT-ILS and GRASP-CPA over 100 independent runs. Light gray emphasizes the best results. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Problem** & **EFT-ILS** & **GRASP-CPA** & **Optimum** & **Reference** \\ \hline Ahmad-3-9 & 27 & 27 & 27 & [42] \\ Daoud-2-11 & 56 & 56 & 56 & [43] \\ Eswari-21 & 56 & 56 & 56 & [44] \\ Hamid-3-10 & 100 & 100 & 100 & [45] \\ Heteropar-4-12 & 136 & 124 & 124 & [46] \\ Hsu-3-10 & 80 & 80 & 80 & [47] \\ Ilavarasan-3-10 & 73 & 73 & 73 & [48] \\ Kang1-3-10 & 73 & 73 & 73 & [49] \\ Kang2-3-10 & 83 & 82 & 79 & [50] \\ Kuan-3-10 & 26 & 26 & 26 & [51] \\ Liang-3-10 & 73 & 73 & 73 & [52] \\ Liang-3-10 & 73 & 73 & 73 & [52] \\ Sample-3-8 & 81 & 81 & 81 & [11] \\ SampleFig-3-8 & 66 & 66 & 66 & [11] \\ YCLee-3-8 & 66 & 66 & 66 & [53] \\ \hline \hline \end{tabular}
\end{table}