## 3 Materials and Methods
### Problem Description and Formulation
The resulting software, in which HHMO_CF_GDA was applied, was more optimized and achieved lower coupling with higher cohesion and better modularization quality. Moreover, the structure of the software was more robust and easier to maintain because of its software modularity. As a future work, we intend to add a multi-objective evolutionary algorithm based on the decomposition algorithm instead of MOGA to HHMO_CF_GDA to improve its performance in solving the module clustering optimization problem. More optimized software with high modularity can lead to more maintainable software. To enhance the modularity of the software in the optimization process, some possible methods can be applied, such as the k-means-like clustering algorithm based on the silhouette analysis approach [38], to estimate the optimal number of clusters in the clustering categorical data. The algorithm uses the kernel-density estimation approach to define the cluster centers for the clustering step. It also uses information theory-based dissimilarity to measure the distance between the centers and objects in each cluster. Moreover, it evaluates the quality of the cluster obtained in the first step to select the best k. Another algorithm is the hierarchical agglomerative clustering algorithm for restructuring software systems (HARS) [39], which identifies the refactoring required to restructure a software system. The HARS algorithm is used to obtain an improved software system structure by identifying the required refactoring. Data curation, H.A. ; formal analysis, M.M. and H.A. ; investigation, M.M. and H.A. ; methodology, H.A. ; project administration, M.M. ; resources, M.M. ; software, H.A. ; supervision, M.M. ; writing--original draft, H.A. ; writing--review and editing, M.M. All authors will be informed about each step of manuscript processing including submission, revision, and revision reminders via emails from our system or the assigned Assistant Editor. All authors have read and agreed to the published version of the manuscript. The authors received funding from the Deanship of Scientific Research at King Saud University for this study. [PERSON]. [[https://dsrs.ksu.edu.sa/](https://dsrs.ksu.edu.sa/)]([https://dsrs.ksu.edu.sa/](https://dsrs.ksu.edu.sa/)), accessed on 1 May 2022. Not applicable. The data that support the findings of this study are available on request from the corresponding author, [[PERSON]]. The authors thank the Deanship of Scientific Research at King Saud University for funding and supporting this research through the initiative of DSR Graduate Students' Research Support. ## References

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