Model transformation programs are iteratively refined, restructured, and evolved due to many reasons such as fixing bugs and adapting existing transformation rules to new metamodels version. Thus, modular design is a desirable property for model transformations as it can significantly improve their evolution, comprehensibility, maintainability, reusability, and thus, their overall quality. Although language support for modularization of model transformations is emerging, model transformations are created as monolithic artifacts containing a huge number of rules. To the best of our knowledge, the problem of automatically modularizing model transformation programs was not addressed before in the current literature. These programs written in transformation languages, such as ATL, are implemented as one main module including a huge number of rules. To tackle this problem and improve the quality and maintainability of model transformation programs, we propose an automated search-based approach to modularize model transformations based on higher-order transformations. Their application and execution is guided by our search framework which combines an in-place transformation engine and a search-based algorithm framework. We demonstrate the feasibility of our approach by using ATL as concrete transformation language and NSGA-III as search algorithm to find a trade-off between different well-known conflicting design metrics for the fitness functions to evaluate the generated modularized solutions. To validate our approach, we apply it to a comprehensive dataset of model transformations. As the study shows, ATL transformations can be modularized automatically, efficiently, and effectively by our approach. We found that, on average, the majority of recommended modules, for all the ATL programs, by NSGA-III are considered correct with more than 84% of precision and 86% of recall when compared to manual solutions provided by active developers. The statistical analysis of our experiments over several runs shows that NSGA-III performed significantly better than multi-objective algorithms and random search. We were not able to compare with existing model transformations modularization approaches since our study is the first to address this problem. The software developers considered in our experiments confirm the relevance of the recommended modularization solutions for several maintenance activities based on different scenarios and interviews.

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