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\begin{document}

\title{OCL-Based Test Case Optimisation with Modified APFD Metric}



\author[1]{Kunxiang Jin}%
\author[1]{Kevin Lano}%
\affil[1]{King's College London Department of Informatics}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\begin{abstract}
Testing is one of the most time-consuming and unpredictable processes
within the software development life cycle. As a result, many Test Case
Optimisation (TCO) techniques have been proposed to make this process
more scalable. Object Constraint Language (OCL) was initially introduced
as a constraint language to provide additional details to UML models.
However, as OCL continues to evolve, an increasing number of systems are
being expressed by this language. Despite this growth, a noticeable
research gap exists for the testing of systems whose specifications are
expressed in OCL. In our previous work, we verified the effectiveness
and efficiency of performing the Test Case Prioritisation (TCP) process
for these systems. In this study, we extend our previous work by
integrating the Test Case Minimisation (TCM) process to determine
whether TCM can also benefit the testing process under the context of
OCL. The evaluation of TCO approaches often relies on well-established
metrics such as the Average Percentage of Fault Detection (APFD).
However, the suitability of APFD for Model-Based Testing (MBT) is not
ideal. This paper addresses this limitation by proposing a modification
to the APFD metric to enhance its viability for MBT scenarios. We
conducted four case studies to evaluate the feasibility of integrating
the TCM and TCP processes in our proposed approach. In these studies, we
applied the multi-objective optimisation algorithm NSGA-II and the
genetic algorithm independently to the TCM and TCP processes. The
objective was to assess the effectiveness and efficiency of combining
TCM and TCP in enhancing the testing phase. Through experimental
analysis, the results highlight the benefits of integrating TCM and TCP
in the context of OCL-based testing, providing valuable insights for
practitioners and researchers aiming to optimise their testing efforts.
Specifically, the main contributions of this work include: \textbf{1).}
We introduce the integration of the TCM process into the TCO process for
systems expressed by OCL. This integration benefits the testing process
further by reducing redundant test cases while ensuring sufficient
coverage. \textbf{2).} We comprehensively analyse the limitations
associated with the commonly used metric, APFD, and then a modified
version of the APFD metric has been proposed to overcome these
weaknesses. \textbf{3).} We systematically evaluate the effectiveness
and efficiency of OCL-based TCO processes on four real-world case
studies with different complexities.%
\end{abstract}%



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