An Adaptive Penalty based Parallel Tabu Search for Constrained Covering Array Generation

Context: The generation of the optimal constrained covering arrays is a key challenge in the research field of combinatorial testing, where a variety of Constrained Covering Array Generation (CCAG) algorithms have been developed. However, existing algorithms typically reuse constraint solver or forbidden tuple-based techniques to handle constraints, which might restrict their potentials on finding smaller arrays. Objective: This work dedicates to exploring more effective constraint handling techniques for CCAG, so that the sizes of constrained covering arrays can be further minimized. Methods: We propose a novel Adaptive Penalty based Parallel Tabu Search (APPTS) algorithm to address the CCAG problem. APPTS incorporates a penalty term into the fitness function to handle the constrained search space, and employs an adaptive penalty mechanism to dynamically adjust the penalty weight in different search phases. Moreover, APPTS adopts Java Parallel Stream to compute the fitness values of candidate solutions to speed up the generation process. Results: The performance of APPTS is evaluated against three alternative tabu search-based algorithms (with different penalty and parallelization mechanisms), and seven state-of-the-art algorithms for CCAG. The results demonstrate the superiority of APPTS over these existing algorithms. In particular, APPTS finds 22 new upper bounds on the sizes of 2-way and 3-way constrained covering arrays. Conclusion: The adaptive penalty mechanism provides an effective choice for handling constraints in CCAG, and the parallelization can help APPTS reduce the generation cost.