Test Coverage Estimation Using Threshold Accepting

Abstract

This paper is concerned with model-based testing of hybrid systems. In our previous work [6], we proposed a test generation algorithm, called gRRT, guided by a coverage measure defined using the star discrepancy notion. An important ingredient in this algorithm is a procedure for dynamically estimating the coverage, which is done based on a box partition of the continuous state space. The goal of this estimation is to identify the areas in the state space which have not been sufficiently visited. A drawback of this guiding method is that its complexity depends on the number of the boxes in the partition, which needs to be fine enough to guarantee a good coverage estimate. Thus in high dimensions the method can become very costly. To enhance the scalability of the algorithm gRRT we propose in this paper a new guiding method, motivated by the observation that trying to optimize the coverage in each exploration step is, on one hand, computationally costly, and on the other hand, not always a good choice since this may make the system try to expand in the directions which are not reachable (due to the controllability of the system). Instead of considering all the boxes in the partition, we propose to use a randomized search to quickly find a region that yields a high local discrepancy value. This randomized search is based on threshold accepting, a well-known integer optimization heuristic. We also present some experimental results obtained on a challenging circuit benchmark and a number of randomly generated examples, which shows that the new guiding method allows achieving better time and coverage efficiency.