Search-based inference of polynomial metamorphic relations

Metamorphic testing (MT) is an effective methodology for testing those so-called ``non-testable'' programs (e.g., scientific programs), where it is sometimes very difficult for testers to know whether the outputs are correct. In metamorphic testing, metamorphic relations (MRs) (which specify how particular changes to the input of the program under test would change the output) play an essential role. However, testers may typically have to obtain MRs manually. In this paper, we propose a search-based approach to automatic inference of polynomial MRs for a program under test. In particular, we use a set of parameters to represent a particular class of MRs, which we refer to as polynomial MRs, and turn the problem of inferring MRs into a problem of searching for suitable values of the parameters. We then dynamically analyze multiple executions of the program, and use particle swarm optimization to solve the search problem. To improve the quality of inferred MRs, we further use MR filtering to remove some inferred MRs. We also conducted three empirical studies to evaluate our approach using four scientific libraries (including 189 scientific functions). From our empirical results, our approach is able to infer many high-quality MRs in acceptable time (i.e., from 9.87 seconds to 1231.16 seconds), which are effective in detecting faults with no false detection.