Application of metamorphic testing monitored by test adequacy in a Monte Carlo simulation program

One of the grand challenges for adequately testing complex software is due to the oracle problem. Metamorphic Testing (MT) is a promising technique to alleviate the oracle problem through using one or multiple Metamorphic Relations (MRs) as test oracles. MT checks the satisfaction of every MR among the outputs of the MR-related tests instead of the correctness of individual test outputs. In practice, it is fairly easy to find MRs for testing any program, but it is very difficult to develop “good” MRs and evaluate their adequacy. A systematic approach for developing MRs and evaluating their adequacy in MT remains to be developed. In this paper, we propose a framework for evaluating MT and iteratively developing adequate MRs monitored by MT adequacy evaluation. The MT adequacy is measured by program coverages, mutation testing, and testing MRs with mutation tests. The MT evaluation results are used for guiding the iterative development of MRs, generating tests, and analyzing test outputs. We explain the framework through a testing example on an image processing program that is used for building the 3-dimensional structure of a biology cell based on its confocal image sections. In order to demonstrate the effectiveness of the proposed framework, we reported a case study of testing a complex scientific program: a Monte Carlo modeling program that simulates photon propagations in turbid tissue phantoms for accurate and efficient generation of reflectance images from biological tissues. The case study has shown the effectiveness of proposed MT framework for testing scientific software in general and the necessity of the MT enhancement in the development of adequate MRs. The case study results can be easily adapted for testing other software.