AUTOMATIC VERIFICATION OF OPTIMIZATION ALGORITHMS: A CASE STUDY OF A QUADRATIC ASSIGNMENT PROBLEM SOLVER

Metamorphic testing is a technique for the verification of software output without a complete testing oracle. Mathematical optimization, implemented in software, is a problem for which verification can often be challenging. In this paper, we apply metamorphic testing to one such optimization problem, the quadratic assignment problem (QAP). From simple observations of the properties of the QAP, we describe how to derive a number of metamorphic relations useful for verifying the correctness of a QAP solver. We then compare the effectiveness of these metamorphic relations, in killing mutant versions of an exact QAP solver, to a simulated oracle. We show that metamorphic testing can be as effective as the simulated oracle for killing mutants. We examine the relative effectiveness of different metamorphic relations, both singly and in combination, and conclude that combining metamorphic relations can be significantly more effective than using a single relation.