Verification of Optimization Algorithms: a Case Study of a Quadratic Assignment Problem Solver

It is often difficult to verify the solutions of computationally intensive mathematical optimization problems. Metamorphic testing is a technique to verify software test output even when a complete testing oracle is not present. We apply metamorphic testing to a classic optimization problem, the quadratic assignment problem (QAP). A number of metamorphic relations for the QAP are described in detail, and their effectiveness in “killing” mutated versions of an exact QAP solver is compared. We show that metamorphic testing can be effectively applied to the QAP in the absence of an oracle, and discuss the implications for the testing of solvers for other hard optimization problems.