On the Relationship Between the Order of Mutation Testing and the Properties of Generated Higher Order Mutants

The goal of higher order mutation testing is to improve mutation testing effectiveness in particular and test effectiveness in general. There are different approaches which have been proposed in the area of second order mutation testing and higher order mutation testing with mutants order ranging from 2 to 70. Unfortunately, the empirical evidence on the relationship between the order of mutation testing and the desired properties of generated mutants is scarce except the conviction that the number of generated mutants could grow exponentially with the order of mutation testing. In this paper, we present the study of finding the relationships between the order of mutation testing and the properties of mutants in terms of number of generated high quality and reasonable mutants as well as generated live mutants. Our approach includes higher order mutants classification, objective functions and fitness functions to classify and identify generated higher order mutants. We use four multi-objective optimization algorithms for constructing higher order mutants. Obtained empirical results indicate that 5 is a relevant highest order in higher order mutation testing.