For testing the numerical methods developed in Chap. 4 on their effi- ciency, in this chapter several test problems with various difficulties are solved. Test problems are important to get to know the properties of the discussed procedures. Large collections of test problems mainly developed for testing evolutionary algorithms are given in [41, 45, 46, 228]. Some of the problems of these collections test difficulties especially designed for evolutionary algorithms, which are not a task using the scalarization approaches of this book. For instance, arbitrarily generated points of the constraint set are mapped by the objective functions mainly in areas far away from the efficient set and only few of them have images near the efficient set.
Other test problems have a non-convex image set or gaps in the ef- ficient set, i. e. non-connected efficient sets. We examine such problems among others in this chapter. In the remaining chapters of this book, we discuss the application of the methods of Chap. 4 on a concrete application problem in medical engineering as well as on a multiobjective bilevel optimization problem.