Adaptive Parameter Control

In this chapter we use the preceding results for developing an algorithm for adaptively controlling the choice of the parameters in several scalarization approaches. The aim is an approximation of the efficient set of the multiobjective optimization problem with a high quality. The quality can be measured with different criteria, which we discuss first. This leads us to the aim of equidistant approximation points.

For reaching this aim we mainly use the scalarization approach of Pascoletti and Serafini. This scalarization is parameter dependent and we develop a procedure how these parameters can be chosen adaptively such that the distances between the found approximation points of the efficient set are controlled. For this adaptive parameter choice we apply the sensitivity results of Chap. 3. Because many other scalarizations can be considered as a special case of the Pascoletti-Serafini problem, as we have seen in Sect. 2.5, we can apply our results for the adaptive parameter control to other scalarizations as the ε-constraint or the normal boundary intersection problem, too.