Adaptive Scalarization Methods In Multiobjective Optimization

Gabriele Eichfelder3540791574, 978-3-540-79157-7

This book presents adaptive solution methods for multiobjective optimization problems based on parameter dependent scalarization approaches. With the help of sensitivity results an adaptive parameter control is developed such that high-quality approximations of the efficient set are generated. These examinations are based on a special scalarization approach, but the application of these results to many other well-known scalarization methods is also presented. Thereby very general multiobjective optimization problems are considered with an arbitrary partial ordering defined by a closed pointed convex cone in the objective space. The effectiveness of these new methods is demonstrated with several test problems as well as with a recent problem in intensity-modulated radiotherapy. The book concludes with a further application: a procedure for solving multiobjective bilevel optimization problems is given and is applied to a bicriteria bilevel problem in medical engineering.