Beschreibung
This book presents new adaptive solution methods for multiobjective optimization problems based on parameter dependent scalarizations. With the help of sensitivity results an adaptive parameter control is developed so that high-quality approximations of the efficient set are generated. These examinations are based on a general scalarization approach for arbitrary partial orderings defined by a closed pointed convex cone in the objective space. The application of the results to many other well-known scalarization methods is also presented. Background material of multiobjective optimization and scalarization approaches is concisely summarized at the beginning. The effectiveness of these new methods is demonstrated by test problems and a recent problem in intensity-modulated radiotherapy. The book concludes with a further application: a procedure for solving multiobjective bilevel optimization problems.
Inhaltsverzeichnis
Part I Theory: Theoretical Basics of Multiobjective Optimization.- Scalarization Approaches.- Sensitivity.- Results for the Scalarizations.- Part II Numerical Methods and Results: Adaptive Parameter Control.- Numerical Results.- Application to Intensity Modulated Radiotherapy.- Part III Multiobjective Bilevel Optimization: Application to Multiobjective Bilevel Optimization.
