Adaptive Scalarization Methods in Multiobjective Optimization

ISBN-13: 9783540791577 / Angielski / Twarda / 2008 / 241 str.

Gabriele Eichfelder

Opis

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.

Recenzje

From the reviews:

"This monograph on vector optimization is besides theoretical basics ... dedicated to skillful approximations of the whole efficient set. ... This monograph shows experience of the author in the big field of the contents of this book and can be highly recommended to all who work (or want to work) with multicriteria problems." (Alfred Göpfert, Zentralblatt MATH, Vol. 1145, 2008)

Spis treści

Theory.- Theoretical Basics of Multiobjective Optimization.- Scalarization Approaches.- Sensitivity Results for the Scalarizations.- Numerical Methods and Results.- Adaptive Parameter Control.- Numerical Results.- Application to Intensity Modulated Radiotherapy.- Multiobjective Bilevel Optimization.- Application to Multiobjective Bilevel Optimization.

Blurb

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.