Adaptive Scalarization Methods in Multiobjective Optimization

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.

List of contents

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.

Summary

This book presents adaptive solution methods for multiobjective optimization problems based on parameter dependent scalarization approaches. Readers will benefit from the new adaptive methods and ideas for solving multiobjective optimization.

Additional text

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)

Report

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)

Product details

• Authors: Gabriele Eichfelder
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 12.10.2010
• EAN: 9783642098048
• ISBN: 978-3-642-09804-8
• No. of pages: 241
• Dimensions: 155 mm x 14 mm x 235 mm
• Weight: 394 g
• Illustrations: XIII, 241 p.
• Series: Vector Optimization; Vector Optimization
• Subjects: Natural sciences, medicine, IT, technology > IT, data processing > IT; Social sciences, law, business > Business > General, dictionaries; Operations Research, C, computer science, Operations Research/Decision Theory, Operations Research and Decision Theory, Theory of Computation, Management & management techniques, Operations Research, Management Science, Discrete Mathematics in Computer Science, Discrete Mathematics, Management decision making, Management science, Computers, Mathematical theory of computation, Operational research, Decision Making, Computer science—Mathematics, Maths for computer scientists