Adaptive Scalarization Methods in Multiobjective Optimization

  • Gabriele Eichfelder

Part of the Vector Optimization book series (VECTOROPT)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Theory

  3. Numerical Methods and Results

  4. Multiobjective Bilevel Optimization

  5. Back Matter
    Pages 219-241

About this book

Introduction

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.

Keywords

Decision Making Mulitobjective Optimization Multiobjective Bilevel Optimization Scalarization Sensitivity Vector Optimization linear optimization optimization

Authors and affiliations

  • Gabriele Eichfelder
    • 1
  1. 1.Department of MathematicsUniversity of Erlangen-NürnbergErlangenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-79159-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science
  • Print ISBN 978-3-540-79157-7
  • Online ISBN 978-3-540-79159-1
  • Series Print ISSN 1867-8971
  • About this book