Eichfelder Adaptive Scalarization Methods in Multiobjective Optimization

1. Auflage 2008
ISBN: 978-3-540-79159-1
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 241 Seiten

Autoren/Hrsg.

Eichfelder, Gabriele

Inhaltsverzeichnis

1;Preface;7
2;Contents;11
3;Part I Theory;15
3.1;1 Theoretical Basics of Multiobjective Optimization;16
3.1.1;1.1 Basic Concepts;16
3.1.2;1.2 Polyhedral Ordering Cones;28
3.2;2 Scalarization Approaches;34
3.2.1;2.1 Pascoletti-Serafini Scalarization;36
3.2.2;2.2 Properties of the Pascoletti-Serafini Scalarization;38
3.2.3;2.3 Parameter Set Restriction for the Pascoletti-Serafini Scalarization;44
3.2.4;2.4 Modified Pascoletti-Serafini Scalarization;57
3.2.5;2.5 Relations Between Scalarizations;62
3.3;3 Sensitivity Results for the Scalarizations;80
3.3.1;3.1 Sensitivity Results in Partially Ordered Spaces;81
3.3.2;3.2 Sensitivity Results in Naturally Ordered Spaces;96
3.3.3;3.3 Sensitivity Results for the;107
4;Part II Numerical Methods and Results;112
4.1;4 Adaptive Parameter Control;114
4.1.1;4.1 Quality Criteria for Approximations;114
4.1.2;4.2 Adaptive Parameter Control in the Bicriteria Case;120
4.1.3;4.3 Adaptive Parameter Control in the Multicriteria Case;147
4.2;5 Numerical Results;154
4.2.1;5.1 Bicriteria Test Problems;154
4.2.2;5.2 Tricriteria Test Problems;168
4.3;6 Application to Intensity Modulated Radiotherapy;180
4.3.1;6.1 Problem Formulation Using a Bicriteria Approach;181
4.3.2;6.2 Problem Formulation Using a Tricriteria Approach;189
5;Part III Multiobjective Bilevel Optimization;194
5.1;7 Application to Multiobjective Bilevel Optimization;196
5.1.1;7.1 Basic Concepts of Bilevel Optimization;197
5.1.2;7.2 Induced Set Approximation;199
5.1.3;7.3 Induced Set Refinement;206
5.1.4;7.4 Algorithm;210
5.1.5;7.5 Numerical Results;212
5.1.6;7.6 Multiobjective Bilevel Optimization Problems with Coupled Upper Level Constraints;223
6;References;232
7;Index;252