Ebook: Adaptive Scalarization Methods in Multiobjective Optimization
Author: Dr. Gabriele Eichfelder (auth.)
- Tags: Operations Research/Decision Theory, Operations Research Mathematical Programming, Discrete Mathematics in Computer Science
- Series: Vector Optimization
- Year: 2008
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
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.
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.
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.
Content:
Front Matter....Pages i-xiii
Theoretical Basics of Multiobjective Optimization....Pages 3-20
Scalarization Approaches....Pages 21-66
Sensitivity Results for the Scalarizations....Pages 67-98
Adaptive Parameter Control....Pages 101-139
Numerical Results....Pages 141-165
Application to Intensity Modulated Radiotherapy....Pages 167-179
Application to Multiobjective Bilevel Optimization....Pages 183-217
Back Matter....Pages 219-241
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.
Content:
Front Matter....Pages i-xiii
Theoretical Basics of Multiobjective Optimization....Pages 3-20
Scalarization Approaches....Pages 21-66
Sensitivity Results for the Scalarizations....Pages 67-98
Adaptive Parameter Control....Pages 101-139
Numerical Results....Pages 141-165
Application to Intensity Modulated Radiotherapy....Pages 167-179
Application to Multiobjective Bilevel Optimization....Pages 183-217
Back Matter....Pages 219-241
....