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Adaptive Scalarization Methods in Multiobjective Optimization

Adaptive Scalarization Methods in Multiobjective Optimization

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  • ISBN:9783540791577
  • Editorial: Springer Verlag
  • Fecha de la edición:
  • Encuadernación:
  • Nº Pág.:254
  • Idiomas:Ingles

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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.

Pt. I Theory
1 Theoretical Basics of Multiobjective Optimization 3
2 Scalarization Approaches 21
3 Sensitivity Results for the Scalarizations 67
Pt. II Numerical Methods and Results
4 Adaptive Parameter Control 101
5 Numerical Results 141
6 Application to Intensity Modulated Radiotherapy 167
Pt. III Multiobjective Bilevel Optimization
7 Application to Multiobjective Bilevel Optimization 183
References 219
Index

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