Adaptive parametric scalarizations in multicriteria optimization / vorgelegt von Kerstein Dächert. 2014
Inhalt
- Introduction
- Preliminaries
- Terminology and Definitions
- Representation and Approximation of the Nondominated Set
- Scalarization Methods
- Parametric Algorithms
- Literature Review on Parametric Algorithms
- Theoretical Findings for Adaptive Parametric Algorithms
- Adaptive Parameters for Scalarizations with Augmentation
- Introduction
- Parameters of the Augmented Weighted Tchebycheff Norm
- Parameters of a Generalized Augmented Weighted Tchebycheff Norm
- Parameters of Augmented -Constraint Scalarizations
- Conclusion and Further Ideas
- A Parametric Algorithm with a New Bound on the Number of Subproblems
- Introduction
- Split of the Search Region for Multicriteria Problems
- An Improved Split in the Tricriteria Case
- Individual Subsets and the v-Split
- The v-Split Algorithm
- A Linear Bound on the Number of Subproblems
- Quasi Non-Redundancy
- The -Constraint Method in Combination with the v-Split
- Generalization of the v-Split Algorithm for m 3
- Conclusion and Further Ideas
- Practical Application of Adaptive Parametric Algorithms
- Generation of Complete Representations for Discrete Test Problems
- Introduction
- Bicriteria Problems
- Implementation of the Full 2-Split Algorithm
- Local Ideal Points as Reference Points
- Computational Setup
- Computational Results
- Tricriteria Problems
- Conclusion and Further Ideas
- Generation of Incomplete Representations for Continuous Test Problems
- Multiobjective Optimal Control of Sewer Networks
- Introduction
- Objectives in Wastewater Management
- Computational Setup
- Computational Results
- Conclusion and Further Ideas
- Conclusion
- Notation
- Acknowledgement
- Bibliography