Ordinal costs in multi-objective combinatorial optimization / vorgelegt von Julia Sudhoff. Wuppertal, September 2022
Content
- Contents
- Introduction
- Basic Concepts and Notation
- Binary Relations and Cones
- Optimization Problems and Optimality Concepts
- Scalarizations
- Graphs
- Matroids
- Single-objective Matroid Optimization and Multi-objective Minimum Spanning Tree Problem
- Single-objective Shortest Path Problem
- Single-objective Matroid Intersection Problem
- Multi-objective Knapsack Problem
- Multi-objective Assignment Problem
- Bi-objective Matroid Optimization Problems with Binary Costs
- Problem Formulation
- Theoretical Results
- Efficient Swap Algorithm
- Numerical Results
- Conclusion and Further Ideas
- Single- and Multi-objective Matroid Optimization Problems with Ordinal Costs
- Single-objective Matroid Optimization with Ordinal Costs
- Bi-objective Matroid Optimization with Ordinal Costs
- Matroid Intersection Algorithm for Ordinal Constraints
- Multi-objective Matroid Optimization with Ordinal Costs
- Numerical Results
- Conclusion and Further Ideas
- Single- and Multi-objective Combinatorial Optimization Problems with Ordinal Costs
- Single-objective Combinatorial Optimization with Ordinal Costs
- Ordinal Optimality versus Pareto Optimality: An Interpretation based on Ordering Cones
- Solution Strategies
- Excursus: Olympic Medals and Ordinal Weight Space Decomposition
- Numerical Results
- Multi-objective Combinatorial Optimization with Ordinal Costs
- Conclusion and Further Ideas
- Conclusion and Further Ideas
- Bibliography
- A Story About Ordinal Optimization Through Multi-objective Reformulation