Multi-objective combinatorial optimization : supportedness, representations, and integer network flows / vorgelegt von David Könen. Wuppertal, [2025]
Inhalt
- Contents
- Introduction
- Preliminaries
- Computational Complexity
- Polyhedral Theory and Linear Programming
- Multi-Objective Optimization
- Graph and Network
- Single and Multi-objective Minimum Cost Flow Problem
- Generic Scalarization Based Algorithms
- Introduction
- Scalarization Methods
- Search Region and Search Zones
- Survey of Literature
- Generic Algorithms
- Conclusion
- On Supportdness in Multi-Objective Combinatorial Optimization
- Supported Nondominated Points as a Representation for Multi-Objective Integer Minimum Cost Flow Problems
- Finding all Minimum Cost Flows
- Introduction
- Problem Definition and Notation
- Getting From one Minimum Cost Flow to Another
- The All Optimal Integer Flow Algorithm
- Improved Running Time for the k-Best Flow Problem
- Bounds on the Number of Feasible and Optimal Flows
- Conclusion
- Output-sensitive Complexity for Multi-Objective Integer Minimum Cost Flow Problems
- Introduction
- An Output-Polynomial Time Algorithm to Determine all Supported Efficient Solutions
- Output-Sensitive Analysis For Supported Nondominated Points
- Conclusion
- Determining the Supported Nondominated Points for Bi-Objective Integer Minimum Cost Flow Problems
- Introduction
- Adjusted Algorithm
- Epsilon-Scalarizations on Reduced Networks
- A more Compact Formulation for the ILP in the Epsilon-Constraint Method
- Numerical Experiments
- Conclusion
- Conclusion
- Bibliography