Hartisch, Michael: Quantified integer programming with polyhedral and decision-dependent uncertaintyQuantifizierte ganzzahlige Programmierung unter polyedrischer und entscheidungsabhängiger UnsicherheitQuantifizierte ganzzahlige Programmierung unter polyedrischer und entscheidungsabhängiger Unsicherheit. 2020
Inhalt
- Zusammenfassung
- Abstract
- Contents
- Glossaries
- List of Figures
- List of Tables
- Introduction
- Multistage Optimization under Uncertainty
- Quantified (Mixed) Integer Programming
- Problem Statement and Notation
- Quantified Integer Programming as Two-Person Zero-Sum Game
- The Open-Source QMIP Solver Yasol
- Related Work
- Quantification of Variables
- Optimization under Uncertainty
- Optimization under Decision-Dependent Uncertainty
- Examples
- Algorithmic Properties of QIPs
- Quantified Integer Programming with Polyhedral Uncertainty Set
- Quantified Integer Programming with Interdependent Domains
- Motivation
- Problem Statement QIPID
- Use of Game Trees for QIPID
- Computational Complexity of QIPID
- Relaxations
- Solution Techniques for QIPID
- Simply Restricted QIPID
- Implementation Details and Experimental Results
- QLP File Format for QIPID and General Input Requirements for Yasol
- Main Modifications and Enhancements of Yasol
- Implementation of the Reduction Function
- Deduction Techniques in the Presence of Universal Constraints
- Used Relaxations
- Computational Experiments
- Conclusion and Outlook
- Appendix
- Examples and Algorithms
- Example of Reduction QIPID p QIP
- Heuristic Strategies for Example 4.4.2
- Tic-Tac-Toe as QIPID
- Alpha-Beta Algorithm for QIPID
- Supplemental Data
- Additional Data on Multistage Selection Experiments
- Data Table of Multistage Selection Instances
- Performance Profiles for Multistage Selection Experiments
- Optimal Robust Strategy vs. Heuristic Selection Strategy
- Additional Data on Multistage Assignment Experiments
- Bibliography