Advanced Ordered Weighted Averaging Methods in Robust Optimization

In decision-making under uncertainty, robust optimization is a critical tool across various fields, providing solutions that perform effectively across a range of scenarios where precise probabilities are unavailable or unreliable. Traditional approaches, such as min-max and min-max regret, focus on minimizing the worst-case outcomes and worst-case regret, respectively, often resulting in highly conservative solutions. To address this limitation, this dissertation investigates the Ordered Weighted Averaging (OWA) operator, which offers a flexible framework for aggregating outcomes according to varying risk preferences, from risk-averse to risk-neutral, encompassing traditional robust approaches as special cases. This work is organized around three primary contributions that expand the application and understanding of OWA in robust optimization. The first contribution develops a preference elicitation framework for OWA weights, enabling decision-makers to derive weighting schemes based on observed historical decisions, thereby aligning aggregation strategies with specific risk attitudes. The second contribution introduces a novel variant of OWA for robust optimization, integrating OWA into a regret minimization framework to generalize both robust min-max and min-max regret approaches. This model is complemented by new complexity results, including insights into the inapproximability and approximability of OWA regret, providing stronger approximation bounds that asymptotically improve on previously established results for classic OWA models. These advancements position the OWA regret model as a powerful alternative to min-max regret, offering a more adaptable approach to risk-sensitive decision-making. The third contribution addresses interval uncertainty, extending the OWA framework to scenarios where outcomes are represented as bounded intervals instead of discrete points. This interval-based OWA model accommodates real-world decision-making needs, where scenario data are uncertain or costly to specify. By using Value-at-Risk (VaR) in our definition, we provide a natural way to handle continuous ranges of uncertainty while maintaining computational tractability for large-scale problems. Together, these contributions advance both the theoretical and practical applications of OWA in decision making, establishing OWA-based methods as versatile tools for addressing complex uncertainties across a variety of decision-making environments.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Passau

Year

2025

Author dc:creator

• Baak, Werner

Contributors dc:contributor

• Goerigk, Marc
• Otto, Alena

• decision-making
• uncertainty
• risk

Statement dc:rights

• Standardbedingung laut Einverständniserklärung

Repository record source_url

https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/1587

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-passau:1587