OWA Regret – Decision Making beyond Ordered Weighted Averaging and Min-Max Regret

• Applicant: Professor Dr. Marc Goerigk
• Subject Area: Accounting and Finance ; Theoretical Computer Science
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 448792059

• Final Report Year: 2024

Final Report Abstract

When a decision maker needs to choose between different alternative, he or she needs some guiding principle how to rank them. The classic literature offers several such solutions for decision making under uncertainty, including the principle of minimizing what is called the “regret” of an alternative, and the ordered weighted averaging (OWA) method, which is expressed through a preference vector that reflects the decision maker’s attitude towards risk. This project studies a novel combination of these methods, where both OWA and regret are used, in the context of decision-making problems with too many alternatives to enumerate them all. This means that efficient algorithms are required to identify the best of all alternatives in little processing time. For classic min-max regret problem, such a setting is often difficult to solve. Our approach is even more general, and those poses even greater challenges. We studied the complexity of such problems and developed heuristic solution methods that give guarantees on the quality of solutions found. The performance of these heuristics depend on the prefernce vector of the decision maker. Furthermore, extended the OWA framework towards continuous scenarios sets, and developed methods to elicit the preference vector of a decision maker. Our results thus offer new possibilities to find the best possible alternative whenever we are faced with a decision making problem under uncertainty.

Publications

• Robust optimization with belief functions. International Journal of Approximate Reasoning, 159, 108941.
  Goerigk, Marc; Guillaume, Romain; Kasperski, Adam & Zieliński, Paweł
  
• A preference elicitation approach for the ordered weighted averaging criterion using solution choice observations. European Journal of Operational Research, 314(3), 1098-1110.
  Baak, Werner; Goerigk, Marc & Hartisch, Michael
  
• Ordered weighted averaging for combinatorial decision problems with interval uncertainty
  Werner Baak & Marc Goerigk
  
• Robust min-max (regret) optimization using ordered weighted averaging. European Journal of Operational Research, 322(1), 171-181.
  Baak, Werner; Goerigk, Marc; Kasperski, Adam & Zieliński, Paweł