2026. Relatively Robust Multicriteria Optimization
Invited abstract in session TC-51: Multiobjective Decision Making, stream Multiobjective and vector optimization.
Tuesday, 12:30-14:00Room: Parkinson B22
Authors (first author is the speaker)
| 1. | Thomas Weber
|
| Chair of Operations, Economics and Strategy, EPFL |
Abstract
For a general multicriteria decision problem with linear scalarization and unknown weights, we propose relatively robust decisions that are Pareto-efficient while maximizing a performance index. This index measures the worst-case ratio of the weighted objective to its maximum value across all possible weights. Key results include a simple boundary representation of the performance index as the minimum of criterion-specific performance ratios and an efficient method for determining a relatively robust decision within any given performance tolerance by maximizing an εε-augmented performance index. Our approach requires only the continuity of criterion functions and the compactness of the feasible decision set, accommodating nonconvex sets without restriction for finite action sets. A notable feature of our method is its endogenous derivation of trade-offs between criteria, providing a performance guarantee relative to any weighting. We illustrate its effectiveness through structural results, examples, and applications.
Keywords
- Programming, Multi-Objective
- Robust Optimization
- Decision Theory
Status: accepted
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