arXiv subjects

Werner Baak

Publications and source records attributed to Werner Baak.

3 recordsLinked to original sources

arXiv2026

An extension of Ordered Weighted Averaging over intervals with application to optimization under risk

The Ordered Weighted Averaging (OWA) operator is a traditional and commonly used criterion for aggregating discrete values of uncertain quantities. In this paper, it is shown that the discrete OWA naturally extends to the continuous case by using the concept of a distortion risk measure. It is shown how to apply the distortion risk measure to optimization problems with a linear objective function, whose coefficients are random variables with continuous distribution functions supported on intervals. The case where these coefficients are independent, uniformly distributed random variables is explored in more detail. The computational complexity of the resulting optimization problem is analyzed, and solution methods with approximation guarantees are proposed. These methods are also verified through computational experiments.

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arXiv2024

Robust Min-Max (Regret) Optimization using Ordered Weighted Averaging

In decision-making under uncertainty, several criteria have been studied to aggregate the performance of a solution over multiple possible scenarios. This paper introduces a novel variant of ordered weighted averaging (OWA) for optimization problems. It generalizes the classic OWA approach, which includes robust min-max optimization as a special case, as well as min-max regret optimization. We derive new complexity results for this setting, including insights into the inapproximability and approximability of this problem. In particular, we provide stronger positive approximation results that asymptotically improve the previously best-known bounds for the classic OWA approach. In computational experiments, we evaluate the quality of the proposed methods and compare the proposed setting with classic OWA and min-max regret approaches.

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arXiv2023

A Preference Elicitation Approach for the Ordered Weighted Averaging Criterion using Solution Choice Observations

Decisions under uncertainty or with multiple objectives usually require the decision maker to formulate a preference regarding risks or trade-offs. If this preference is known, the ordered weighted averaging (OWA) criterion can be applied to aggregate scenarios or objectives into a single function. Formulating this preference, however, can be challenging, as we need to make explicit what is usually only implicit knowledge. We explore an optimization-based method of preference elicitation to identify appropriate OWA weights. We follow a data-driven approach, assuming the existence of observations, where the decision maker has chosen the preferred solution, but otherwise remains passive during the elicitation process. We then use these observations to determine the underlying preference by finding the preference vector that is at minimum distance to the polyhedra of feasible vectors for each of the observations. Using our optimization-based model, weights are determined by solving an alternating sequence of linear programs and standard OWA problems. Numerical experiments on risk-averse preference vectors for selection, assignment and knapsack problems show that our passive elicitation method compares well against having to conduct pairwise comparisons and performs particularly well when there are inconsistencies in the decision maker's choices.

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