Picking a Representative Set of Solutions in Multiobjective Optimization: Axioms, Algorithms, and Experiments
This work addresses the challenge of reducing cognitive load for decision makers in multiobjective optimization, though it is incremental as it builds on existing Pareto pruning methods.
The paper tackled the problem of selecting a representative subset of Pareto optimal solutions in multiobjective optimization by reframing it as a multiwinner voting problem, conducting an axiomatic analysis, introducing a new measure called directed coverage, and showing that it performs competitively or favorably in experiments.
Many real-world decision-making problems involve optimizing multiple objectives simultaneously, rendering the selection of the most preferred solution a non-trivial problem: All Pareto optimal solutions are viable candidates, and it is typically up to a decision maker to select one for implementation based on their subjective preferences. To reduce the cognitive load on the decision maker, previous work has introduced the Pareto pruning problem, where the goal is to compute a fixed-size subset of Pareto optimal solutions that best represent the full set, as evaluated by a given quality measure. Reframing Pareto pruning as a multiwinner voting problem, we conduct an axiomatic analysis of existing quality measures, uncovering several unintuitive behaviors. Motivated by these findings, we introduce a new measure, directed coverage. We also analyze the computational complexity of optimizing various quality measures, identifying previously unknown boundaries between tractable and intractable cases depending on the number and structure of the objectives. Finally, we present an experimental evaluation, demonstrating that the choice of quality measure has a decisive impact on the characteristics of the selected set of solutions and that our proposed measure performs competitively or even favorably across a range of settings.