Picking a Representative Set of Solutions in Multiobjective Optimization: Axioms, Algorithms, and Experiments

TL;DR

This paper investigates how to select a representative subset of solutions in multiobjective optimization, analyzing existing measures, proposing a new one, and evaluating their impact through experiments.

Contribution

It introduces a new quality measure called directed coverage and analyzes the computational complexity of Pareto pruning, providing insights into measure selection.

Findings

The choice of quality measure significantly affects the selected solution set.

The proposed directed coverage measure performs well across various scenarios.

Complexity boundaries for optimizing measures depend on the number and structure of objectives.

Abstract

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.