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

2025-11-13

AI Summary

In multi-objective optimization, the Pareto-optimal solution set is often excessively large, imposing heavy cognitive burden on decision-makers. Method: This paper proposes “Directional Coverage,” a novel representativeness metric, and conducts axiomatic analysis within a multi-winner voting framework to expose counterintuitive behaviors of existing indicators and characterize their computational complexity boundaries under varying objective structures. The approach integrates axiomatic modeling, computational complexity theory, and empirical evaluation to systematically compare how diverse quality metrics affect solution set representativeness. Results: Experiments demonstrate that Directional Coverage achieves superior or comparable performance to state-of-the-art metrics in diversity, convergence, and directional sensitivity. Crucially, the choice of quality metric fundamentally determines representativeness outcomes—providing both theoretical foundations and practical tools for Pareto set reduction.

Technology Category

• Search and Optimization: Metareasoning and Metaheuristics
• Knowledge Representation and Reasoning: Preferences
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• Selecting representative Pareto optimal solutions to reduce decision maker cognitive load
• Analyzing quality measures for multiobjective optimization through axiomatic study
• Developing new directed coverage measure and computational complexity analysis

Innovation

• Reframed Pareto pruning as multiwinner voting problem
• Introduced new quality measure called directed coverage
• Analyzed computational complexity for tractable optimization cases