Unpacking Interpretability: Human-Centered Criteria for Optimal Combinatorial Solutions

TL;DR

This paper investigates what makes optimal solutions in combinatorial problems more interpretable to humans by identifying structural properties that influence human preferences and reaction times.

Contribution

It introduces an experimental paradigm to quantify interpretability of solutions and identifies key structural features that enhance human understanding of optimal packing solutions.

Findings

Preferences favor ordered representations and heuristic alignment.

Simple within-bin composition also correlates with interpretability.

Reaction times are faster when heuristic differences are large.

Abstract

Algorithmic support systems often return optimal solutions that are hard to understand. Effective human-algorithm collaboration, however, requires interpretability. When machine solutions are equally optimal, humans must select one, but a precise account of what makes one solution more interpretable than another remains missing. To identify structural properties of interpretable machine solutions, we present an experimental paradigm in which participants chose which of two equally optimal solutions for packing items into bins was easier to understand. We show that preferences reliably track three quantifiable properties of solution structure: alignment with a greedy heuristic, simple within-bin composition, and ordered visual representation. The strongest associations were observed for ordered representations and heuristic alignment, with compositional simplicity also showing a consistent association. Reaction-time evidence was mixed, with faster responses observed primarily when heuristic differences were larger, and aggregate webcam-based gaze did not show reliable effects of complexity. These results provide a concrete, feature-based account of interpretability in optimal packing solutions, linking solution structure to human preference. By identifying actionable properties (simple compositions, ordered representation, and heuristic alignment), our findings enable interpretability-aware optimization and presentation of machine solutions, and outline a path to quantify trade-offs between optimality and interpretability in real-world allocation and design tasks.