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Feature-Based Interpretable Surrogates for Optimization

Marc Goerigk, Michael Hartisch, Sebastian Merten, Kartikey Sharma

TL;DR

This work investigates how to use more general optimization rules to further increase interpretability and give more freedom to the decision-maker and presents an exact methodology using mixed-integer programming formulations as well as heuristics.

Abstract

For optimization models to be used in practice, it is crucial that users trust the results. A key factor in this aspect is the interpretability of the solution process. A previous framework for inherently interpretable optimization models used decision trees to map instances to solutions of the underlying optimization model. Based on this work, we investigate how we can use more general optimization rules to further increase interpretability and, at the same time, give more freedom to the decision-maker. The proposed rules do not map to a concrete solution but to a set of solutions characterized by common features. To find such optimization rules, we present an exact methodology using mixed-integer programming formulations as well as heuristics. We also outline the challenges and opportunities that these methods present. In particular, we demonstrate the improvement in solution quality that our approach offers compared to existing interpretable surrogates for optimization, and we discuss the relationship between interpretability and performance. These findings are supported by experiments using both synthetic and real-world data.

Feature-Based Interpretable Surrogates for Optimization

TL;DR

This work investigates how to use more general optimization rules to further increase interpretability and give more freedom to the decision-maker and presents an exact methodology using mixed-integer programming formulations as well as heuristics.

Abstract

For optimization models to be used in practice, it is crucial that users trust the results. A key factor in this aspect is the interpretability of the solution process. A previous framework for inherently interpretable optimization models used decision trees to map instances to solutions of the underlying optimization model. Based on this work, we investigate how we can use more general optimization rules to further increase interpretability and, at the same time, give more freedom to the decision-maker. The proposed rules do not map to a concrete solution but to a set of solutions characterized by common features. To find such optimization rules, we present an exact methodology using mixed-integer programming formulations as well as heuristics. We also outline the challenges and opportunities that these methods present. In particular, we demonstrate the improvement in solution quality that our approach offers compared to existing interpretable surrogates for optimization, and we discuss the relationship between interpretability and performance. These findings are supported by experiments using both synthetic and real-world data.
Paper Structure (38 sections, 2 theorems, 21 equations, 15 figures, 3 tables, 1 algorithm)

This paper contains 38 sections, 2 theorems, 21 equations, 15 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related Literature
  4. Interpretable optimization approaches.
  5. Explainable optimization.
  6. Other related research.
  7. Contribution and Structure
  8. Feature-Based Framework for Finding Interpretable Surrogates
  9. The Framework
  10. Scope of the Framework
  11. Knapsack.
  12. Shortest path.
  13. Other domains.
  14. Models
  15. Inner Tree Structure
  16. ...and 23 more sections

Key Result

Theorem 1

The following problem is NP-complete: Given a graph $G = (V, E)$ and a meta-path, decide whether there is a path from node $s$ to node $t$ in $G$ that corresponds to the meta-path.

Figures (15)

  • Figure 1: Comparison of the proposed feature-based framework with related approaches for solving optimization problems. In our method, the traditional use of a black-box solver is replaced by an interpretable surrogate model, which is first trained on available data. For a new problem instance, the surrogate specifies a restricted solution space using comprehensible features, enabling the user to select a solution suitable for their situation.
  • Figure 2: Traffic scenarios assumed in the shortest path example. The day of the week is depicted on the horizontal and the time of day on the vertical axis.
  • Figure 3: Traffic scenarios in the city of Chicago.
  • Figure 4: Optimization rule obtained from using the solution-based framework for interpretable surrogates.
  • Figure 5: Decision tree.
  • ...and 10 more figures

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof