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Mining Potentially Explanatory Patterns via Partial Solutions

GianCarlo Catalano, Alexander E. I. Brownlee, David Cairns, John McCall, Russell Ainslie

TL;DR

This work tackles the explainability gap in genetic algorithms for combinatorial optimization by introducing Partial Solutions (PSs): explicit, interpretable sub-configurations extracted from high-fitness solutions. A PS catalog, mined from a fixed reference population, acts as a probabilistic model from which new solutions can be generated via a Pick & Merge process, balancing simplicity, mean fitness, and atomicity through the $F^{\psi}$ objective. The approach yields both global and local explanations and can match or exceed GA performance on benchmark problems while enabling explainability, albeit at a computational cost associated with evaluating $F^{\psi}$. By linking explainability with search efficiency, the PS framework offers a pathway to surrogate modeling and model-based sampling in optimization, with potential extensions to full EDAs and real-world scheduling tasks.

Abstract

Genetic Algorithms have established their capability for solving many complex optimization problems. Even as good solutions are produced, the user's understanding of a problem is not necessarily improved, which can lead to a lack of confidence in the results. To mitigate this issue, explainability aims to give insight to the user by presenting them with the knowledge obtained by the algorithm. In this paper we introduce Partial Solutions in order to improve the explainability of solutions to combinatorial optimization problems. Partial Solutions represent beneficial traits found by analyzing a population, and are presented to the user for explainability, but also provide an explicit model from which new solutions can be generated. We present an algorithm that assembles a collection of Partial Solutions chosen to strike a balance between high fitness, simplicity and atomicity. Experiments with standard benchmarks show that the proposed algorithm is able to find Partial Solutions which improve explainability at reasonable computational cost without affecting search performance.

Mining Potentially Explanatory Patterns via Partial Solutions

TL;DR

This work tackles the explainability gap in genetic algorithms for combinatorial optimization by introducing Partial Solutions (PSs): explicit, interpretable sub-configurations extracted from high-fitness solutions. A PS catalog, mined from a fixed reference population, acts as a probabilistic model from which new solutions can be generated via a Pick & Merge process, balancing simplicity, mean fitness, and atomicity through the objective. The approach yields both global and local explanations and can match or exceed GA performance on benchmark problems while enabling explainability, albeit at a computational cost associated with evaluating . By linking explainability with search efficiency, the PS framework offers a pathway to surrogate modeling and model-based sampling in optimization, with potential extensions to full EDAs and real-world scheduling tasks.

Abstract

Genetic Algorithms have established their capability for solving many complex optimization problems. Even as good solutions are produced, the user's understanding of a problem is not necessarily improved, which can lead to a lack of confidence in the results. To mitigate this issue, explainability aims to give insight to the user by presenting them with the knowledge obtained by the algorithm. In this paper we introduce Partial Solutions in order to improve the explainability of solutions to combinatorial optimization problems. Partial Solutions represent beneficial traits found by analyzing a population, and are presented to the user for explainability, but also provide an explicit model from which new solutions can be generated. We present an algorithm that assembles a collection of Partial Solutions chosen to strike a balance between high fitness, simplicity and atomicity. Experiments with standard benchmarks show that the proposed algorithm is able to find Partial Solutions which improve explainability at reasonable computational cost without affecting search performance.
Paper Structure (29 sections, 11 equations, 4 figures, 7 tables, 2 algorithms)

This paper contains 29 sections, 11 equations, 4 figures, 7 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Optimization problems
  3. Related work
  4. Models within GAs and EDAs
  5. Backbones and building blocks
  6. Partial Solutions
  7. Informal Introduction
  8. Formal definition
  9. Partial Solution metrics
  10. Novelty
  11. Overall system
  12. Finding Partial Solution Catalogs
  13. Reference Population
  14. Multiple objectives and $F^\psi$
  15. Exclusion archive
  16. ...and 14 more sections

Figures (4)

  • Figure 1: The positive traits in a collection of full solutions $\text{P}_\text{Ref}$ can be described by a collection of Partial Solutions $X^\psi$
  • Figure 2: The proposed system, which uses the PS catalog for both explainability and to generate full solutions.
  • Figure 3: Comparison of the RR and RRO problems, where RRO has more complex global optima
  • Figure 4: (Relating to T3) Mean fitness obtained by dedicating some of the evaluation budget to PS catalog mining.