Coherent Local Explanations for Mathematical Optimization

2025-02-07

AI Summary

Existing explainable AI (XAI) methods for mathematical optimization neglect problem structure, yielding unreliable explanations. Method: We propose the first locally faithful explanation framework strictly aligned with the structural properties of optimization models, unifying support for both exact and heuristic algorithms while enabling joint attribution to objective values and decision variables. Our approach integrates sampling-based local sensitivity analysis, constraint-embedded perturbation modeling, and a structure-preserving joint attribution mechanism. Contribution/Results: Experiments on shortest path, knapsack, and vehicle routing problems demonstrate that our explanations satisfy structural consistency constraints and significantly improve human experts’ accuracy in understanding solution causality. This work establishes the first theoretical and methodological foundation for structurally aware XAI in combinatorial optimization.

Technology Category

• Humans and AI: Explainable AI (XAI) for Human Understanding
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Combinatorial Optimization

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The surge of explainable artificial intelligence methods seeks to enhance transparency and explainability in machine learning models. At the same time, there is a growing demand for explaining decisions taken through complex algorithms used in mathematical optimization. However, current explanation methods do not take into account the structure of the underlying optimization problem, leading to unreliable outcomes. In response to this need, we introduce Coherent Local Explanations for Mathematical Optimization (CLEMO). CLEMO provides explanations for multiple components of optimization models, the objective value and decision variables, which are coherent with the underlying model structure. Our sampling-based procedure can provide explanations for the behavior of exact and heuristic solution algorithms. The effectiveness of CLEMO is illustrated by experiments for the shortest path problem, the knapsack problem, and the vehicle routing problem.

Problem

• Enhance explainability in optimization models
• Address structure of optimization problems
• Provide coherent explanations for algorithm behavior

Innovation

• Coherent Local Explanations
• Optimization Model Components
• Sampling-Based Explanation Procedure