Optimization models fix mistakes by learning from past decisions
TACIT: Optimization Models that Learn from Their Mistakes
Artificial Intelligence
Summary
Optimization models often fail because they miss key facts experts know but can’t easily write down. This paper shows a way to improve these models by using past decisions and corrections as learning signals. The authors combine artificial intelligence language models with traditional optimization to suggest fixes and verify them. Their method, tested on many problem types, fixes more issues than previous techniques.
What this means in practice
- •For operations teams: Improve planning models by automatically updating them using past decision data and corrections to better match real-world constraints.
- •For supply chain managers: Fix errors in supply chain optimization models by learning from historical adjustments made by human planners.
Authors
Maxime Bouscary, Marco Molinaro, Sirui Li, Saurabh Amin, Ishai Menache, Konstantina Mellou
Abstract
Real-world optimization problems are difficult to model accurately because many objectives and constraints reside in domain experts' tacit knowledge, making them hard to formalize. As a result, optimization models often contain miscalibrated objectives, missing constraints, or omitted decision variables, leading to solutions that fail to reflect operational realities. We address this challenge by automatically repairing misspecified formulations using historical data consisting of past solutions and subsequent user overrides. Traditional approaches such as inverse optimization and constraint learning tend to overfit sparse data and produce complex formulations. Our central idea is to combine the reasoning capabilities and prior knowledge of LLMs with the formal grounding provided by optimization. We realize this idea through two complementary paradigms. Top-down, an LLM proposes structural repairs, including new constraints and variables, whose numerical parameters are calibrated and validated through optimization. Bottom-up, optimization infers cuts from observed decisions, which the LLM contextualizes into interpretable, generalizable modeling constraints. We evaluate our approach on 38 misspecification scenarios spanning nine classes of optimization problems, several drawn from real-world applications, and show that TACIT can repair 78.9% of them (vs. 60.5% for the best baseline).