Exploratory Study on the Integration of Optimization and Machine Learning for Complex Constrained Problems

Abstract

Constrained optimization problems are common in the industrial field, where operational complexity and the need to accurately model reality lead to formulations of a complex nature or even computationally intractable. In this context, operations research (OR) faces serious challenges in solving these problems, even for small-scale instances, due to factors such as reliance on imprecise data, the combinatorial nature of the models, and high data dimensionality. On the other hand, machine learning (ML) has proven to be a valuable tool for addressing large-scale and highly complex problems. However, it still has limitations in scenarios where strict compliance with a set of constraints is required. This work explores an emerging line of research aimed at achieving a functional integration between optimization and machine learning techniques, with the goal of tackling problems that are inefficient to solve from the perspective of either discipline alone. In this regard, we present the first stage in the development of an OR-ML integration methodology. The scope of the proposal is evaluated through the implementation and solution of a case study related to global agricultural production, which allows us to identify the main solution challenges and propose improvement strategies. While the preliminary results do not fully resolve the problem, they show improvements of up to 96% in model size and lead to robust, high-quality solutions.