Optimization with Constraint Learning: A Framework and Survey
This provides a systematic approach for researchers and practitioners dealing with data-driven optimization problems, but it is incremental as it organizes existing ideas into a framework.
The paper tackles the problem of optimization with constraints that lack explicit formulas by proposing a framework for Optimization with Constraint Learning (OCL) to formalize learning constraints from data, resulting in a structured process with steps like model setup, data handling, and verification.
Many real-life optimization problems frequently contain one or more constraints or objectives for which there are no explicit formulas. If data is however available, these data can be used to learn the constraints. The benefits of this approach are clearly seen, however there is a need for this process to be carried out in a structured manner. This paper therefore provides a framework for Optimization with Constraint Learning (OCL) which we believe will help to formalize and direct the process of learning constraints from data. This framework includes the following steps: (i) setup of the conceptual optimization model, (ii) data gathering and preprocessing, (iii) selection and training of predictive models, (iv) resolution of the optimization model, and (v) verification and improvement of the optimization model. We then review the recent OCL literature in light of this framework, and highlight current trends, as well as areas for future research.