On data-driven chance constraint learning for mixed-integer optimization problems Articles uri icon

publication date

  • April 2023

start page

  • 445

end page

  • 462

volume

  • 121

International Standard Serial Number (ISSN)

  • 0307-904X

abstract

  • When dealing with optimization problems, decision-makers often face high levels of un- certainty associated with partial information, unknown parameters, or complex relation- ships between these and the problem decision variables. In this work, we develop a novel Chance Constraint Learning (CCL) methodology with a focus on mixed-integer linear opti- mization problems, which combines and extends ideas from the literature on chance con- straint and constraint learning. While constraint learning aims to model the functional re- lationship between straight-forward and non-tractable decision variables through the em- bedding of predictive models within the optimization problem, chance constraints set a probabilistic confidence level for a single or a set of constraints to be fulfilled. One of the main issues when establishing a learned constraint arises when we need to set further bounds for its response variable: the fulfillment of these is directly related to the accuracy of the predictive model and its probabilistic behavior. Therefore, the proposed CCL makes use of piece-wise linearizable machine learning models to estimate conditional quantiles of learned variables, providing a data-driven solution for chance constraints and adding prob- abilistic guarantees over constraints for learned variables. Open access software has been developed for use by practitioners. Furthermore, the benefits of CCL have been tested in two real-world case studies, demonstrating how robustness is added to optimal solutions when probabilistic bounds are established for learned constraints.

subjects

  • Statistics

keywords

  • chance constraint; constraint learning; data-driven optimization; quantile estimation; machine learning