On data-driven chance constraint learning for mixed-integer optimization
problems
- URL: http://arxiv.org/abs/2207.03844v1
- Date: Fri, 8 Jul 2022 11:54:39 GMT
- Title: On data-driven chance constraint learning for mixed-integer optimization
problems
- Authors: Antonio Alc\'antara and Carlos Ruiz
- Abstract summary: We develop a Chance Constraint Learning (CCL) methodology with a focus on mixed-integer linear optimization problems.
CCL makes use of linearizable machine learning models to estimate conditional quantiles of the learned variables.
An open-access software has been developed to be used by practitioners.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: When dealing with real-world optimization problems, decision-makers usually
face high levels of uncertainty associated with partial information, unknown
parameters, or complex relationships 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 optimization problems which
combines ideas from the chance constraint and constraint learning literature.
Chance constraints set a probabilistic confidence level for a single or a set
of constraints to be fulfilled, whereas the constraint learning methodology
aims to model the functional relationship between the problem variables through
predictive models. 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 behaviour. In this sense, CCL makes use of
linearizable machine learning models to estimate conditional quantiles of the
learned variables, providing a data-driven solution for chance constraints. An
open-access software has been developed to be used by practitioners.
Furthermore, benefits from CCL have been tested in two real-world case studies,
proving how robustness is added to optimal solutions when probabilistic bounds
are set for learned constraints.
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