1330. On spline surrogate models and reformulation techniques for MINLPs with separable non-convexities
Invited abstract in session WA-4: Mathematical Optimization for Interpretable Supervised Learning, stream Machine Learning and Mathematical Optimization.
Wednesday, 8:30-10:00Room: D
Authors (first author is the speaker)
| 1. | Vanesa Guerrero
|
| Department of Statistics, Universidad Carlos III de Madrid | |
| 2. | Claudia D'Ambrosio
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| LIX, CNRS - Ecole Polytechnique | |
| 3. | Renan Spencer Trindade
|
| LIX, CNRS, École Polytechnique |
Abstract
The vast amount of data available nowadays makes possible to model complex phenomena in accurate ways. However, being able to use these models within a mathematical optimization framework to solve instances of real problems is often a challenge. Many of these data-driven models are `black-box', in the sense that they do not have an explicit mathematical formula which describes it. In other cases, even if an explicit expression exists, including it into a mathematical optimization model may make solving the problem computationally intractable.
In this work we propose the use of a special kind of surrogate models, regression splines, together with some reformulation techniques to deal with `black-box' or too complex functions involved in Mixed Integer Nonlinear Programming (MINLP) problems. The choice of spline functions is not arbitrary. On one hand, they offer a good compromise between accuracy in capturing the main trends in the data and complexity, since they are piecewise polynomials. On the other hand, their functional form allows us to approximate general non-convex MINLPs by a more tractable subclass of problems which can be efficiently solved by customized algorithms.
Our approach is tested in real instances of problems arising in industry and in an application of the use of machine learning tools for the configurations of optimization solvers.
Keywords
- Programming, Mixed-Integer
- Analytics and Data Science
Status: accepted
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