A learning-based mathematical programming formulation for the automatic configuration of optimization solvers

Gabriele Iommazzo (1) , Claudia D’ambrosio (2, 3) , Antonio Frangioni (4) , Leo Liberti (2, 3)

1 ZIB - Konrad-Zuse-Zentrum für Informationstechnik Berlin
2 OptimiX - Optimization at LIX
3 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
4 University of Pisa - Università di Pisa

We propose a methodology, based on machine learning and optimization, for selecting a solver configuration for a given instance. First, we employ a set of solved instances and configurations in order to learn a performance function of the solver. Secondly, we formulate a mixed-integer nonlinear program where the objective/constraints explicitly encode the learnt information, and which we solve, upon the arrival of an unknown instance, to find the best solver configuration for that instance, based on the performance function. The main novelty of our approach lies in the fact that the configuration set search problem is formulated as a mathematical program, which allows us to a) enforce hard dependence and compatibility constraints on the configurations, and b) solve it efficiently with off-the-shelf optimization tools.

Mots clés: automatic algorithm configuration; mathematical program- ming; machine learning; optimization solver configuration; hydro unit committment

Domaines: Recherche opérationnelle [math.OC]

Gabriele Iommazzo, Claudia D’ambrosio, Antonio Frangioni, Leo Liberti. A learning-based mathematical programming formulation for the automatic configuration of optimization solvers. Lecture Notes in Computer Science, In press, Lecture Notes in Computer Science, 12565, pp.700-712. ⟨10.1007/978-3-030-64583-0_61⟩. ⟨hal-03008720⟩