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

TL;DR

This work tackles instance-wise automatic configuration of general MP solvers by learning how performance depends on instance features and configuration. It introduces a two-phase framework: Performance Map Learning Phase (PMLP) using SVR to produce a predictor $\bar{p}_{\mathcal{A}}(f,c,\theta)$, and a Configuration Space Search Problem (CSSP) formulated as a MINLP that optimizes over configurations using the learned predictor. The CSSP is embedded with compatibility constraints and solved with Bonmin; feature selection and FS scenarios reduce problem size, enabling practical computation. Experimental validation on Hydro Unit Commitment with 250 instances and CPLEX parameter settings shows that the approach yields better primal/dual gaps than default CPLEX, and that FS improves robustness and solvability. This data-driven, white-box embedding of ML into MP formulations offers a scalable, principled route to automatic solver configuration.

Abstract

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.