Learning to Configure Mathematical Programming Solvers by Mathematical Programming
This work addresses the challenge of automated solver configuration for mathematical programming, which is incremental as it builds on existing learning and optimization methods to handle parameter dependencies in a domain-specific context.
The paper tackles the problem of finding optimal solver configurations for mathematical programming instances by proposing a two-phase approach that learns performance relationships and enforces parameter constraints through optimization. Computational results on a unit commitment problem using logistic regression and CPLEX show improved solver performance, though specific numerical gains are not detailed.
We discuss the issue of finding a good mathematical programming solver configuration for a particular instance of a given problem, and we propose a two-phase approach to solve it. In the first phase we learn the relationships between the instance, the configuration and the performance of the configured solver on the given instance. A specific difficulty of learning a good solver configuration is that parameter settings may not all be independent; this requires enforcing (hard) constraints, something that many widely used supervised learning methods cannot natively achieve. We tackle this issue in the second phase of our approach, where we use the learnt information to construct and solve an optimization problem having an explicit representation of the dependency/consistency constraints on the configuration parameter settings. We discuss computational results for two different instantiations of this approach on a unit commitment problem arising in the short-term planning of hydro valleys. We use logistic regression as the supervised learning methodology and consider CPLEX as the solver of interest.