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.

翻译：我们探讨了为给定问题的特定实例寻找良好数学规划求解器配置的问题，并提出了一种两阶段方法来解决该问题。在第一阶段，我们学习实例、配置以及已配置求解器在给定实例上的性能之间的关系。学习良好求解器配置的一个具体困难在于参数设置可能并非全部独立；这需要强制执行（硬性）约束，而许多广泛使用的监督学习方法无法原生实现这一点。我们在方法的第二阶段解决这个问题，通过利用已学信息构建并求解一个优化问题，该问题显式表达了配置参数设置上的依赖/一致性约束。我们讨论了该方法在水电站短期规划中的机组组合问题上的两种不同实例化计算效果，并采用逻辑回归作为监督学习方法，CPLEX作为目标求解器。