Abstract. Most state-of-the-art algorithms for large-scale optimization problems expose free parameters, giving rise to combinatorial spaces of possible configurations. Typically, these spaces are hard for humans to understand. In this work, we study a model-based approach for identifying a small set of both algorithm parameters and instance features that suffices for predicting empirical algorithm performance well. Our empirical analyses on a wide variety of hard combinatorial problem benchmarks (spanning SAT, MIP, and TSP) show that—for parameter configurations sampled uniformly at random—very good performance predictions can typically be obtained based on just two key parameters, and that similarly, few instance features and algorithm parameters suffice to predict the most salient algorithm performance characteristics in the combined configuration/feature space. We also use these models to identify settings of these key parameters that are predicted to achieve the best overall performance, both on average across instances and in an instance-specific way. This serves as a further way of evaluating model quality and also provides a tool for further understanding the parameter space. We provide software for carrying out this analysis on arbitrary problem domains and hope that it will help algorithm developers gain insights into the key parameters of their algorithms, the key features of their instances, and their interactions.
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