Learning the Empirical Hardness of Optimization Problems: The Case of Combinatorial Auctions

We propose a new approach to understanding the algorithm-specific empirical hardness of NP-Hard optimization problems. In this work we focus on the empirical hardness of the winner determination problem—an optimization problem arising in combinatorial auctions—when solved by ILOG’s CPLEX software. We consider nine widely-used problem distributions and sample randomly from a continuum of parameter settings for each distribution. First, we contrast the overall empirical hardness of the different distributions. Second, we identify a large number of distribution-nonspecific features of data instances and use statistical regression techniques to learn, evaluate and interpret a function from these features to the predicted hardness of an instance.