SAT and propagation solvers often underperform for optimisation models whose objective sums many single-variable terms. MaxSAT solvers avoid this by detecting and exploiting cores: subsets of these terms that cannot collectively take their lower bounds. Previous work has shown manual analysis of cores can help define model reformulations likely to speed up solving for many model instances. This paper presents a method to automate this process. For each selected core the method identifies the instance constraints that caused it; infers the model constraints and parameters that explain how these instance constraints were formed; and learns the conditions that made those model constraint instances generate cores, while others did not. It then uses this information to reformulate the objective. The empirical evaluation shows this method can produce useful reformulations. Importantly, the method can be useful in many other situations that require explaining a set of constraints.

Decision systems for solving real-world combinatorial problems must be able to report infeasibility in such a way that users can understand the reasons behind it, and understand how to modify the problem to restore feasibility. Current methods mainly focus on reporting one or more subsets of the problem constraints that cause infeasibility. Methods that also show users how to restore feasibility tend to be less flexible and/or problem-dependent. We describe a problem-independent approach to feasibility restoration that combines existing techniques from the literature in novel ways to yield meaningful, useful, practical and flexible user support. We evaluate the resulting framework on two real-world applications.