Recovering Indirect Solution Densities for Counting-Based Branching Heuristics

Counting-based branching heuristics in CP have been very successful on a number of problems. Among the few remaining hurdles limiting their general applicability are the integration of counting information from auxiliary variables and the ability to handle combinatorial optimization problems. This paper proposes to answer these challenges by generalizing existing solution counting algorithms for constraints and by relaying counting information to the main branching variables through augmented element constraints. It offers more easily comparable solution counting information on variables and stronger back-propagation from the objective function in optimization problems. We provide supporting experimental results for the Capacitated Facility Location Problem.