Explaining propagators for edge-valued decision diagrams

Propagators that combine reasoning about satisfiability and reasoning about the cost of a solution, such as weighted all-different, or global cardinality with costs, can be much more effective than reasoning separately about satisfiability and cost. The cost-mdd constraint is a generic propagator for reasoning about reachability in a multi-decision diagram with costs attached to edges (a generalization of cost-regular). Previous work has demonstrated that adding nogood learning for mdd propagators substantially increases the size and complexity of problems that can be handled by state-of-the-art solvers. In this paper we show how to add explanation to the cost-mdd propagator. We demonstrate on scheduling benchmarks the advantages of a learning cost-mdd global propagator, over both decompositions of cost-mdd and mdd with a separate objective constraint using learning.