  Domain-specific heuristics are an important technique for solving
combinatorial problems efficiently. We propose a novel semantics for
declarative specifications of domain-specific heuristics in Answer Set
Programming (ASP). Decision procedures that are based on a partial solution are
a frequent ingredient of existing domain-specific heuristics, e.g., for placing
an item that has not been placed yet in bin packing. Therefore, in our novel
semantics negation as failure and aggregates in heuristic conditions are
evaluated on a partial solver state. State-of-the-art solvers do not allow such
a declarative specification. Our implementation in the lazy-grounding ASP
system Alpha supports heuristic directives under this semantics. By that, we
also provide the first implementation for incorporating declaratively specified
domain-specific heuristics in a lazy-grounding setting. Experiments confirm
that the combination of ASP solving with lazy grounding and our novel
heuristics can be a vital ingredient for solving industrial-size problems.
